Network Working Group M. Horowitz
Cygnus Solutions
Internet-Draft March, 1997
Key Derivation for Authentication, Integrity, and Privacy
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Abstract
Recent advances in cryptography have made it desirable to use longer
cryptographic keys, and to make more careful use of these keys. In
particular, it is considered unwise by some cryptographers to use the
same key for multiple purposes. Since most cryptographic-based
systems perform a range of functions, such as authentication, key
exchange, integrity, and encryption, it is desirable to use different
cryptographic keys for these purposes.
This document does not define a particular protocol, but defines a set of
cryptographic transformations for use with arbitrary network
protocols and block cryptographic algorithm.
Deriving Keys
In order to use multiple keys for different functions, there are two
possibilities:
- Each protocol ``key'' contains multiple cryptographic keys. The
implementation would know how to break up the protocol ``key'' for
use by the underlying cryptographic routines.
- The protocol ``key'' is used to derive the cryptographic keys.
The implementation would perform this derivation before calling
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the underlying cryptographic routines.
In the first solution, the system has the opportunity to provide
separate keys for different functions. This has the advantage that
if one of these keys is broken, the others remain secret. However,
this comes at the cost of larger ``keys'' at the protocol layer. In
addition, since these ``keys'' may be encrypted, compromising the
cryptographic key which is used to encrypt them compromises all the
component keys. Also, the not all ``keys'' are used for all possible
functions. Some ``keys'', especially those derived from passwords,
are generated from limited amounts of entropy. Wasting some of this
entropy on cryptographic keys which are never used is unwise.
The second solution uses keys derived from a base key to perform
cryptographic operations. By carefully specifying how this key is
used, all of the advantages of the first solution can be kept, while
eliminating some disadvantages. In particular, the base key must be
used only for generating the derived keys, and this derivation must
be non-invertible and entropy-preserving. Given these restrictions,
compromise of one derived keys does not compromise the other subkeys.
Attack of the base key is limited, since it is only used for
derivation, and is not exposed to any user data.
Since the derived key has as much entropy as the base keys (if the
cryptosystem is good), password-derived keys have the full benefit of
all the entropy in the password.
To generate a derived key from a base key:
Derived Key = DK(Base Key, Well-Known Constant)
where
DK(Key, Constant) = n-truncate(E(Key, Constant))
In this construction, E(Key, Plaintext) is a block cipher, Constant
is a well-known constant defined by the protocol, and n-truncate
truncates its argument by taking the first n bits; here, n is the key
size of E.
If the output of E is is shorter than n bits, then some entropy in
the key will be lost. If the Constant is smaller than the block size
of E, then it must be padded so it may be encrypted. If the Constant
is larger than the block size, then it must be folded down to the
block size to avoid chaining, which affects the distribution of
entropy.
In any of these situations, a variation of the above construction is
used, where the folded Constant is encrypted, and the resulting
output is fed back into the encryption as necessary (the | indicates
concatentation):
K1 = E(Key, n-fold(Constant))
K2 = E(Key, K1)
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K3 = E(Key, K2)
K4 = ...
DK(Key, Constant) = n-truncate(K1 | K2 | K3 | K4 ...)
n-fold is an algorithm which takes m input bits and ``stretches''
them to form n output bits with no loss of entropy, as described in
[Blumenthal96]. In this document, n-fold is always used to produce n
bits of output, where n is the key size of E.
If the size of the Constant is not equal to the block size of E, then
the Constant must be n-folded to the block size of E. This number is
used as input to E. If the block size of E is less than the key
size, then the output from E is taken as input to a second invocation
of E. This process is repeated until the number of bits accumulated
is greater than or equal to the key size of E. When enough bits have
been computed, the first n are taken as the derived key.
Since the derived key is the result of one or more encryptions in the
base key, deriving the base key from the derived key is equivalent to
determining the key from a very small number of plaintext/ciphertext
pairs. Thus, this construction is as strong as the cryptosystem
itself.
Deriving Keys from Passwords
When protecting information with a password or other user data, it is
necessary to convert an arbitrary bit string into an encryption key.
In addition, it is sometimes desirable that the transformation from
password to key be difficult to reverse. A simple variation on the
construction in the prior section can be used:
Key = DK(n-fold(Password), Well-Known Constant)
The n-fold algorithm is reversible, so recovery of the n-fold output
is equivalent to recovery of Password. However, recovering the n-
fold output is difficult for the same reason recovering the base key
from a derived key is difficult.
Traditionally, the transformation from plaintext to ciphertext, or
vice versa, is determined by the cryptographic algorithm and the key.
A simple way to think of derived keys is that the transformation is
determined by the cryptographic algorithm, the constant, and the key.
For interoperability, the constants used to derive keys for different
purposes must be specified in the protocol specification. The
constants must not be specified on the wire, or else an attacker who
determined one derived key could provide the associated constant and
spoof data using that derived key, rather than the one the protocol
designer intended.
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Determining which parts of a protocol require their own constants is
an issue for the designer of protocol using derived keys.
Security Considerations
This entire document deals with security considerations relating to
the use of cryptography in network protocols.
Acknowledgements
I would like to thank Uri Blumenthal, Hugo Krawczyk, and Bill
Sommerfeld for their contributions to this document.
References
[Blumenthal96] Blumenthal, U., "A Better Key Schedule for DES-Like
Ciphers", Proceedings of PRAGOCRYPT '96, 1996.
Author's Address
Marc Horowitz
Cygnus Solutions
955 Massachusetts Avenue
Cambridge, MA 02139
Phone: +1 617 354 7688
Email: marc@cygnus.com
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