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Network Working Group P. Fahn
INTERNET-DRAFT [CRYPTOGRAPHY-FAQ] RSA Laboratories
<draft-ietf-saag-cryptography-faq-00.txt> 22 September 1993
ANSWERS TO
FREQUENTLY ASKED QUESTIONS
ABOUT TODAY'S CRYPTOGRAPHY
STATUS OF THIS MEMO
This document is an Internet Draft. Internet Drafts are working
documents of the Internet Engineering Task Force (IETF), its Areas,
and its Working Groups. Note that other groups may also distribute
working documents as Internet Drafts.
Internet Drafts are draft documents valid for a maximum of six
months. Internet Drafts may be updated, replaced, or obsoleted by
other documents at any time. It is not appropriate to use Internet
Drafts as reference material or to cite them other than as a "working
draft" or "work in progress."
Please check the I-D abstract listing contained in each Internet
Draft directory to learn the current status of this or any other
Internet Draft. This draft document will be submitted to the RFC
editor as a standards document.
This document is being distributed to members of the Internet
community in order to provide basic information about today's
cryptography. While the issues discussed may not be directly relevant
to the research problems of the Internet, they may be interesting to
a number of researchers and implementers. The distribution of this
document may provide a basis for more in-depth discussion about
cryptography.
Distribution of this memo is unlimited. Please send comments and
corrections to <faq-editor@rsa.com>.
ACKNOWLEDGEMENT
I would like to thank the following people, who have provided
information and helpful suggestions: Burt Kaliski, Jim Bidzos, Matt
Robshaw, Steve Dusse, Kurt Stammberger, George Parsons, John Gilmore,
Stuart Haber, Dorothy Denning, and Dennis Branstad.
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TABLE OF CONTENTS
STATUS OF THIS MEMO 1
ACKNOWLEDGEMENT 1
TABLE OF CONTENTS 2
1 General 4
1.1 What is encryption? 4
1.2 What is authentication? What is a digital signature? 5
1.3 What is public-key cryptography? 5
1.4 What are the advantages and disadvantages of public-key
cryptography over secret-key cryptography?} 6
1.5 Is cryptography patentable in the U.S.? 7
1.6 Is cryptography exportable from the U.S.? 8
2 RSA 9
2.1 What is RSA? 9
2.2 Why use RSA rather than DES? 10
2.3 How fast is RSA? 11
2.4 How much extra message length is caused by using RSA? 11
2.5 What would it take to break RSA? 11
2.6 Are strong primes necessary in RSA? 13
2.7 How large a modulus (key) should be used in RSA? 13
2.8 How large should the primes be? 14
2.9 How does one find random numbers for keys? 14
2.10 What if users of RSA run out of distinct primes? 15
2.11 How do you know if a number is prime? 15
2.12 How is RSA used for encryption in practice? 15
2.13 How is RSA used for authentication in practice? 15
2.14 Does RSA help detect altered documents and transmission
errors? 16
2.15 What are alternatives to RSA? 17
2.16 Is RSA currently in use today? 18
2.17 Is RSA an official standard today? 18
2.18 Is RSA a de facto standard? Why is a de facto standard
important? 19
2.19 Is RSA patented? 19
2.20 Can RSA be exported from the U.S.? 20
3 Key Management 20
3.1 What key management issues are involved in public-key
cryptography? 20
3.2 Who needs a key? 21
3.3 How does one get a key pair? 21
3.4 Should a public key or private key be shared among users? 21
3.5 What are certificates? 22
3.6 How are certificates used? 22
3.7 Who issues certificates and how? 23
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3.8 What is a CSU, or, How do certifying authorities store their
private keys? 24
3.9 Are certifying authorities susceptible to attack? 24
3.10 What if the certifying authority's key is lost or
compromised? 26
3.11 What are Certificate Revocation Lists (CRLs)? 26
3.12 What happens when a key expires? 27
3.13 What happens if I lose my private key? 28
3.14 What happens if my private key is compromised? 28
3.15 How should I store my private key? 28
3.16 How do I find someone else's public key? 29
3.17 How can signatures remain valid beyond the expiration dates
of their keys, or, How do you verify a 20-year-old
signature? 29
3.18 What is a digital time-stamping service? 30
4 Factoring and Discrete Log 31
4.1 What is a one-way function? 31
4.2 What is the significance of one-way functions for
cryptography? 31
4.3 What is the factoring problem? 32
4.4 What is the significance of factoring in cryptography? 32
4.5 Has factoring been getting easier? 32
4.6 What are the best factoring methods in use today? 33
4.7 What are the prospects for theoretical factoring
breakthroughs? 34
4.8 What is the RSA Factoring Challenge? 35
4.9 What is the discrete log problem? 35
4.10 Which is easier, factoring or discrete log? 35
5 DES 36
5.1 What is DES? 36
5.2 Has DES been broken? 36
5.3 How does one use DES securely? 37
5.4 Can DES be exported from the U.S.? 38
5.5 What are the alternatives to DES? 38
5.6 Is DES a group? 39
6 Capstone, Clipper, and DSS 39
6.1 What is Capstone? 39
6.2 What is Clipper? 40
6.3 How does the Clipper chip work? 40
6.4 Who are the escrow agencies? 41
6.5 What is Skipjack? 41
6.6 Why is Clipper controversial? 42
6.7 What is the current status of Clipper? 43
6.8 What is DSS? 43
6.9 Is DSS secure? 44
6.10 Is use of DSS covered by any patents? 44
6.11 What is the current status of DSS? 44
7 NIST and NSA 45
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7.1 What is NIST? 45
7.2 What role does NIST play in cryptography? 45
7.3 What is the NSA? 45
7.4 What role does the NSA play in commercial cryptography? 46
8 Miscellaneous 47
8.1 What is the legal status of documents signed with digital
signatures? 47
8.2 What is a hash function? What is a message digest? 48
8.3 What are MD2, MD4 and MD5? 49
8.4 What is SHS? 49
8.5 What is Kerberos? 50
8.6 What are RC2 and RC4? 50
8.7 What is PEM? 51
8.8 What is RIPEM? 51
8.9 What is PKCS? 52
8.10 What is RSAREF? 52
BIBLIOGRAPHY 52
Author's Address 58
1 General
1.1 What is encryption?
Encryption is the transformation of data into a form unreadable by
anyone without a secret decryption key. Its purpose is to ensure
privacy by keeping the information hidden from anyone for whom it is
not intended, even those who can see the encrypted data. For example,
one may wish to encrypt files on a hard disk to prevent an intruder
from reading them.
In a multi-user setting, encryption allows secure communication over
an insecure channel. The general scenario is as follows: Alice wishes
to send a message to Bob so that no one else besides Bob can read it.
Alice encrypts the message, which is called the plaintext, with an
encryption key; the encrypted message, called the ciphertext, is sent
to Bob. Bob decrypts the ciphertext with the decryption key and reads
the message. An attacker, Charlie, may either try to obtain the
secret key or to recover the plaintext without using the secret key.
In a secure cryptosystem, the plaintext cannot be recovered from the
ciphertext except by using the decryption key. In a symmetric
cryptosystem, a single key serves as both the encryption and
decryption keys.
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Cryptography has been around for millennia; see Kahn [37] for a good
history of cryptography; see Rivest [69] and Brassard [10] for an
introduction to modern cryptography.
1.2 What is authentication? What is a digital signature?
Authentication in a digital setting is a process whereby the receiver
of a digital message can be confident of the identity of the sender
and/or the integrity of the message. Authentication protocols can be
based on either conventional secret-key cryptosystems like DES or on
public-key systems like RSA; authentication in public-key systems
uses digital signatures.
In this document, authentication will generally refer to the use of
digital signatures, which play a function for digital documents
similar to that played by handwritten signatures for printed
documents: the signature is an unforgeable piece of data asserting
that a named person wrote or otherwise agreed to the document to
which the signature is attached. The recipient, as well as a third
party, can verify both that the document did indeed originate from
the person whose signature is attached and that the document has not
been altered since it was signed. A secure digital signature system
thus consists of two parts: a method of signing a document such that
forgery is infeasible, and a method of verifying that a signature was
actually generated by whomever it represents. Furthermore, secure
digital signatures cannot be repudiated; i.e., the signer of a
document cannot later disown it by claiming it was forged.
Unlike encryption, digital signatures are a recent development, the
need for which has arisen with the proliferation of digital
communications.
1.3 What is public-key cryptography?
Traditional cryptography is based on the sender and receiver of a
message knowing and using the same secret key: the sender uses the
secret key to encrypt the message, and the receiver uses the same
secret key to decrypt the message. This method is known as secret-key
cryptography. The main problem is getting the sender and receiver to
agree on the secret key without anyone else finding out. If they are
in separate physical locations, they must trust a courier, or a phone
system, or some other transmission system to not disclose the secret
key being communicated. Anyone who overhears or intercepts the key in
transit can later read all messages encrypted using that key. The
generation, transmission and storage of keys is called key
management; all cryptosystems must deal with key management issues.
Secret-key cryptography often has difficulty providing secure key
management.
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Public-key cryptography was invented in 1976 by Whitfield Diffie and
Martin Hellman [29] in order to solve the key management problem. In
the new system, each person gets a pair of keys, called the public
key and the private key. Each person's public key is published while
the private key is kept secret. The need for sender and receiver to
share secret information is eliminated: all communications involve
only public keys, and no private key is ever transmitted or shared.
No longer is it necessary to trust some communications channel to be
secure against eavesdropping or betrayal. Anyone can send a
confidential message just using public information, but it can only
be decrypted with a private key that is in the sole possession of the
intended recipient. Furthermore, public-key cryptography can be used
for authentication (digital signatures) as well as for privacy
(encryption).
Here's how it works for encryption: when Alice wishes to send a
message to Bob, she looks up Bob's public key in a directory, uses it
to encrypt the message and sends it off. Bob then uses his private
key to decrypt the message and read it. No one listening in can
decrypt the message. Anyone can send an encrypted message to Bob but
only Bob can read it. Clearly, one requirement is that no one can
figure out the private key from the corresponding public key.
Here's how it works for authentication: Alice, to sign a message,
does a computation involving both her private key and the message
itself; the output is called the digital signature and is attached to
the message, which is then sent. Bob, to verify the signature, does
some computation involving the message, the purported signature, and
Alice's public key. If the results properly hold in a simple
mathematical relation, the signature is verified as genuine;
otherwise, the signature may be fraudulent or the message altered,
and they are discarded.
A good history of public-key cryptography, by one of its inventors,
is given by Diffie [27].
1.4 What are the advantages and disadvantages of public-key cryptography
over secret-key cryptography?}
The primary advantage of public-key cryptography is increased
security: the private keys do not ever need to be transmitted or
revealed to anyone. In a secret-key system, by contrast, there is
always a chance that an enemy could discover the secret key while it
is being transmitted.
Another major advantage of public-key systems is that they can
provide a method for digital signatures. Authentication via secret-
key systems requires the sharing of some secret and sometimes
requires trust of a third party as well. A sender can then repudiate
a previously signed message by claiming that the shared secret was
somehow compromised by one of the parties sharing the secret. For
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example, the Kerberos secret-key authentication system [79] involves
a central database that keeps copies of the secret keys of all users;
a Kerberos-authenticated message would most likely not be held
legally binding, since an attack on the database would allow
widespread forgery. Public-key authentication, on the other hand,
prevents this type of repudiation; each user has sole responsibility
for protecting his or her private key. This property of public-key
authentication is often called non-repudiation.
Furthermore, digitally signed messages can be proved authentic to a
third party, such as a judge, thus allowing such messages to be
legally binding. Secret-key authentication systems such as Kerberos
were designed to authenticate access to network resources, rather
than to authenticate documents, a task which is better achieved via
digital signatures.
A disadvantage of using public-key cryptography for encryption is
speed: there are popular secret-key encryption methods which are
significantly faster than any currently available public-key
encryption method. But public-key cryptography can share the burden
with secret-key cryptography to get the best of both worlds.
For encryption, the best solution is to combine public- and secret-
key systems in order to get both the security advantages of public-
key systems and the speed advantages of secret-key systems. The
public-key system can be used to encrypt a secret key which is then
used to encrypt the bulk of a file or message. This is explained in
more detail in Question 2.12 in the case of RSA. Public-key
cryptography is not meant to replace secret-key cryptography, but
rather to supplement it, to make it more secure. The first use of
public-key techniques was for secure key exchange in an otherwise
secret-key system [29]; this is still one of its primary functions.
Secret-key cryptography remains extremely important and is the
subject of much ongoing study and research. Some secret-key
encryption systems are discussed in Questions 5.1 and 5.5.
1.5 Is cryptography patentable in the U.S.?
Cryptographic systems are patentable. Many secret-key cryptosystems
have been patented, including DES (see Question 5.1). The basic ideas
of public-key cryptography are contained in U.S. Patent 4,200,770, by
M. Hellman, W. Diffie, and R. Merkle, issued 4/29/80 and in U.S.
Patent 4,218,582, by M. Hellman and R. Merkle, issued 8/19/80;
similar patents have been issued throughout the world. The exclusive
licensing rights to both patents are held by Public Key Partners
(PKP), of Sunnyvale, California, which also holds the rights to the
RSA patent (see Question 2.19). Usually all of these public-key
patents are licensed together.
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All legal challenges to public-key patents have been settled before
judgment. In a recent case, for example, PKP brought suit against the
TRW Corporation which was using public-key cryptography (the ElGamal
system) without a license; TRW claimed it did not need to license. In
June 1992 a settlement was reached in which TRW agreed to license to
the patents.
Some patent applications for cryptosystems have been blocked by
intervention by the NSA (see Question 7.3) or other intelligence or
defense agencies, under the authority of the Invention Secrecy Act of
1940 and the National Security Act of 1947; see Landau [46] for some
recent cases related to cryptography.
1.6 Is cryptography exportable from the U.S.?
All cryptographic products need export licenses from the State
Department, acting under authority of the International Traffic in
Arms Regulation (ITAR), which defines cryptographic devices,
including software, as munitions. The U.S. government has
historically been reluctant to grant export licenses for encryption
products stronger than some basic level (not publicly stated).
Under current regulations, a vendor seeking to export a product using
cryptography first submits an request to the State Department's
Defense Trade Control office. Export jurisdiction may then be passed
to the Department of Commerce, whose export procedures are generally
simple and efficient. If jurisdiction remains with the State
Department, further review, perhaps lengthy, is required before
export is either approved or denied; the National Security Agency
(NSA, see Question 7.3) may become directly involved at this point.
The details of the export approval process change frequently.
The NSA has de facto control over export of cryptographic products.
The State Department will not grant a license without NSA approval
and routinely grants licenses whenever NSA does approve. Therefore,
the policy decisions over exporting cryptography ultimately rest with
the NSA.
It is the stated policy of the NSA not to restrict export of
cryptography for authentication; it is only concerned with the use of
cryptography for privacy. A vendor seeking to export a product for
authentication only will be granted an export license as long as it
can demonstrate that the product cannot be easily modified for
encryption; this is true even for very strong systems, such as RSA
with large key sizes. Furthermore, the bureaucratic procedures are
simpler for authentication products than for privacy products. An
authentication product needs NSA and State Dept. approval only once,
whereas an encryption product may need approval for every sale or
every product revision.
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Export policy is currently a matter of great controversy, as many
software and hardware vendors consider current export regulations
overly restrictive and burdensome. The Software Publishers
Association (SPA), a software industry group, has recently been
negotiating with the government in order to get export license
restrictions eased; one agreement was reached that allows simplified
procedures for export of two bulk encryption ciphers, RC2 and RC4
(see Question 8.6), when the key size is limited. Also, export policy
is less restrictive for foreign subsidiaries and overseas offices of
U.S. companies.
In March 1992, the Computer Security and Privacy Advisory Board voted
unanimously to recommend a national review of cryptography policy,
including export policy. The Board is an official advisory board to
NIST (see Question 7.1) whose members are drawn from both the
government and the private sector. The Board stated that a public
debate is the only way to reach a consensus policy to best satisfy
competing interests: national security and law enforcement agencies
like restrictions on cryptography, especially for export, whereas
other government agencies and private industry want greater freedom
for using and exporting cryptography. Export policy has traditionally
been decided solely by agencies concerned with national security,
without much input from those who wish to encourage commerce in
cryptography. U.S. export policy may undergo significant change in
the next few years.
2 RSA
2.1 What is RSA?
RSA is a public-key cryptosystem for both encryption and
authentication; it was invented in 1977 by Ron Rivest, Adi Shamir,
and Leonard Adleman [74]. It works as follows: take two large primes,
p and q, and find their product n = pq; n is called the modulus.
Choose a number, e, less than n and relatively prime to (p-1)(q-1),
and find its inverse, d, mod (p-1)(q-1), which means that ed = 1 mod
(p-1)(q-1); e and d are called the public and private exponents,
respectively. The public key is the pair (n,e); the private key is d.
The factors p and q must be kept secret, or destroyed.
It is difficult (presumably) to obtain the private key d from the
public key (n,e). If one could factor n into p and q, however, then
one could obtain the private key d. Thus the entire security of RSA
is predicated on the assumption that factoring is difficult; an easy
factoring method would "break" RSA (see Questions 2.5 and 4.4).
Here is how RSA can be used for privacy and authentication (in
practice, actual use is slightly different; see Questions 2.12 and
2.13):
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RSA privacy (encryption): suppose Alice wants to send a private
message, m, to Bob. Alice creates the ciphertext c by exponentiating:
c = m^e mod n, where e and n are Bob's public key. To decrypt, Bob
also exponentiates: m = c^d mod n, and recovers the original message
m; the relationship between e and d ensures that Bob correctly
recovers m. Since only Bob knows d, only Bob can decrypt.
RSA authentication: suppose Alice wants to send a signed document m
to Bob. Alice creates a digital signature s by exponentiating: s =
m^d mod n, where d and n belong to Alice's key pair. She sends s and
m to Bob. To verify the signature, Bob exponentiates and checks that
the message m is recovered: m = s^e mod n, where e and n belong to
Alice's public key.
Thus encryption and authentication take place without any sharing of
private keys: each person uses only other people's public keys and
his or her own private key. Anyone can send an encrypted message or
verify a signed message, using only public keys, but only someone in
possession of the correct private key can decrypt or sign a message.
2.2 Why use RSA rather than DES?
RSA is not an alternative or replacement for DES; rather it
supplements DES (or any other fast bulk encryption cipher) and is
used together with DES in a secure communications environment. (Note:
for an explanation of DES, see Question 5.1.)
RSA allows two important functions not provided by DES: secure key
exchange without prior exchange of secrets, and digital signatures.
For encrypting messages, RSA and DES are usually combined as follows:
first the message is encrypted with a random DES key, and then,
before being sent over an insecure communications channel, the DES
key is encrypted with RSA. Together, the DES-encrypted message and
the RSA-encrypted DES key are sent. This protocol is known as an RSA
digital envelope.
One may wonder, why not just use RSA to encrypt the whole message and
not use DES at all? Although this may be fine for small messages, DES
(or another cipher) is preferable for larger messages because it is
much faster than RSA (see Question 2.3).
In some situations, RSA is not necessary and DES alone is sufficient.
This includes multi-user environments where secure DES-key agreement
can take place, for example by the two parties meeting in private.
Also, RSA is usually not necessary in a single-user environment; for
example, if you want to keep your personal files encrypted, just do
so with DES using, say, your personal password as the DES key. RSA,
and public-key cryptography in general, is best suited for a multi-
user environment. Also, any system in which digital signatures are
desired needs RSA or some other public-key system.
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2.3 How fast is RSA?
An "RSA operation," whether for encrypting or decrypting, signing or
verifying, is essentially a modular exponentiation, which can be
performed by a series of modular multiplications.
In practical applications, it is common to choose a small public
exponent for the public key; in fact, entire groups of users can use
the same public exponent. This makes encryption faster than
decryption and verification faster than signing. Algorithmically,
public-key operations take O(k^2) steps, private key operations take
O(k^3) steps, and key generation takes O(k^4) steps, where k is the
number of bits in the modulus; O-notation refers to the an upper
bound on the asymptotic running time of an algorithm [22].
There are many commercially available hardware implementations of
RSA, and there are frequent announcements of newer and faster chips.
The fastest current RSA chip [76] has a throughput greater than 600
Kbits per second with a 512-bit modulus, implying that it performs
over 1000 RSA private-key operations per second. It is expected that
RSA speeds will reach 1 Mbit/second within a year or so.
By comparison, DES is much faster than RSA. In software, DES is
generally at least 100 times as fast as RSA. In hardware, DES is
between 1,000 and 10,000 times as fast, depending on the
implementations. RSA will probably narrow the gap a bit in coming
years, as it finds growing commercial markets, but will never match
the performance of DES.
2.4 How much extra message length is caused by using RSA?
Only a very small amount of data expansion is involved when using
RSA. For encryption, a message may be padded to a length that is a
multiple of the block length, usually 64 bits, since RSA is usually
combined with a secret-key block cipher such as DES (see Question
2.12). Encrypting the DES key takes as many additional bits as the
size of the RSA modulus.
For authentication, an RSA digital signature is appended to a
document. An RSA signature, including information such as the name of
the signer, is typically a few hundred bytes long. One or more
certificates (see Question 3.5) may be included as well; certificates
can be used in conjunction with any digital signature method. A
typical RSA certificate is a few hundred bytes long.
2.5 What would it take to break RSA?
There are a few possible interpretations of "breaking RSA". The most
damaging would be for an attacker to discover the private key
corresponding to a given public key; this would enable the attacker
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both to read all messages encrypted with the public key and to forge
signatures. The obvious way to do this attack is to factor the public
modulus, n, into its two prime factors, p and q. From p, q, and e,
the public exponent, the attacker can easily get d, the private key.
The hard part is factoring n; the security of RSA depends of
factoring being difficult. In fact, the task of recovering the
private key is equivalent to the task of factoring the modulus: you
can use d to factor n, as well as use the factorization of n to find
d. See Questions 4.5 and 4.6 regarding the state of the art in
factoring. It should be noted that hardware improvements alone will
not weaken RSA, as long as appropriate key lengths are used; in fact,
hardware improvements should increase the security of RSA (see
Question 4.5).
Another way to break RSA is to find a technique to compute e-th roots
mod n. Since c = m^e, the e-th root of c is the message m. This
attack would allow someone to recover encrypted messages and forge
signatures even without knowing the private key. This attack is not
known to be equivalent to factoring. No methods are currently known
that attempt to break RSA in this way.
The attacks just mentioned are the only ways to break RSA in such a
way as to be able to recover all messages encrypted under a given
key. There are other methods, however, which aim to recover single
messages; success would not enable the attacker to recover other
messages encrypted with the same key.
The simplest single-message attack is the guessed plaintext attack.
An attacker sees a ciphertext, guesses that the message might be
"Attack at dawn", and encrypts this guess with the public key of the
recipient; by comparison with the actual ciphertext, the attacker
knows whether or not the guess was correct. This attack can be
thwarted by appending some random bits to the message. Another
single-message attack can occur if someone sends the same message m
to three others, who each have public exponent e=3. An attacker who
knows this and sees the three messages will be able to recover the
message m; this attack and ways to prevent it are discussed by Hastad
[35]. There are also some "chosen ciphertext" attacks, in which the
attacker creates some ciphertext and gets to see the corresponding
plaintext, perhaps by tricking a legitimate user into decrypting a
fake message; Davida [23] gives some examples.
Of course, there are also attacks that aim not at RSA itself but at a
given insecure implementation of RSA; these do not count as "breaking
RSA" because it is not any weakness in the RSA algorithm that is
exploited, but rather a weakness in a specific implementation. For
example, if someone stores his private key insecurely, an attacker
may discover it. One cannot emphasize strongly enough that to be
truly secure RSA requires a secure implementation; mathematical
security measures, such as choosing a long key size, are not enough.
In practice, most successful attacks will likely be aimed at insecure
implementations and at the key management stages of an RSA system.
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See Section 3 for discussion of secure key management in an RSA
system.
2.6 Are strong primes necessary in RSA?
In the literature pertaining to RSA, it has often been suggested that
in choosing a key pair, one should use "strong" primes p and q to
generate the modulus n. Strong primes are those with certain
properties that make the product n hard to factor by specific
factoring methods; such properties have included, for example, the
existence of a large prime factor of p-1 and a large prime factor of
p+1. The reason for these concerns is that some factoring methods are
especially suited to primes p such that p-1 or p+1 has only small
factors; strong primes are resistant to these attacks.
However, recent advances in factoring (see Question 4.6) appear to
have obviated the advantage of strong primes; the elliptic curve
factoring algorithm is one such advance. The new factoring methods
have as good a chance of success on strong primes as on "weak"
primes; therefore, choosing strong primes does not significantly
increase resistance to attacks. So for now the answer is negative:
strong primes are not necessary when using RSA, although there is no
danger in using them, except that it takes longer to generate a key
pair. However, new factoring algorithms may be developed in the
future which once again target primes with certain properties; if so,
choosing strong primes may again help to increase security.
2.7 How large a modulus (key) should be used in RSA?
The best size for an RSA modulus depends on one's security needs. The
larger the modulus, the greater the security but also the slower the
RSA operations. One should choose a modulus length upon
consideration, first, of one's security needs, such as the value of
the protected data and how long it needs to be protected, and,
second, of how powerful one's potential enemy is. It is also possible
that a larger key size will allow a digitally signed document to be
valid for a longer time; see Question 3.17.
A good analysis of the security obtained by a given modulus length is
given by Rivest [72], in the context of discrete logarithms modulo a
prime, but it applies to RSA as well. Rivest's estimates imply that a
512-bit modulus can be factored with an $8.2 million effort, less in
the future. It may therefore be advisable to use a longer modulus,
perhaps 768 bits in length. Those with extremely valuable data (or
large potential damage from digital forgery) may want to use a still
longer modulus. A certifying authority (see Question 3.5) might use a
modulus of length 1000 bits or more, because the validity of so many
other key pairs depends on the security of the one central key.
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The key of an individual user will expire after a certain time, say,
two years (see Question 3.12). Upon expiration, the user will
generate a new key which should be at least a few digits longer than
the old key to reflect the speed increases of computers over the two
years. Recommended key length schedules will probably be published by
some authority or public body.
Users should keep in mind that the estimated times to break RSA are
averages only. A large factoring effort, attacking many thousands of
RSA moduli, may succeed in factoring at least one in a reasonable
time. Although the security of any individual key is still strong,
with some factoring methods there is always a small chance that the
attacker may get lucky and factor it quickly.
As for the slowdown caused by increasing the key size (see Question
2.3), doubling the modulus length would, on average, increase the
time required for public-key operations (encryption and signature
verification) by a factor of 4, and increase the time taken by
private key operations (decryption and signing) by a factor of 8. The
reason that public-key operations are affected less than private-key
operations is that the public exponent can remain fixed when the
modulus is increased, whereas the private exponent increases
proportionally. Key generation time would increase by a factor of 16
upon doubling the modulus, but this is a relatively infrequent
operation for most users.
2.8 How large should the primes be?
The two primes, p and q, which compose the modulus, should be of
roughly equal length; this will make the modulus harder to factor
than if one of the primes was very small. Thus if one chooses to use
a 512-bit modulus, the primes should each have length approximately
256 bits.
2.9 How does one find random numbers for keys?
One needs a source of random numbers in order to find two random
primes to compose the modulus. If one used a predictable method of
generating the primes, an adversary could mount an attack by trying
to recreate the key generation process.
Random numbers obtained from a physical process are in principle the
best. One could use a hardware device, such as a diode; some are sold
commercially on computer add-in boards for this purpose. Another idea
is to use physical movements of the computer user, such as keystroke
timings measured in microseconds. By whichever method, the random
numbers may still contain some correlations preventing sufficient
statistical randomness. Therefore, it is best to run them through a
good hash function (see Question 8.2) before actually using them.
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Another approach is to use a pseudorandom number generator fed by a
random seed. Since these are deterministic algorithms, it is
important to find one that is very unpredictable and also to use a
truly random seed. There is a wide literature on the subject of
pseudorandom number generators. See Knuth [41] for an introduction.
Note that one does not need random numbers to determine the public
and private exponents in RSA, after choosing the modulus. One can
simply choose an arbitrary value for the public exponent, which then
determines the private exponent, or vice versa.
2.10 What if users of RSA run out of distinct primes?
There are enough prime numbers that RSA users will never run out of
them. For example, the number of primes of length 512 bits or less
exceeds 10^{150}, according to the prime number theorem; this is more
than the number of atoms in the known universe.
2.11 How do you know if a number is prime?
It is generally recommended to use probabilistic primality testing,
which is much quicker than actually proving a number prime. One can
use a probabilistic test that decides if a number is prime with
probability of error less than 2^{-100}. For further discussion of
some primality testing algorithms, see the papers in the bibliography
of [5]. For some empirical results on the reliability of simple
primality tests see Rivest [70]; one can perform very fast primality
tests and be extremely confident in the results. A simple algorithm
for choosing probable primes was recently analyzed by Brandt and
Damgard [9].
2.12 How is RSA used for encryption in practice?
RSA is combined with a secret-key cryptosystem, such as DES, to
encrypt a message by means of an RSA digital envelope.
Suppose Alice wishes to send an encrypted message to Bob. She first
encrypts the message with DES, using a randomly chosen DES key. Then
she looks up Bob's public key and uses it to encrypt the DES key. The
DES-encrypted message and the RSA-encrypted DES key together form the
RSA digital envelope and are sent to Bob. Upon receiving the digital
envelope, Bob decrypts the DES key with his private key, then uses
the DES key to decrypt to message itself.
2.13 How is RSA used for authentication in practice?
Suppose Alice wishes to send a signed message to Bob. She uses a hash
function on the message (see Question 8.2) to create a message
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digest, which serves as a "digital fingerprint" of the message. She
then encrypts the message digest with her RSA private key; this is
the digital signature, which she sends to Bob along with the message
itself. Bob, upon receiving the message and signature, decrypts the
signature with Alice's public key to recover the message digest. He
then hashes the message with the same hash function Alice used and
compares the result to the message digest decrypted from the
signature. If they are exactly equal, the signature has been
successfully verified and he can be confident that the message did
indeed come from Alice. If, however, they are not equal, then the
message either originated elsewhere or was altered after it was
signed, and he rejects the message. Note that for authentication, the
roles of the public and private keys are converse to their roles in
encryption, where the public key is used to encrypt and the private
key to decrypt.
In practice, the public exponent is usually much smaller than the
private exponent; this means that the verification of a signature is
faster than the signing. This is desirable because a message or
document will only be signed by an individual once, but the signature
may be verified many times.
It must be infeasible for anyone to either find a message that hashes
to a given value or to find two messages that hash to the same value.
If either were feasible, an intruder could attach a false message
onto Alice's signature. Hash functions such as MD4 and MD5 (see
Question 8.3) have been designed specifically to have the property
that finding a match is infeasible, and are therefore considered
suitable for use in cryptography.
One or more certificates (see Question 3.5) may accompany a digital
signature. A certificate is a signed document attesting to the
identity and public key of the person signing the message. Its
purpose is to prevent someone from impersonating someone else, using
a phony key pair. If a certificate is present, the recipient (or a
third party) can check the authenticity of the public key, assuming
the certifier's public key is itself trusted.
2.14 Does RSA help detect altered documents and transmission errors?
An RSA digital signature is superior to a handwritten signature in
that it attests to the contents of a message as well as to the
identity of the signer. As long as a secure hash function (see
Question 8.2) is used, there is no way to take someone's signature
from one document and attach it to another, or to alter the signed
message in any way. The slightest change in a signed document will
cause the digital signature verification process to fail. Thus, RSA
authentication allows people to check the integrity of signed
documents. Of course, if a signature verification fails, it may be
unclear whether there was an attempted forgery or simply a
transmission error.
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2.15 What are alternatives to RSA?
Many other public-key cryptosystems have been proposed, as a look
through the proceedings of the annual Crypto and Eurocrypt
conferences quickly reveals. A mathematical problem called the
knapsack problem was the basis for several systems [52], but these
have lost favor because several versions were broken. Another system,
designed by ElGamal [30], is based on the discrete logarithm problem.
The ElGamal system was, in part, the basis for several later
signature methods, including one by Schnorr [75], which in turn was
the basis for DSS, the digital signature standard proposed by NIST
(see Question 6.8). Because of the NIST proposal, the relative merits
of these signature systems versus RSA signatures has received a lot
of attention; see [57] for a discussion. The ElGamal system has been
used successfully in applications; it is slower for encryption and
verification than RSA and its signatures are larger than RSA
signatures.
In 1976, before RSA, Diffie and Hellman [29] proposed a system for
key exchange only; it permits secure exchange of keys in an otherwise
conventional secret-key system. This system is in use today.
Cryptosystems based on mathematical operations on elliptic curves
have also been proposed [43,56], as have cryptosystems based on
discrete exponentiation in the finite field GF(2^n). The latter are
very fast in hardware; however, doubts have been raised about their
security because the underlying problem may be easier to solve than
factoring [64,34]. There are also some probabilistic encryption
methods [8,32], which have the attraction of being resistant to a
guessed ciphertext attack (see Question 2.5), but at a cost of data
expansion. In probabilistic encryption, the same plaintext encrypted
twice under the same key will give, with high probability, two
different ciphertexts.
For digital signatures, Rabin [68] proposed a system which is
provably equivalent to factoring; this is an advantage over RSA,
where one may still have a lingering worry about an attack unrelated
to factoring. Rabin's method is susceptible to a chosen message
attack, however, in which the attacker tricks the user into signing
messages of a special form. Another signature scheme, by Fiat and
Shamir [31], is based on interactive zero-knowledge protocols, but
can be adapted for signatures. It is faster than RSA and is provably
equivalent to factoring, but the signatures are much larger than RSA
signatures. Other variations, however, lessen the necessary signature
length; see [17] for references. A system is "equivalent to
factoring" if recovering the private key is provably as hard as
factoring; forgery may be easier than factoring in some of the
systems.
Advantages of RSA over other public-key cryptosystems include the
fact that it can be used for both encryption and authentication, and
that it has been around for many years and has successfully withstood
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much scrutiny. RSA has received far more attention, study, and actual
use than any other public-key cryptosystem, and thus RSA has more
empirical evidence of its security than more recent and less
scrutinized systems. In fact, a large number of public-key
cryptosystems which at first appeared secure were later broken; see
[13] for some case histories.
2.16 Is RSA currently in use today?
The use of RSA is undergoing a period of rapid expansion and may
become ubiquitous within a few years. It is currently used in a wide
variety of products, platforms and industries around the world. It is
found in many commercial software products and planned for many more.
RSA is built into current or planned operating systems by Microsoft,
Apple, Sun, and Novell. In hardware, RSA can be found in secure
telephones, on Ethernet network cards, and on smart cards. RSA is
also used internally in many institutions, including branches of the
U.S. government, major corporations, national laboratories, and
universities.
Adoption of RSA seems to be proceeding more quickly for
authentication (digital signatures) than for privacy (encryption),
perhaps in part because products for authentication are easier to
export than those for privacy (see Question 1.6).
2.17 Is RSA an official standard today?
RSA is part of many official standards worldwide. The ISO
(International Standards Organization) 9796 standard lists RSA as a
compatible cryptographic algorithm, as does the Consultative
Committee in International Telegraphy and Telephony (CCITT) X.509
security standard. RSA is part of the Society for Worldwide Interbank
Financial Telecommunications (SWIFT) standard, the French financial
industry's ETEBAC 5 standard, and the ANSI X9.31 draft standard for
the U.S. banking industry. The Australian key management standard,
AS2805.6.5.3, also specifies RSA.
RSA is found in Internet's proposed PEM (Privacy Enhanced Mail)
standard (see Question 8.7) and the PKCS standard for the software
industry (see Question 8.9). The OSI Implementors' Workshop (OIW) has
issued implementers' agreements referring to PKCS and PEM, which each
include RSA.
A number of other standards are currently being developed and will be
announced over the next couple of years; many are expected to include
RSA as either an endorsed or a recommended system for privacy and/or
authentication. See [38] for a more comprehensive survey of
cryptography standards.
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2.18 Is RSA a de facto standard? Why is a de facto standard important?
RSA is the most widely used public-key cryptosystem today and has
often been called a de facto standard. Regardless of the official
standards, the existence of a de facto standard is extremely
important for the development of a digital economy. If one public-key
system is used everywhere for authentication, then signed digital
documents can be exchanged between users in different nations using
different software on different platforms; this interoperability is
necessary for a true digital economy to develop.
The lack of secure authentication has been a major obstacle in
achieving the promise that computers would replace paper; paper is
still necessary almost everywhere for contracts, checks, official
letters, legal documents, and identification. With this core of
necessary paper transaction, it has not been feasible to evolve
completely into a society based on electronic transactions. Digital
signatures are the exact tool necessary to convert the most essential
paper-based documents to digital electronic media. Digital signatures
makes it possible, for example, to have leases, wills, passports,
college transcripts, checks, and voter registration forms that exist
only in electronic form; any paper version would just be a "copy" of
the electronic original. All of this is enabled by an accepted
standard for digital signatures.
2.19 Is RSA patented?
RSA is patented under U.S. Patent 4,405,829, issued 9/20/83 and held
by Public Key Partners (PKP), of Sunnyvale, California; the patent
expires 17 years after issue, in 2000. RSA is usually licensed
together with other public-key cryptography patents (see Question
1.5). PKP has a standard, royalty-based licensing policy which can be
modified for special circumstances. If a software vendor, having
licensed the public-key patents, incorporates RSA into a commercial
product, then anyone who purchases the end product has the legal
right to use RSA within the context of that software. The U.S.
government can use RSA without a license because it was invented at
MIT with partial government funding. RSA is not patented outside
North America.
In North America, a license is needed to "make, use or sell" RSA.
However, PKP usually allows free non-commercial use of RSA, with
written permission, for personal, academic or intellectual reasons.
Furthermore, RSA Laboratories has made available (in the U.S. and
Canada) at no charge a collection of cryptographic routines in source
code, including the RSA algorithm; it can be used, improved and
redistributed non-commercially (see Question 8.10).
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2.20 Can RSA be exported from the U.S.?
Export of RSA falls under the same U.S. laws as all other
cryptographic products. See Question 1.6 for details.
RSA used for authentication is more easily exported than when used
for privacy. In the former case, export is allowed regardless of key
(modulus) size, although the exporter must demonstrate that the
product cannot be easily converted to use for encryption. In the case
of RSA used for privacy (encryption), the U.S. government generally
does not allow export if the key size exceeds 512 bits. Export policy
is currently a subject of debate, and the export status of RSA may
well change in the next year or two.
Regardless of U.S. export policy, RSA is available abroad in non-U.S.
products.
3 Key Management
3.1 What key management issues are involved in public-key cryptography?
Secure methods of key management are extremely important. In
practice, most attacks on public-key systems will probably be aimed
at the key management levels, rather than at the cryptographic
algorithm itself. The key management issues mentioned here are
discussed in detail in later questions.
Users must be able to obtain securely a key pair suited to their
efficiency and security needs. There must be a way to look up other
people's public keys and to publicize one's own key. Users must have
confidence in the legitimacy of others' public keys; otherwise an
intruder can either change public keys listed in a directory, or
impersonate another user. Certificates are used for this purpose.
Certificates must be unforgeable, obtainable in a secure manner, and
processed in such a way that an intruder cannot misuse them. The
issuance of certificates must proceed in a secure way, impervious to
attack. If someone's private key is lost or compromised, others must
be made aware of this, so that they will no longer encrypt messages
under the invalid public key nor accept messages signed with the
invalid private key. Users must be able to store their private keys
securely, so that no intruder can find it, yet the keys must be
readily accessible for legitimate use. Keys need to be valid only
until a specified expiration date. The expiration date must be chosen
properly and publicized securely. Some documents need to have
verifiable signatures beyond the time when the key used to sign them
has expired.
Although most of these key management issues arise in any public-key
cryptosystem, for convenience they are discussed here in the context
of RSA.
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3.2 Who needs a key?
Anyone who wishes to sign messages or to receive encrypted messages
must have a key pair. People may have more than one key. For example,
someone might have a key affiliated with his or her work and a
separate key for personal use. Other entities will also have keys,
including electronic entities such as modems, workstations, and
printers, as well as organizational entities such as a corporate
department, a hotel registration desk, or a university registrar's
office.
3.3 How does one get a key pair?
Each user should generate his or her own key pair. It may be tempting
within an organization to have a single site that generates keys for
all members who request one, but this is a security risk because it
involves the transmission of private keys over a network as well as
catastrophic consequences if an attacker infiltrates the key-
generation site. Each node on a network should be capable of local
key generation, so that private keys are never transmitted and no
external key source need be trusted. Of course, the local key
generation software must itself be trustworthy. Secret-key
authentication systems, such as Kerberos, often do not allow local
key generation but instead use a central server to generate keys.
Once generated, a user must register his or her public key with some
central administration, called a certifying authority. The certifying
authority returns to the user a certificate attesting to the veracity
of the user's public key along with other information (see Questions
3.5 and following). Most users should not obtain more than one
certificate for the same key, in order to simplify various
bookkeeping tasks associated with the key.
3.4 Should a public key or private key be shared among users?
In RSA, each person should have a unique modulus and private
exponent, i.e., a unique private key. The public exponent, on the
other hand, can be common to a group of users without security being
compromised. Some public exponents in common use today are 3 and
2^{16}+1; because these numbers are small, the public-key operations
(encryption and signature verification) are fast relative to the
private key operations (decryption and signing). If one public
exponent becomes a standard, software and hardware can be optimized
for that value.
In public-key systems based on discrete logarithms, such as ElGamal,
Diffie-Hellman, or DSS, it has often been suggested that a group of
people should share a modulus. This would make breaking a key more
attractive to an attacker, however, because one could break every key
with only slightly more effort than it would take to break a single
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key. To an attacker, therefore, the average cost to break a key is
much lower with a common modulus than if every key has a distinct
modulus. Thus one should be very cautious about using a common
modulus; if a common modulus is chosen, it should be very large.
3.5 What are certificates?
Certificates are digital documents attesting to the binding of a
public key to an individual or other entity. They allow verification
of the claim that a given public key does in fact belong to a given
individual. Certificates help prevent someone from using a phony key
to impersonate someone else.
In their simplest form, certificates contain a public key and a name.
As commonly used, they also contain the expiration date of the key,
the name of the certifying authority that issued the certificate, the
serial number of the certificate, and perhaps other information. Most
importantly, it contains the digital signature of the certificate
issuer. The most widely accepted format for certificates is defined
by the CCITT X.509 international standard [19]; thus certificates can
be read or written by any application complying with X.509. Further
refinements are found in the PKCS set of standards (see Question
8.9), and the PEM standard (see Question 8.7). A detailed discussion
of certificate format can also be found in Kent [40].
A certificate is issued by a certifying authority (see Question 3.7)
and signed with the certifying authority's private key.
3.6 How are certificates used?
A certificate is displayed in order to generate confidence in the
legitimacy of a public key. Someone verifying a signature can also
verify the signer's certificate, to insure that no forgery or false
representation has occurred. These steps can be performed with
greater or lesser rigor depending on the context.
The most secure use of authentication involves enclosing one or more
certificates with every signed message. The receiver of the message
would verify the certificate using the certifying authority's public
key and, now confident of the public key of the sender, verify the
message's signature. There may be two or more certificates enclosed
with the message, forming a hierarchical chain, wherein one
certificate testifies to the authenticity of the previous
certificate. At the end of a certificate hierarchy is a top-level
certifying authority, which is trusted without a certificate from any
other certifying authority. The public key of the top-level
certifying authority must be independently known, for example by
being widely published.
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The more familiar the sender is to the receiver of the message, the
less need there is to enclose, and to verify, certificates. If Alice
sends messages to Bob every day, Alice can enclose a certificate
chain on the first day, which Bob verifies. Bob thereafter stores
Alice's public key and no more certificates or certificate
verifications are necessary. A sender whose company is known to the
receiver may need to enclose only one certificate (issued by the
company), whereas a sender whose company is unknown to the receiver
may need to enclose two certificates. A good rule of thumb is to
enclose just enough of a certificate chain so that the issuer of the
highest level certificate in the chain is well-known to the receiver.
According to the PKCS standards for public-key cryptography (see
Question 8.9), every signature points to a certificate that validates
the public key of the signer. Specifically, each signature contains
the name of the issuer of the certificate and the serial number of
the certificate. Thus even if no certificates are enclosed with a
message, a verifier can still use the certificate chain to check the
status of the public key.
3.7 Who issues certificates and how?
Certificates are issued by a certifying authority (CA), which can be
any trusted central administration willing to vouch for the
identities of those to whom it issues certificates. A company may
issue certificates to its employees, a university to its students, a
town to its citizens. In order to prevent forged certificates, the
CA's public key must be trustworthy: a CA must either publicize its
public key or provide a certificate from a higher-level CA attesting
to the validity of its public key. The latter solution gives rise to
hierarchies of CAs.
Certificate issuance proceeds as follows. Alice generates her own key
pair and sends the public key to an appropriate CA with some proof of
her identification. The CA checks the identification and takes any
other steps necessary to assure itself that the request really did
come from Alice, and then sends her a certificate attesting to the
binding between Alice and her public key, along with a hierarchy of
certificates verifying the CA's public key. Alice can present this
certificate chain whenever desired in order to demonstrate the
legitimacy of her public key.
Since the CA must check for proper identification, organizations will
find it convenient to act as a CA for its own members and employees.
There will also be CAs that issue certificates to unaffiliated
individuals.
Different CAs may issue certificates with varying levels of
identification requirements. One CA may insist on seeing a driver's
license, another may want the certificate request form to be
notarized, yet another may want fingerprints of anyone requesting a
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certificate. Each CA should publish its own identification
requirements and standards, so that verifiers can attach the
appropriate level of confidence in the certified name-key bindings.
An example of a certificate-issuing protocol is Apple Computer's Open
Collaborative Environment (OCE). Apple OCE users can generate a key
pair and then request and receive a certificate for the public key;
the certificate request must be notarized.
3.8 What is a CSU, or, How do certifying authorities store their private
keys?
It is extremely important that private keys of certifying authorities
are stored securely, because compromise would enable undetectable
forgeries. One way to achieve the desired security is to store the
key in a tamperproof box; such a box is called a Certificate Signing
Unit, or CSU. The CSU would, preferably, destroy its contents if ever
opened, and be shielded against attacks using electromagnetic
radiation. Not even employees of the certifying authority should have
access to the private key itself, but only the ability to use the
private key in the process of issuing certificates.
There are many possible designs for CSUs; here is a description of
one design found in some current implementations. The CSU is
activated by a set of data keys, which are physical keys capable of
storing digital information. The data keys use secret-sharing
technology such that several people must all use their data keys to
activate the CSU. This prevents one disgruntled CA employee from
producing phony certificates.
Note that if the CSU is destroyed, say in a fire, no security is
compromised. Certificates signed by the CSU are still valid, as long
as the verifier uses the correct public key. Some CSUs will be
manufactured so that a lost private key can be restored into a new
CSU. See Question 3.10 for discussion of lost CA private keys.
Bolt, Beranek, and Newman (BBN) currently sells a CSU, and RSA Data
Security sells a full-fledged certificate issuing system built around
the BBN CSU.
3.9 Are certifying authorities susceptible to attack?
One can think of many attacks aimed at the certifying authority,
which must be prepared against them.
Consider the following attack. Suppose Bob wishes to impersonate
Alice. If Bob can convincingly sign messages as Alice, he can send a
message to Alice's bank saying "I wish to withdraw $10,000 from my
account. Please send me the money." To carry out this attack, Bob
generates a key pair and sends the public key to a certifying
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authority saying "I'm Alice. Here is my public key. Please send me a
certificate." If the CA is fooled and sends him such a certificate,
he can then fool the bank, and his attack will succeed. In order to
prevent such an attack the CA must verify that a certificate request
did indeed come from its purported author, i.e., it must require
sufficient evidence that it is actually Alice who is requesting the
certificate. The CA may, for example, require Alice to appear in
person and show a birth certificate. Some CAs may require very little
identification, but the bank should not honor messages authenticated
with such low-assurance certificates. Every CA must publicly state
its identification requirements and policies; others can then attach
an appropriate level of confidence to the certificates.
An attacker who discovers the private key of a certifying authority
could then forge certificates. For this reason, a certifying
authority must take extreme precautions to prevent illegitimate
access to its private key. The private key should be kept in a high-
security box, known as a Certificate Signing Unit, or CSU (see
Question 3.8).
The certifying authority's public key might be the target of an
extensive factoring attack. For this reason, CAs should use very long
keys, preferably 1000 bits or longer, and should also change keys
regularly. Top-level certifying authorities are exceptions: it may
not be practical for them to change keys frequently because the key
may be written into software used by a large number of verifiers.
In another attack, Alice bribes Bob, who works for the certifying
authority, to issue to her a certificate in the name of Fred. Now
Alice can send messages signed in Fred's name and anyone receiving
such a message will believe it authentic because a full and
verifiable certificate chain will accompany the message. This attack
can be hindered by requiring the cooperation of two (or more)
employees to generate a certificate; the attacker now has to bribe
two employees rather than one. For example, in some of today's CSUs,
three employees must each insert a data key containing secret
information in order to authorize the CSU to generate certificates.
Unfortunately, there may be other ways to generate a forged
certificate by bribing only one employee. If each certificate request
is checked by only one employee, that one employee can be bribed and
slip a false request into a stack of real certificate requests. Note
that a corrupt employee cannot reveal the certifying authority's
private key, as long as it is properly stored.
Another attack involves forging old documents. Alice tries to factor
the modulus of the certifying authority. It takes her 15 years, but
she finally succeeds, and she now has the old private key of the
certifying authority. The key has long since expired, but she can
forge a certificate dated 15 years ago attesting to a phony public
key of some other person, say Bob; she can now forge a document with
a signature of Bob dated 15 year ago, perhaps a will leaving
everything to Alice. The underlying issue raised by this attack is
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how to authenticate a signed document dated many years ago; this
issue is discussed in Question 3.17.
Note that these attacks on certifying authorities do not threaten the
privacy of messages between users, as might result from an attack on
a secret-key distribution center.
3.10 What if the certifying authority's key is lost or compromised?
If the certifying authority's key is lost or destroyed but not
compromised, certificates signed with the old key are still valid, as
long as the verifier knows to use the old public key to verify the
certificate.
In some CSU designs, encrypted backup copies of the CA's private key
are kept. A CA which loses its key can then restore it by loading the
encrypted backup into the CSU, which can decrypt it using some unique
information stored inside the CSU; the encrypted backup can only be
decrypted using the CSU. If the CSU itself is destroyed, the
manufacturer may be able to supply another with the same internal
information, thus allowing recovery of the key.
A compromised CA key is a much more dangerous situation. An attacker
who discovers a certifying authority's private key can issue phony
certificates in the name of the certifying authority, which would
enable undetectable forgeries; for this reason, all precautions must
be taken to prevent compromise, including those outlined in Questions
3.8 and 3.9. If a compromise does occur, the CA must immediately
cease issuing certificates under its old key and change to a new key.
If it is suspected that some phony certificates were issued, all
certificates should be recalled, and then reissued with a new CA key.
These measures could be relaxed somewhat if certificates were
registered with a digital time-stamping service (see Question 3.18).
Note that compromise of a CA key does not invalidate users' keys, but
only the certificates that authenticate them. Compromise of a top-
level CA's key should be considered catastrophic, since the key may
be built into applications that verify certificates.
3.11 What are Certificate Revocation Lists (CRLs)?
A Certificate Revocation List (CRL) is a list of public keys that
have been revoked before their scheduled expiration date. There are
several reasons why a key might need to be revoked and placed on a
CRL. A key might have been compromised. A key might be used
professionally by an individual for a company; for example, the
official name associated with a key might be "Alice Avery, Vice
President, Argo Corp." If Alice were fired, her company would not
want her to be able to sign messages with that key and therefore the
company would place the key on the CRL.
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When verifying a signature, one can check the relevant CRL to make
sure the signer's key has not been revoked. Whether it is worth the
time to perform this check depends on the importance of the signed
document.
CRLs are maintained by certifying authorities (CAs) and provide
information about revoked keys originally certified by the CA. CRLs
only list current keys, since expired keys should not be accepted in
any case; when a revoked key is past its original expiration date it
is removed from the CRL. Although CRLs are maintained in a
distributed manner, there may be central repositories for CRLs, that
is, sites on networks containing the latest CRLs from many
organizations. An institution like a bank might want an in-house CRL
repository to make CRL searches feasible on every transaction.
3.12 What happens when a key expires?
In order to guard against a long-term factoring attack, every key
must have an expiration date after which it is no longer valid. The
time to expiration must therefore be much shorter than the expected
factoring time, or equivalently, the key length must be long enough
to make the chances of factoring before expiration extremely small.
The validity period for a key pair may also depend on the
circumstances in which the key will be used, although there will also
be a standard period. The validity period, together with the value of
the key and the estimated strength of an expected attacker, then
determines the appropriate key size.
The expiration date of a key accompanies the public key in a
certificate or a directory listing. The signature verification
program should check for expiration and should not accept a message
signed with an expired key. This means that when one's own key
expires, everything signed with it will no longer be considered
valid. Of course, there will be cases where it is important that a
signed document be considered valid for a much longer period of time;
Question 3.17 discusses ways to achieve this.
After expiration, the user chooses a new key, which should be longer
than the old key, perhaps by several digits, to reflect both the
performance increase of computer hardware and any recent improvements
in factoring algorithms. Recommended key length schedules will likely
be published. A user may recertify a key that has expired, if it is
sufficiently long and has not been compromised. The certifying
authority would then issue a new certificate for the same key, and
all new signatures would point to the new certificate instead of the
old. However, the fact that computer hardware continues to improve
argues for replacing expired keys with new, longer keys every few
years. Key replacement enables one to take advantage of the hardware
improvements to increase the security of the cryptosystem. Faster
hardware has the effect of increasing security, perhaps vastly, but
only if key lengths are increased regularly (see Question 4.5).
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3.13 What happens if I lose my private key?
If your private key is lost or destroyed, but not compromised, you
can no longer sign or decrypt messages, but anything previously
signed with the lost key is still valid. This can happen, for
example, if you forget the password used to access your key, or if
the disk on which the key is stored is damaged. You need to choose a
new key right away, to minimize the number of messages people send
you encrypted under your old key, messages which you can no longer
read.
3.14 What happens if my private key is compromised?
If your private key is compromised, that is, if you suspect an
attacker may have obtained your private key, then you must assume
that some enemy can read encrypted messages sent to you and forge
your name on documents. The seriousness of these consequences
underscores the importance of protecting your private key with
extremely strong mechanisms (see Question 3.15).
You must immediately notify your certifying authority and have your
old key placed on a Certificate Revocation List (see Question 3.11);
this will inform people that the key has been revoked. Then choose a
new key and obtain the proper certificates for it. You may wish to
use the new key to re-sign documents that you had signed with the
compromised key; documents that had been time-stamped as well as
signed might still be valid. You should also change the way you store
your private key, to prevent compromise of the new key.
3.15 How should I store my private key?
Private keys must be stored securely, since forgery and loss of
privacy could result from compromise. The private key should never be
stored anywhere in plaintext form. The simplest storage mechanism is
to encrypt the private key under a password and store the result on a
disk. Of course, the password itself must be maintained with high
security, not written down and not easily guessed. Storing the
encrypted key on a disk that is not accessible through a computer
network, such as a floppy disk or a local hard disk, will make some
attacks more difficult. Ultimately, private keys may be stored on
portable hardware, such as a smart card. Furthermore, a challenge-
response protocol will be more secure than simple password access.
Users with extremely high security needs, such as certifying
authorities, should use special hardware devices to protect their
keys (see Question 3.8).
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3.16 How do I find someone else's public key?
Suppose you want to find Bob's public key. There are several possible
ways. You could call him up and ask him to send you his public key
via e-mail; you could request it via e-mail as well. Certifying
authorities may provide directory services; if Bob works for company
Z, look in the directory kept by Z's certifying authority.
Directories must be secure against unauthorized tampering, so that
users can be confident that a public key listed in the directory
actually belongs to the person listed. Otherwise, you might send
private encrypted information to the wrong person.
Eventually, full-fledged directories will arise, serving as online
white or yellow pages. If they are compliant with CCITT X.509
standards [19], the directories will contain certificates as well as
public keys; the presence of certificates will lower the directories'
security needs.
3.17 How can signatures remain valid beyond the expiration dates of
their keys, or, How do you verify a 20-year-old signature?
Normally, a key expires after, say, two years and a document signed
with an expired key should not be accepted. However, there are many
cases where it is necessary for signed documents to be regarded as
legally valid for much longer than two years; long-term leases and
contracts are examples. How should these cases be handled? Many
solutions have been suggested but it is unclear which will prove the
best. Here are some possibilities.
One can have special long-term keys as well as the normal two-year
keys. Long-term keys should have much longer modulus lengths and be
stored more securely than two-year keys. If a long-term key expires
in 50 years, any document signed with it would remain valid within
that time. A problem with this method is that any compromised key
must remain on the relevant CRL until expiration (see Question 3.11);
if 50-year keys are routinely placed on CRLs, the CRLs could grow in
size to unmanageable proportions. This idea can be modified as
follows. Register the long-term key by the normal procedure, i.e.,
for two years. At expiration time, if it has not been compromised,
the key can be recertified, that is, issued a new certificate by the
certifying authority, so that the key will be valid for another two
years. Now a compromised key only needs to be kept on a CRL for at
most two years, not fifty.
One problem with the previous method is that someone might try to
invalidate a long-term contract by refusing to renew his key. This
problem can be circumvented by registering the contract with a
digital time-stamping service (see Question 3.18) at the time it is
originally signed. If all parties to the contract keep a copy of the
time-stamp, then each can prove that the contract was signed with
valid keys. In fact, the time-stamp can prove the validity of a
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contract even if one signer's key gets compromised at some point
after the contract was signed. This time-stamping solution can work
with all signed digital documents, not just multi-party contracts.
3.18 What is a digital time-stamping service?
A digital time-stamping service (DTS) issues time-stamps which
associate a date and time with a digital document in a
cryptographically strong way. The digital time-stamp can be used at a
later date to prove that an electronic document existed at the time
stated on its time-stamp. For example, a physicist who has a
brilliant idea can write about it with a word processor and have the
document time-stamped. The time-stamp and document together can later
prove that the scientist deserves the Nobel Prize, even though an
arch rival may have been the first to publish.
Here's one way such a system could work. Suppose Alice signs a
document and wants it time-stamped. She computes a message digest of
the document using a secure hash function (see Question 8.2) and then
sends the message digest (but not the document itself) to the DTS,
which sends her in return a digital time-stamp consisting of the
message digest, the date and time it was received at the DTS, and the
signature of the DTS. Since the message digest does not reveal any
information about the content of the document, the DTS cannot
eavesdrop on the documents it time-stamps. Later, Alice can present
the document and time-stamp together to prove when the document was
written. A verifier computes the message digest of the document,
makes sure it matches the digest in the time-stamp, and then verifies
the signature of the DTS on the time-stamp.
To be reliable, the time-stamps must not be forgeable. Consider the
requirements for a DTS of the type just described. First, the DTS
itself must have a long key if we want the time-stamps to be reliable
for, say, several decades. Second, the private key of the DTS must be
stored with utmost security, as in a tamperproof box. Third, the date
and time must come from a clock, also inside the tamperproof box,
which cannot be reset and which will keep accurate time for years or
perhaps for decades. Fourth, it must be infeasible to create time-
stamps without using the apparatus in the tamperproof box.
A cryptographically strong DTS using only software [4] has been
implemented by Bellcore; it avoids many of the requirements just
described, such as tamperproof hardware. The Bellcore DTS essentially
combines hash values of documents into data structures called binary
trees, whose "root" values are periodically published in the
newspaper. A time-stamp consists of a set of hash values which allow
a verifier to recompute the root of the tree. Since the hash
functions are one-way (see Question 8.2), the set of validating hash
values cannot be forged. The time associated with the document by the
time-stamp is the date of publication.
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The use of a DTS would appear to be extremely important, if not
essential, for maintaining the validity of documents over many years
(see Question 3.17). Suppose a landlord and tenant sign a twenty-year
lease. The public keys used to sign the lease will expire after, say,
two years; solutions such as recertifying the keys or resigning every
two years with new keys require the cooperation of both parties
several years after the original signing. If one party becomes
dissatisfied with the lease, he or she may refuse to cooperate. The
solution is to register the lease with the DTS at the time of the
original signing; both parties would then receive a copy of the time-
stamp, which can be used years later to enforce the integrity of the
original lease.
In the future, it is likely that a DTS will be used for everything
from long-term corporate contracts to personal diaries and letters.
Today, if an historian discovers some lost letters of Mark Twain,
their authenticity is checked by physical means. But a similar find
100 years from now may consist of an author's computer files; digital
time-stamps may be the only way to authenticate the find.
4 Factoring and Discrete Log
4.1 What is a one-way function?
A one-way function is a mathematical function that is significantly
easier to perform in one direction (the forward direction) than in
the opposite direction (the inverse direction). One might, for
example, compute the function in minutes but only be able to compute
the inverse in months or years. A trap-door one-way function is a
one-way function where the inverse direction is easy if you know a
certain piece of information (the trap door), but difficult
otherwise.
4.2 What is the significance of one-way functions for cryptography?
Public-key cryptosystems are based on (presumed) trap-door one-way
functions. The public key gives information about the particular
instance of the function; the private key gives information about the
trap door. Whoever knows the trap door can perform the function
easily in both directions, but anyone lacking the trap door can
perform the function only in the forward direction. The forward
direction is used for encryption and signature verification; the
inverse direction is used for decryption and signature generation.
In almost all public-key systems, the size of the key corresponds to
the size of the inputs to the one-way function; the larger the key,
the greater the difference between the efforts necessary to compute
the function in the forward and inverse directions (for someone
lacking the trap door). For a digital signature to be secure for
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years, for example, it is necessary to use a trap-door one-way
function with inputs large enough that someone without the trap door
would need many years to compute the inverse function.
All practical public-key cryptosystems are based on functions that
are believed to be one-way, but have not been proven to be so. This
means that it is theoretically possible that an algorithm will be
discovered that can compute the inverse function easily without a
trap door; this development would render any cryptosystem based on
that one-way function insecure and useless.
4.3 What is the factoring problem?
Factoring is the act of splitting an integer into a set of smaller
integers (factors) which, when multiplied together, form the original
integer. For example, the factors of 15 are 3 and 5; the factoring
problem is to find 3 and 5 when given 15. Prime factorization
requires splitting an integer into factors that are prime numbers;
every integer has a unique prime factorization. Multiplying two prime
integers together is easy, but as far as we know, factoring the
product is much more difficult.
4.4 What is the significance of factoring in cryptography?
Factoring is the underlying, presumably hard problem upon which
several public-key cryptosystems are based, including RSA. Factoring
an RSA modulus (see Question 2.1) would allow an attacker to figure
out the private key; thus, anyone who can factor the modulus can
decrypt messages and forge signatures. The security of RSA therefore
depends on the factoring problem being difficult. Unfortunately, it
has not been proven that factoring must be difficult, and there
remains a possibility that a quick and easy factoring method might be
discovered (see Question 4.7), although factoring researchers
consider this possibility remote.
Factoring large numbers takes more time than factoring smaller
numbers. This is why the size of the modulus in RSA determines how
secure an actual use of RSA is; the larger the modulus, the longer it
would take an attacker to factor, and thus the more resistant to
attack the RSA implementation is.
4.5 Has factoring been getting easier?
Factoring has become easier over the last fifteen years for two
reasons: computer hardware has become more powerful, and better
factoring algorithms have been developed.
Hardware improvement will continue inexorably, but it is important to
realize that hardware improvements make RSA more secure, not less.
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This is because a hardware improvement that allows an attacker to
factor a number two digits longer than before will at the same time
allow a legitimate RSA user to use a key dozens of digits longer than
before; a user can choose a new key a dozen digits longer than the
old one without any performance slowdown, yet a factoring attack will
become much more difficult. Thus although the hardware improvement
does help the attacker, it helps the legitimate user much more. This
general rule may fail in the sense that factoring may take place
using fast machines of the future, attacking RSA keys of the past; in
this scenario, only the attacker gets the advantage of the hardware
improvement. This consideration argues for using a larger key size
today than one might otherwise consider warranted. It also argues for
replacing one's RSA key with a longer key every few years, in order
to take advantage of the extra security offered by hardware
improvements. This point holds for other public-key systems as well.
Better factoring algorithms have been more help to the RSA attacker
than have hardware improvements. As the RSA system, and cryptography
in general, have attracted much attention, so has the factoring
problem, and many researchers have found new factoring methods or
improved upon others. This has made factoring easier, for numbers of
any size and irrespective of the speed of the hardware. However,
factoring is still a very difficult problem.
Overall, any recent decrease in security due to algorithm improvement
can be offset by increasing the key size. In fact, between general
computer hardware improvements and special-purpose RSA hardware
improvements, increases in key size (maintaining a constant speed of
RSA operations) have kept pace or exceeded increases in algorithm
efficiency, resulting in no net loss of security. As long as hardware
continues to improve at a faster rate than that at which the
complexity of factoring algorithms decreases, the security of RSA
will increase, assuming RSA users regularly increase their key size
by appropriate amounts. The open question is how much faster
factoring algorithms can get; there must be some intrinsic limit to
factoring speed, but this limit remains unknown.
4.6 What are the best factoring methods in use today?
Factoring is a very active field of research among mathematicians and
computer scientists; the best factoring algorithms are mentioned
below with some references and their big-O asymptotic efficiency. O
notation measures how fast an algorithm is; it gives an upper bound
on the number of operations (to order of magnitude) in terms of n,
the number to be factored, and p, a prime factor of n. For textbook
treatment of factoring algorithms, see [41], [42], [47], and [11];
for a detailed explanation of big-O notation, see [22].
Factoring algorithms come in two flavors, special purpose and general
purpose; the efficiency of the former depends on the unknown factors,
whereas the efficiency of the latter depends on the number to be
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factored. Special purpose algorithms are best for factoring numbers
with small factors, but the numbers used for the modulus in the RSA
system do not have any small factors. Therefore, general purpose
factoring algorithms are the more important ones in the context of
cryptographic systems and their security.
Special purpose factoring algorithms include the Pollard rho method
[66], with expected running time O(sqrt(p)), and the Pollard p-1
method [67], with running time O(p'), where p' is the largest prime
factor of p-1. Both of these take an amount of time that is
exponential in the size of p, the prime factor that they find; thus
these algorithms are too slow for most factoring jobs. The elliptic
curve method (ECM) [50] is superior to these; its asymptotic running
time is O(exp (sqrt (2 ln p ln ln p)) ). The ECM is often used in
practice to find factors of randomly generated numbers; it is not
strong enough to factor a large RSA modulus.
The best general purpose factoring algorithm today is the number
field sieve [16], which runs in time approximately O(exp ( 1.9 (ln
n)^{1/3} (ln ln n)^{2/3}) ). It has only recently been implemented
[15], and is not yet practical enough to perform the most desired
factorizations. Instead, the most widely used general purpose
algorithm is the multiple polynomial quadratic sieve (mpqs) [77],
which has running time O(exp ( sqrt (ln n ln ln n)) ). The mpqs (and
some of its variations) is the only general purpose algorithm that
has successfully factored numbers greater than 110 digits; a
variation known as ppmpqs [49] has been particularly popular.
It is expected that within a few years the number field sieve will
overtake the mpqs as the most widely used factoring algorithm, as the
size of the numbers being factored increases from about 120 digits,
which is the current threshold of general numbers which can be
factored, to 130 or 140 digits. A "general number" is one with no
special form that might make it easier to factor; an RSA modulus is a
general number. Note that a 512-bit number has about 155 digits.
Numbers that have a special form can already be factored up to 155
digits or more [48]. The Cunningham Project [14] keeps track of the
factorizations of numbers with these special forms and maintains a
"10 Most Wanted" list of desired factorizations. Also, a good way to
survey current factoring capability is to look at recent results of
the RSA Factoring Challenge (see Question 4.8).
4.7 What are the prospects for theoretical factoring breakthroughs?
Although factoring is strongly believed to be a difficult
mathematical problem, it has not been proved so. Therefore there
remains a possibility that an easy factoring algorithm will be
discovered. This development, which could seriously weaken RSA, would
be highly surprising and the possibility is considered extremely
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remote by the researchers most actively engaged in factoring
research.
Another possibility is that someone will prove that factoring is
difficult. This negative breakthrough is probably more likely than
the positive breakthrough discussed above, but would also be
unexpected at the current state of theoretical factoring research.
This development would guarantee the security of RSA beyond a certain
key size.
4.8 What is the RSA Factoring Challenge?
RSA Data Security Inc. (RSADSI) administers a factoring contest with
quarterly cash prizes. Those who factor numbers listed by RSADSI earn
points toward the prizes; factoring smaller numbers earns more points
than factoring larger numbers. Results of the contest may be useful
to those who wish to know the state of the art in factoring; the
results show the size of numbers factored, which algorithms are used,
and how much time was required to factor each number. Send e-mail to
<challenge-info@rsa.com> for information.
4.9 What is the discrete log problem?
The discrete log problem, in its most common formulation, is to find
the exponent x in the formula y=g^x mod p; in other words, it seeks
to answer the question, To what power must g be raised in order to
obtain y, modulo the prime number p? There are other, more general,
formulations as well.
Like the factoring problem, the discrete log problem is believed to
be difficult and also to be the hard direction of a one-way function.
For this reason, it has been the basis of several public-key
cryptosystems, including the ElGamal system and DSS (see Questions
2.15 and 6.8). The discrete log problem bears the same relation to
these systems as factoring does to RSA: the security of these systems
rests on the assumption that discrete logs are difficult to compute.
The discrete log problem has received much attention in recent years;
descriptions of some of the most efficient algorithms can be found in
[47], [21], and [33]. The best discrete log problems have expected
running times similar to that of the best factoring algorithms.
Rivest [72] has analyzed the expected time to solve discrete log both
in terms of computing power and money.
4.10 Which is easier, factoring or discrete log?
The asymptotic running time of the best discrete log algorithm is
approximately the same as for the best general purpose factoring
algorithm. Therefore, it requires about as much effort to solve the
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discrete log problem modulo a 512-bit prime as to factor a 512-bit
RSA modulus. One paper [45] cites experimental evidence that the
discrete log problem is slightly harder than factoring: the authors
suggest that the effort necessary to factor a 110-digit integer is
the same as the effort to solve discrete logarithms modulo a 100-
digit prime. This difference is so slight that it should not be a
significant consideration when choosing a cryptosystem.
Historically, it has been the case that an algorithmic advance in
either problem, factoring or discrete logs, was then applied to the
other. This suggests that the degrees of difficulty of both problems
are closely linked, and that any breakthrough, either positive or
negative, will affect both problems equally.
5 DES
5.1 What is DES?
DES is the Data Encryption Standard, an encryption block cipher
defined and endorsed by the U.S. government in 1977 as an official
standard; the details can be found in the official FIPS publication
[59]. It was originally developed at IBM. DES has been extensively
studied over the last 15 years and is the most well-known and widely
used cryptosystem in the world.
DES is a secret-key, symmetric cryptosystem: when used for
communication, both sender and receiver must know the same secret
key, which is used both to encrypt and decrypt the message. DES can
also be used for single-user encryption, such as to store files on a
hard disk in encrypted form. In a multi-user environment, secure key
distribution may be difficult; public-key cryptography was invented
to solve this problem (see Question 1.3). DES operates on 64-bit
blocks with a 56-bit key. It was designed to be implemented in
hardware, and its operation is relatively fast. It works well for
bulk encryption, that is, for encrypting a large set of data.
NIST (see Question 7.1) has recertified DES as an official U.S.
government encryption standard every five years; DES was last
recertified in 1993, by default. NIST has indicated, however, that it
may not recertify DES again.
5.2 Has DES been broken?
DES has never been "broken", despite the efforts of many researchers
over many years. The obvious method of attack is brute-force
exhaustive search of the key space; this takes 2^{55} steps on
average. Early on it was suggested [28] that a rich and powerful
enemy could build a special-purpose computer capable of breaking DES
by exhaustive search in a reasonable amount of time. Later, Hellman
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[36] showed a time-memory trade-off that allows improvement over
exhaustive search if memory space is plentiful, after an exhaustive
precomputation. These ideas fostered doubts about the security of
DES. There were also accusations that the NSA had intentionally
weakened DES. Despite these suspicions, no feasible way to break DES
faster than exhaustive search was discovered. The cost of a
specialized computer to perform exhaustive search has been estimated
by Wiener at one million dollars [80].
Just recently, however, the first attack on DES that is better than
exhaustive search was announced by Eli Biham and Adi Shamir [6,7],
using a new technique known as differential cryptanalysis. This
attack requires encryption of 2^{47} chosen plaintexts, i.e.,
plaintexts chosen by the attacker. Although a theoretical
breakthrough, this attack is not practical under normal circumstances
because it requires the attacker to have easy access to the DES
device in order to encrypt the chosen plaintexts. Another attack,
known as linear cryptanalysis [51], does not require chosen
plaintexts.
The consensus is that DES, when used properly, is secure against all
but the most powerful enemies. In fact, triple encryption DES (see
Question 5.3) may be secure against anyone at all. Biham and Shamir
have stated that they consider DES secure. It is used extensively in
a wide variety of cryptographic systems, and in fact, most
implementations of public-key cryptography include DES at some level.
5.3 How does one use DES securely?
When using DES, there are several practical considerations that can
affect the security of the encrypted data. One should change DES keys
frequently, in order to prevent attacks that require sustained data
analysis. In a communications context, one must also find a secure
way of communicating the DES key to both sender and receiver. Use of
RSA or some other public-key technique for key management solves both
these issues: a different DES key is generated for each session, and
secure key management is provided by encrypting the DES key with the
receiver's RSA public key. RSA, in this circumstance, can be regarded
as a tool for improving the security of DES (or any other secret key
cipher).
If one wishes to use DES to encrypt files stored on a hard disk, it
is not feasible to frequently change the DES keys, as this would
entail decrypting and then re-encrypting all files upon each key
change. Instead, one should have a master DES key with which one
encrypts the list of DES keys used to encrypt the files; one can then
change the master key frequently without much effort.
A powerful technique for improving the security of DES is triple
encryption, that is, encrypting each message block under three
different DES keys in succession. Triple encryption is thought to be
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equivalent to doubling the key size of DES, to 112 bits, and should
prevent decryption by an enemy capable of single-key exhaustive
search [53]. Of course, using triple-encryption takes three times as
long as single-encryption DES.
Aside from the issues mentioned above, DES can be used for encryption
in several officially defined modes. Some are more secure than
others. ECB (electronic codebook) mode simply encrypts each 64-bit
block of plaintext one after another under the same 56-bit DES key.
In CBC (cipher block chaining) mode, each 64-bit plaintext block is
XORed with the previous ciphertext block before being encrypted with
the DES key. Thus the encryption of each block depends on previous
blocks and the same 64-bit plaintext block can encrypt to different
ciphertext depending on its context in the overall message. CBC mode
helps protect against certain attacks, although not against
exhaustive search or differential cryptanalysis. CFB (cipher
feedback) mode allows one to use DES with block lengths less than 64
bits. Detailed descriptions of the various DES modes can be found in
[60].
In practice, CBC is the most widely used mode of DES, and is
specified in several standards. For additional security, one could
use triple encryption with CBC, but since single DES in CBC mode is
usually considered secure enough, triple encryption is not often
used.
5.4 Can DES be exported from the U.S.?
Export of DES, either in hardware or software, is strictly regulated
by the U.S. State Department and the NSA (see Question 1.6). The
government rarely approves export of DES, despite the fact that DES
is widely available overseas; financial institutions and foreign
subsidiaries of U.S. companies are exceptions.
5.5 What are the alternatives to DES?
Over the years, various bulk encryption algorithms have been designed
as alternatives to DES. One is FEAL (Fast Encryption ALgorithm), a
cipher for which attacks have been discovered [6], although new
versions have been proposed. Another recently proposed cipher
designed by Lai and Massey [44] and known as IDEA seems promising,
although it has not yet received sufficient scrutiny to instill full
confidence in its security. The U.S. government recently announced a
new algorithm called Skipjack (see Question 6.5) as part of its
Capstone project. Skipjack operates on 64-bit blocks of data, as does
DES, but uses 80-bit keys, as opposed to 56-bit keys in DES. However,
the details of Skipjack are classified, so Skipjack is only available
in hardware from government-authorized manufacturers.
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Rivest has developed the ciphers RC2 and RC4 (see Question 8.6),
which can be made as secure as necessary because they use variable
key sizes. Faster than DES, at least in software, they have the
further advantage of special U.S. government status whereby the
export approval is simplified and expedited if the key size is
limited to 40 bits.
5.6 Is DES a group?
It has been frequently asked whether DES encryption is closed under
composition; i.e., is encrypting a plaintext under one DES key and
then encrypting the result under another key always equivalent to a
single encryption under a single key? Algebraically, is DES a group?
If so, then DES might be weaker than would otherwise be the case; see
[39] for a more complete discussion. However, the answer is no, DES
is not a group [18]; this issue was settled only recently, after many
years of speculation and circumstantial evidence. This result seems
to imply that techniques such as triple encryption do in fact
increase the security of DES.
6 Capstone, Clipper, and DSS
6.1 What is Capstone?
Capstone is the U.S. government's long-term project to develop a set
of standards for publicly-available cryptography, as authorized by
the Computer Security Act of 1987. The primary agencies responsible
for Capstone are NIST and the NSA (see Section 7). The plan calls for
the elements of Capstone to become official U.S. government
standards, in which case both the government itself and all private
companies doing business with the government would be required to use
Capstone.
There are four major components of Capstone: a bulk data encryption
algorithm, a digital signature algorithm, a key exchange protocol,
and a hash function. The data encryption algorithm is called Skipjack
(see Question 6.5), but is often referred to as Clipper, which is the
encryption chip that includes Skipjack (see Question 6.2). The
digital signature algorithm is DSS (see Question 6.8) and the hash
function is SHS (see Question 8.4 about SHS and Question 8.2 about
hash functions). The key exchange protocol has not yet been
announced.
All the parts of Capstone have 80-bit security: all the keys involved
are 80 bits long and other aspects are also designed to withstand
anything less than an "80-bit" attack, that is, an effort of 2^{80}
operations. Eventually the government plans to place the entire
Capstone cryptographic system on a single chip.
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6.2 What is Clipper?
Clipper is an encryption chip developed and sponsored by the U.S.
government as part of the Capstone project (see Question 6.1).
Announced by the White House in April, 1993 [65], Clipper was
designed to balance the competing concerns of federal law-enforcement
agencies with those of private citizens and industry. The law-
enforcement agencies wish to have access to the communications of
suspected criminals, for example by wire-tapping; these needs are
threatened by secure cryptography. Industry and individual citizens,
however, want secure communications, and look to cryptography to
provide it.
Clipper technology attempts to balance these needs by using escrowed
keys. The idea is that communications would be encrypted with a
secure algorithm, but the keys would be kept by one or more third
parties (the "escrow agencies"), and made available to law-
enforcement agencies when authorized by a court-issued warrant. Thus,
for example, personal communications would be impervious to
recreational eavesdroppers, and commercial communications would be
impervious to industrial espionage, and yet the FBI could listen in
on suspected terrorists or gangsters.
Clipper has been proposed as a U.S. government standard [62]; it
would then be used by anyone doing business with the federal
government as well as for communications within the government. For
anyone else, use of Clipper is strictly voluntary. AT&T has announced
a secure telephone that uses the Clipper chip.
6.3 How does the Clipper chip work?
The Clipper chip contains an encryption algorithm called Skipjack
(see Question 6.5}), whose details have not been made public. Each
chip also contains a unique 80-bit unit key U, which is escrowed in
two parts at two escrow agencies; both parts must be known in order
to recover the key. Also present is a serial number and an 80-bit
"family key" F; the latter is common to all Clipper chips. The chip
is manufactured so that it cannot be reverse engineered; this means
that the Skipjack algorithm and the keys cannot be read off the chip.
When two devices wish to communicate, they first agree on an 80-bit
"session key" K. The method by which they choose this key is left up
to the implementer's discretion; a public-key method such as RSA or
Diffie-Hellman seems a likely choice. The message is encrypted with
the key K and sent; note that the key K is not escrowed. In addition
to the encrypted message, another piece of data, called the law-
enforcement access field (LEAF), is created and sent. It includes the
session key K encrypted with the unit key U, then concatenated with
the serial number of the sender and an authentication string, and
then, finally, all encrypted with the family key. The exact details
of the law-enforcement field are classified.
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The receiver decrypts the law-enforcement field, checks the
authentication string, and decrypts the message with the key K.
Now suppose a law-enforcement agency wishes to tap the line. It uses
the family key to decrypt the law-enforcement field; the agency now
knows the serial number and has an encrypted version of the session
key. It presents an authorization warrant to the two escrow agencies
along with the serial number. The escrow agencies give the two parts
of the unit key to the law-enforcement agency, which then decrypts to
obtain the session key K. Now the agency can use K to decrypt the
actual message.
Further details on the Clipper chip operation, such as the generation
of the unit key, are sketched by Denning [26].
6.4 Who are the escrow agencies?
It has not yet been decided which organizations will serve as the
escrow agencies, that is, keep the Clipper chip keys. No law-
enforcement agency will be an escrow agency, and it is possible that
at least one of the escrow agencies will be an organization outside
the government.
It is essential that the escrow agencies keep the key databases
extremely secure, since unauthorized access to both escrow databases
could allow unauthorized eavesdropping on private communications. In
fact, the escrow agencies are likely to be one of the major targets
for anyone trying to compromise the Clipper system; the Clipper chip
factory is another likely target.
6.5 What is Skipjack?
Skipjack is the encryption algorithm contained in the Clipper chip;
it was designed by the NSA. It uses an 80-bit key to encrypt 64-bit
blocks of data; the same key is used for the decryption. Skipjack can
be used in the same modes as DES (see Question 5.3), and may be more
secure than DES, since it uses 80-bit keys and scrambles the data for
32 steps, or "rounds"; by contrast, DES uses 56-bit keys and
scrambles the data for only 16 rounds.
The details of Skipjack are classified. The decision not to make the
details of the algorithm publicly available has been widely
criticized. Many people are suspicious that Skipjack is not secure,
either due to oversight by its designers, or by the deliberate
introduction of a secret trapdoor. By contrast, there have been many
attempts to find weaknesses in DES over the years, since its details
are public. These numerous attempts (and the fact that they have
failed) have made people confident in the security of DES. Since
Skipjack is not public, the same scrutiny cannot be applied towards
it, and thus a corresponding level of confidence may not arise.
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Aware of such criticism, the government invited a small group of
independent cryptographers to examine the Skipjack algorithm. They
issued a report [12] which stated that, although their study was too
limited to reach a definitive conclusion, they nevertheless believe
that Skipjack is secure.
Another consequence of Skipjack's classified status is that it cannot
be implemented in software, but only in hardware by government-
authorized chip manufacturers.
6.6 Why is Clipper controversial?
The Clipper chip proposal has aroused much controversy and has been
the subject of much criticism. Unfortunately two distinct issues have
become confused in the large volume of public comment and discussion.
First there is controversy about the whole idea of escrowed keys.
Those in favor of escrowed keys see it as a way to provide secure
communications for the public at large while allowing law-enforcement
agencies to monitor the communications of suspected criminals. Those
opposed to escrowed keys see it as an unnecessary and ineffective
intrusion of the government into the private lives of citizens. They
argue that escrowed keys infringe their rights of privacy and free
speech. It will take a lot of time and much public discussion for
society to reach a consensus on what role, if any, escrowed keys
should have.
The second area of controversy concerns various objections to the
specific Clipper proposal, that is, objections to this particular
implementation of escrowed keys, as opposed to the idea of escrowed
keys in general. Common objections include: the Skipjack algorithm is
not public (see Questions 6.5) and may not be secure; the key escrow
agencies will be vulnerable to attack; there are not enough key
escrow agencies; the keys on the Clipper chips are not generated in a
sufficiently secure fashion; there will not be sufficient competition
among implementers, resulting in expensive and slow chips; software
implementations are not possible; and the key size is fixed and
cannot be increased if necessary.
Micali [55] has recently proposed an alternative system that also
attempts to balance the privacy concerns of law-abiding citizens with
the investigative concerns of law-enforcement agencies. Called fair
public-key cryptography, it is similar in function and purpose to the
Clipper chip proposal but users can choose their own keys, which they
register with the escrow agencies. Also, the system does not require
secure hardware, and can be implemented completely in software.
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6.7 What is the current status of Clipper?
Clipper is under review. Both the executive branch and Congress are
considering it, and an advisory panel recently recommended a full
year-long public discussion of cryptography policy. NIST has invited
the public to send comments, as part of its own review.
6.8 What is DSS?
DSS is the proposed Digital Signature Standard, which specifies a
Digital Signature Algorithm (DSA), and is a part of the U.S.
government's Capstone project (see Question 6.1). It was selected by
NIST, in cooperation with the NSA (see Section 7), to be the digital
authentication standard of the U.S. government; whether the
government should in fact adopt it as the official standard is still
under debate.
DSS is based on the discrete log problem (see Question 4.9) and
derives from cryptosystems proposed by Schnorr [75] and ElGamal [30].
It is for authentication only. For a detailed description of DSS, see
[63] or [57].
DSS has, for the most part, been looked upon unfavorably by the
computer industry, much of which had hoped the government would
choose the RSA algorithm as the official standard; RSA is the most
widely used authentication algorithm. Several articles in the press,
such as [54], discuss the industry dissatisfaction with DSS.
Criticism of DSS has focused on a few main issues: it lacks key
exchange capability; the underlying cryptosystem is too recent and
has been subject to too little scrutiny for users to be confident of
its strength; verification of signatures with DSS is too slow; the
existence of a second authentication standard will cause hardship to
computer hardware and software vendors, who have already standardized
on RSA; and that the process by which NIST chose DSS was too
secretive and arbitrary, with too much influence wielded by NSA.
Other criticisms were addressed by NIST by modifying the original
proposal. A more detailed discussion of the various criticisms can be
found in [57], and a detailed response by NIST can be found in [78].
In the DSS system, signature generation is faster than signature
verification, whereas in the RSA system, signature verification is
faster than signature generation (if the public and private exponents
are chosen for this property, which is the usual case). NIST claims
that it is an advantage of DSS that signing is faster, but many
people in cryptography think that it is better for verification to be
the faster operation.
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6.9 Is DSS secure?
The most serious criticisms of DSS involve its security. DSS was
originally proposed with a fixed 512-bit key size. After much
criticism that this is not secure enough, NIST revised DSS to allow
key sizes up to 1024 bits. More critical, however, is the fact that
DSS has not been around long enough to withstand repeated attempts to
break it; although the discrete log problem is old, the particular
form of the problem used in DSS was first proposed for cryptographic
use in 1989 by Schnorr [75] and has not received much public study.
In general, any new cryptosystem could have serious flaws that are
only discovered after years of scrutiny by cryptographers. Indeed
this has happened many times in the past; see [13] for some detailed
examples. RSA has withstood over 15 years of vigorous examination for
weaknesses. In the absence of mathematical proofs of security,
nothing builds confidence in a cryptosystem like sustained attempts
to crack it. Although DSS may well turn out to be a strong
cryptosystem, its relatively short history will leave doubts for
years to come.
Some researchers warned about the existence of "trapdoor" primes in
DSS, which could enable a key to be easily broken. These trapdoor
primes are relatively rare however, and are easily avoided if proper
key generation procedures are followed [78].
6.10 Is use of DSS covered by any patents?
NIST has filed a patent application for DSS and there have been
claims that DSS is covered by other public-key patents. NIST recently
announced its intention to grant exclusive sublicensing rights for
the DSS patent to Public Key Partners (PKP), which also holds the
sublicensing rights to other patents that may cover DSS (see Question
1.5). In the agreement between NIST and PKP, PKP publicly stated
uniform guidelines by which it will grant licenses to practice DSS.
PKP stated that DSS can be used on a royalty-free basis in the case
of personal, noncommercial, or U.S. government use. See [61] for
details on the agreement and the licensing policy.
6.11 What is the current status of DSS?
After NIST issued the DSS proposal in August 1991, there was a period
in which comments from the public were solicited; NIST then revised
its proposal in light of the comments. DSS may be issued as a FIPS
and become the official U.S. government standard, but it is not clear
when this might happen. DSS is currently in the process of becoming a
standard, along with RSA, for the financial services industry; a
recent draft standard [1] contains the revised version of DSS.
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7 NIST and NSA
7.1 What is NIST?
NIST is an acronym for the National Institute of Standards and
Technology, a division of the U.S. Department of Commerce; it was
formerly known as the National Bureau of Standards (NBS). Through its
Computer Systems Laboratory it aims to promote open systems and
interoperability that will spur development of computer-based
economic activity. NIST issues standards and guidelines that it hopes
will be adopted by all computer systems in the U.S., and also
sponsors workshops and seminars. Official standards are published as
FIPS (Federal Information Processing Standards) publications.
In 1987 Congress passed the Computer Security Act, which authorized
NIST to develop standards for ensuring the security of sensitive but
unclassified information in government computer systems. It
encouraged NIST to work with other government agencies and private
industry in evaluating proposed computer security standards.
7.2 What role does NIST play in cryptography?
NIST issues standards for cryptographic routines; U.S. government
agencies are required to use them, and the private sector often
adopts them as well. In January 1977, NIST declared DES (see Question
5.1) the official U.S. encryption standard and published it as FIPS
Publication 46; DES soon became a de facto standard throughout the
U.S.
A few years ago, NIST was asked to choose a set of cryptographic
standards for the U.S.; this has become known as the Capstone project
(see Section 6). After a few years of rather secretive deliberations,
and in cooperation with the NSA, NIST issued proposals for various
standards in cryptography, including digital signatures (DSS) and
data encryption (the Clipper chip); these are pieces of the overall
Capstone project.
NIST has been criticized for allowing the NSA too much power in
setting cryptographic standards, since the interests of the NSA
conflict with that of the Commerce Department and NIST. Yet, the NSA
has much more experience with cryptography, and many more qualified
cryptographers and cryptanalysts, than does NIST; it would be
unrealistic to expect NIST to forego such available assistance.
7.3 What is the NSA?
The NSA is the National Security Agency, a highly secretive agency of
the U.S. government that was created by Harry Truman in 1952; its
very existence was kept secret for many years. For a history of the
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NSA, see Bamford [2]. The NSA has a mandate to listen to and decode
all foreign communications of interest to the security of the United
States. It has also used its power in various ways (see Question 7.4)
to slow the spread of publicly available cryptography, in order to
prevent national enemies from employing encryption methods too strong
for the NSA to break.
As the premier cryptographic government agency, the NSA has huge
financial and computer resources and employs a host of
cryptographers. Developments in cryptography achieved at the NSA are
not made public; this secrecy has led to many rumors about the NSA's
ability to break popular cryptosystems like DES and also to rumors
that the NSA has secretly placed weaknesses, called trap doors, in
government-endorsed cryptosystems, such as DES. These rumors have
never been proved or disproved, and the criteria used by the NSA in
selecting cryptography standards have never been made public.
Recent advances in the computer and telecommunications industries
have placed NSA actions under unprecedented scrutiny, and the agency
has become the target of heavy criticism for hindering U.S.
industries that wish to use or sell strong cryptographic tools. The
two main reasons for this increased criticism are the collapse of the
Soviet Union and the development and spread of commercially available
public-key cryptographic tools. Under pressure, the NSA may be forced
to change its policies.
7.4 What role does the NSA play in commercial cryptography?
The NSA's charter limits its activities to foreign intelligence.
However, the NSA is concerned with the development of commercial
cryptography because the availability of strong encryption tools
through commercial channels could impede the NSA's mission of
decoding international communications; in other words, the NSA is
worried lest strong commercial cryptography fall into the wrong
hands.
The NSA has stated that it has no objection to the use of secure
cryptography by U.S. industry. It also has no objection to
cryptographic tools used for authentication, as opposed to privacy.
However, the NSA is widely viewed as following policies that have the
practical effect of limiting and/or weakening the cryptographic tools
used by law-abiding U.S. citizens and corporations; see Barlow [3]
for a discussion of NSA's effect on commercial cryptography.
The NSA exerts influence over commercial cryptography in several
ways. First, it controls the export of cryptography from the U.S.
(see Question 1.6); the NSA generally does not approve export of
products used for encryption unless the key size is strictly limited.
It does, however, approve for export any products used for
authentication only, no matter how large the key size, so long as the
product cannot be converted to be used for encryption. The NSA has
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also blocked encryption methods from being published or patented,
citing a national security threat; see Landau [46] for a discussion
of this practice. Additionally, the NSA serves an "advisory" role to
NIST in the evaluation and selection of official U.S. government
computer security standards; in this capacity, it has played a
prominent, and controversial, role in the selection of DES and in the
development of the group of standards known as the Capstone project
(see Section 6), which includes DSS and the Clipper chip. The NSA can
also exert market pressure on U.S. companies to produce (or refrain
from producing) cryptographic goods, since the NSA itself is often a
large customer of these companies.
Cryptography is in the public eye as never before and has become the
subject of national public debate. The status of cryptography, and
the NSA's role in it, will probably change over the next few years.
8 Miscellaneous
8.1 What is the legal status of documents signed with digital
signatures?
If digital signatures are to replace handwritten signatures they must
have the same legal status as handwritten signatures, i.e., documents
signed with digital signatures must be legally binding. NIST has
stated that its proposed Digital Signature Standard (see Question
6.8) should be capable of "proving to a third party that data was
actually signed by the generator of the signature." Furthermore, U.S.
federal government purchase orders will be signed by any such
standard; this implies that the government will support the legal
authority of digital signatures in the courts. Some preliminary legal
research has also resulted in the opinion that digital signatures
would meet the requirements of legally binding signatures for most
purposes, including commercial use as defined in the Uniform
Commercial Code (UCC). A GAO (Government Accounting Office) decision
requested by NIST also opines that digital signatures will meet the
legal standards of handwritten signatures [20].
However, since the validity of documents with digital signatures has
never been challenged in court, their legal status is not yet well-
defined. Through such challenges, the courts will issue rulings that
collectively define which digital signature methods, key sizes, and
security precautions are acceptable for a digital signature to be
legally binding.
Digital signatures have the potential to possess greater legal
authority than handwritten signatures. If a ten-page contract is
signed by hand on the tenth page, one cannot be sure that the first
nine pages have not been altered. If the contract was signed by
digital signatures, however, a third party can verify that not one
byte of the contract has been altered.
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Currently, if two people wish to digitally sign a series of
contracts, they may wish to first sign a paper contract in which they
agree to be bound in the future by any contracts digitally signed by
them with a given signature method and minimum key size.
8.2 What is a hash function? What is a message digest?
A hash function is a computation that takes a variable-size input and
returns a fixed-size string, which is called the hash value. If the
hash function is one-way, i.e., hard to invert, it is also called a
message-digest function, and the result is called a message digest.
The idea is that a digest represents concisely the longer message or
document from which it was computed; one can think of a message
digest as a "digital fingerprint" of the larger document. Examples of
well-known hash functions are MD4, MD5, and SHS (see Questions 8.3
and 8.4).
Although hash functions in general have many uses in computer
programs, in cryptography they are used to generate a small string
(the message digest) that can represent securely a much larger
string, such as a file or message. Since the hash functions are
faster than the signing functions, it is much more efficient to
compute a digital signature using a document's message digest, which
is small, than using the arbitrarily large document itself.
Additionally, a digest can be made public without revealing the
contents of the document from which it derives. This is important in
digital time-stamping, where, using hash functions, one can get a
document time-stamped without revealing its contents to the time-
stamping service (see Question 3.18).
A hash function used for digital authentication must have certain
properties that make it secure enough for cryptographic use.
Specifically, it must be infeasible to find a message that hashes to
a given value and it must be infeasible to find two distinct messages
that hash to the same value. The ability to find a message hashing to
a given value would enable an attacker to substitute a fake message
for a real message that was signed. It would also enable someone to
falsely disown a message by claiming that he or she actually signed a
different message hashing to the same value, thus violating the non-
repudiation property of digital signatures. The ability to find two
distinct messages hashing to the same value could enable an attack
whereby someone is tricked into signing a message which hashes to the
same value as another message with a quite different meaning. The
digest must therefore be long enough to prevent an attacker from
doing an exhaustive search for a collision. For example, if a hash
function produces 100-bit strings, exhaustive search would take
2^{100} attempts on average to match a given value, and approximately
2^{50} attempts on average to find two inputs producing the same
digest.
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A digital signature system can be broken by attacking either the
difficult mathematical problem on which the signature method is based
or the hash function used to create the message digests. When
choosing an authentication system, it is generally a good idea to
choose a signature method and a hash function that require comparable
efforts to break; any extra security in one of the two components is
wasted, since attacks will be directed at the weaker component.
Actually, attacking the hash function is harder in practice, since it
requires a large amount of memory and the ability to trick the victim
into signing a special message. With 2^{64} operations, an attacker
can find two messages that hash to the same digest under any of the
MD hash functions; this effort is comparable to that necessary to
break 512-bit RSA; thus MD5 is a good choice when using RSA with a
512-bit modulus. However, those with greater security needs, such as
certifying authorities, should use a longer modulus and a hash
function that produces a longer message digest; either SHS (160-bit
digest) or a modified version of MD4 that produces a 256-bit digest
[71] would suffice.
8.3 What are MD2, MD4 and MD5?
MD2, MD4 and MD5 (MD stands for Message Digest) are widely used hash
functions designed by Ron Rivest specifically for cryptographic use.
They produce 128-bit digests and there is no known attack faster than
exhaustive search.
MD2 is the slowest of the three; MD4 [71] is the fastest. MD5 [73]
has been dubbed "MD4 with safety belts" by Rivest, since it has a
more conservative design than MD4; the design gives it increased
security against attack, but at a cost of being approximately 33%
slower than MD4. MD5 is the most commonly used of the three
algorithms. MD4 and MD5 are publicly available for unrestricted use;
MD2 is available for use with PEM (see Question 8.7). Details of MD2,
MD4, and MD5 with sample C code are available in Internet RFCs
(Requests For Comments) 1319, 1320, and 1321, respectively.
No feasible attacks on any of the MD algorithms have been discovered,
although some recent theoretical work has found some interesting
structural properties [24,25].
8.4 What is SHS?
The Secure Hash Standard (SHS) [58] is a hash function proposed by
NIST (see Question 7.1) and adopted as a U.S. government standard. It
is designed for use with the proposed Digital Signature Standard (see
Question 6.8) and is part of the government's Capstone project (see
Question 6.1}). SHS produces a 160-bit hash value from a variable-
size input. SHS is structurally similar to MD4 and MD5. It is roughly
25% slower than MD5 but may be more secure, because it produces
message digests that are 25% longer than those produced by the MD
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functions. SHS is currently the only part of Capstone that has been
officially adopted as a government standard.
8.5 What is Kerberos?
Kerberos is a secret-key network authentication system developed at
MIT [79]; it uses DES for encryption and authentication. Unlike a
public-key authentication system, it does not produce digital
signatures: Kerberos was designed to authenticate requests for
network resources rather than to authenticate authorship of
documents. Kerberos provides real-time authentication in a
distributed environment, but does not provide for future third-party
verification of documents.
In a Kerberos system, there is a designated site on the network,
called the Kerberos server, which performs centralized key management
and administrative functions. The server maintains a database
containing the secret keys of all users, generates session keys
whenever two users wish to communicate securely, and authenticates
the identity of a user who requests certain network services.
Kerberos, like other secret-key systems, requires trust in a third
party, in this case the Kerberos server. If the server were
compromised, the integrity of the whole system would fall. Public-key
cryptography was designed precisely to avoid the necessity to trust
third parties or communication lines (see Question 1.4). Kerberos may
be adequate for those who do not need the more robust functions and
properties of public-key systems.
8.6 What are RC2 and RC4?
RC2 and RC4 are variable-key-size cipher functions designed by Ron
Rivest for fast bulk encryption. They are alternatives to DES (see
Question 5.1) and are as fast or faster than DES. They can be more
secure than DES because of their ability to use long key sizes; they
can also be less secure than DES if short key sizes are used.
RC2 is a variable-key-size symmetric block cipher and can serve as a
drop-in replacement for DES, for example in export versions of
products otherwise using DES. RC2 can be used in the same modes as
DES (see Question 5.3), including triple encryption. RC2 is
approximately twice as fast as DES, at least in software. RC4 is a
variable-key-size symmetric stream cipher and is 10 or more times as
fast as DES in software. Both RC2 and RC4 are very compact in terms
of code size.
An agreement between the Software Publishers Association (SPA) and
the U.S. government gives RC2 and RC4 special status by means of
which the export approval process is simpler and quicker than the
usual cryptographic export process. However, to qualify for quick
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export approval a product must limit the RC2 and RC4 key sizes to 40
bits; 56 bits is allowed for foreign subsidiaries and overseas
offices of U.S. companies. An additional 40-bit string, called a
salt, can be used to thwart attackers who try to precompute a large
look-up table of possible encryptions. The salt is appended to the
encryption key, and this lengthened key is used to encrypt the
message; the salt is then sent, unencrypted, with the message. RC2
and RC4 have been widely used by developers who want to export their
products; DES is almost never approved for export. RC2 and RC4 are
proprietary algorithms of RSA Data Security, Inc.; details have not
been published.
8.7 What is PEM?
PEM is the Internet Privacy-Enhanced Mail standard, designed,
proposed, but not yet officially adopted, by the Internet Activities
Board in order to provide secure electronic mail over the Internet.
Designed to work with current Internet e-mail formats, PEM includes
encryption, authentication, and key management, and allows use of
both public-key and secret-key cryptosystems. Multiple cryptographic
tools are supported: for each mail message, the specific encryption
algorithm, digital signature algorithm, hash function, and so on are
specified in the header. PEM explicitly supports only a few
cryptographic algorithms; others may be added later. DES in CBC mode
is currently the only message encryption algorithm supported, and
both RSA and DES are supported for the key management. PEM also
supports the use of certificates, endorsing the CCITT X.509 standard
for certificate structure.
The details of PEM can be found in Internet RFCs (Requests For
Comments) 1421 through 1424. PEM is likely to be officially adopted
by the Internet Activities Board within one year. Trusted Information
Systems has developed a free non-commercial implementation of PEM,
and other implementations should soon be available as well.
8.8 What is RIPEM?
RIPEM is a program developed by Mark Riordan that enables secure
Internet e-mail; it provides both encryption and digital signatures,
using RSA and DES routines from RSAREF (see Question 8.10). RIPEM is
not fully PEM-compatible; for example, it does not currently support
certificates. However, future versions will include certificates and
will be fully compliant with the PEM standard. RIPEM is available
free for non-commercial use in the U.S. and Canada. To get RIPEM,
obtain an ftp account at ripem.msu.edu.
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8.9 What is PKCS?
PKCS (Public-Key Cryptography Standards) is a set of standards for
implementation of public-key cryptography. It has been issued by RSA
Data Security, Inc. in cooperation with a computer industry
consortium, including Apple, Microsoft, DEC, Lotus, Sun and MIT. PKCS
has been cited by the OIW (OSI Implementors' Workshop) as a method
for implementation of OSI standards. PKCS is compatible with PEM (see
Question 8.7) but extends beyond PEM. For example, where PEM can only
handle ASCII data, PKCS is designed for binary data as well. PKCS is
also compatible with the CCITT X.509 standard.
PKCS includes both algorithm-specific and algorithm-independent
implementation standards. Specific algorithms supported include RSA,
DES, and Diffie-Hellman key exchange. It also defines algorithm-
independent syntax for digital signatures, digital envelopes (for
encryption), and certificates; this enables someone implementing any
cryptographic algorithm whatsoever to conform to a standard syntax
and thus preserve interoperability. Documents detailing the PKCS
standards can be obtained by sending e-mail to <pkcs@rsa.com> or by
anonymous ftp to <rsa.com>.
8.10 What is RSAREF?
RSAREF is a collection of cryptographic routines in portable C source
code, available at no charge from RSA Laboratories, a division of RSA
Data Security, Inc. It includes RSA, MD2, MD5, and DES; Diffie-
Hellman key exchange will be included in a forthcoming version. It
includes both low-level subroutines, such as modular exponentiation,
and high-level cryptographic functions, such as verification of
digital signatures. The arithmetic routines can handle multiple-
precision integers, and the RSA algorithm routines can handle
variable key sizes. RSAREF is fully compatible with the PEM and PKCS
standards.
RSAREF is available to citizens of the U.S. or Canada and to
permanent residents of the U.S. It can be used in personal, non-
commercial applications but cannot be used commercially or sent
outside the U.S. and Canada. The RSAREF license contains more details
on the usage allowed and disallowed. RSAREF is available on the
Internet by sending e-mail to <rsaref@rsa.com> or by ftp to
<rsa.com>.
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Author's Address
Paul N. Fahn
RSA Laboratories Department of Computer Science
10 Twin Dolphin Drive Stanford University
Redwood City, CA 94065 Stanford, CA 94305
Phone: (415) 595-7703 (415)723-3088
FAX: (415) 595-4126
EMail: <fahn@cs.stanford.edu>
<fahn@rsa.com>