In
cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...
, the so-called
product cipher
In cryptography, a product cipher combines two or more transformations in a manner intending that the resulting cipher is more secure than the individual components to make it resistant to cryptanalysis.Handbook of Applied Cryptography by Alfred J. ...
s are a certain kind of cipher, where the (de-)ciphering of data is typically done as an iteration of ''rounds''. The setup for each round is generally the same, except for round-specific fixed values called a round constant, and round-specific data derived from the
cipher key called a round key. A key schedule is an algorithm that calculates all the round keys from the key.
Some types of key schedules
*Some ciphers have simple key schedules. For example, the block cipher
TEA
Tea is an aromatic beverage prepared by pouring hot or boiling water over cured or fresh leaves of ''Camellia sinensis'', an evergreen shrub native to East Asia which probably originated in the borderlands of southwestern China and north ...
splits the 128-bit key into four 32-bit pieces and uses them repeatedly in successive rounds.
*
DES
Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include:
People
* Des Buckingham, English football manager
* Des Corcoran, (1928–2004), Australian politician
* Des Dillon (disambiguation), sever ...
has a key schedule in which the 56-bit key is divided into two 28-bit halves; each half is thereafter treated separately. In successive rounds, both halves are rotated left by one or two bits (specified for each round), and then 48 round key bits are selected by
Permuted Choice 2 (PC-2) – 24 bits from the left half and 24 from the right. The rotations have the effect that a different set of bits is used in each round key; each bit is used in approximately 14 out of the 16 round keys.
*To avoid simple relationships between the cipher key and the round keys, in order to resist such forms of
cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic sec ...
as
related-key attack
In cryptography, a related-key attack is any form of cryptanalysis where the attacker can observe the operation of a cipher under several different keys whose values are initially unknown, but where some mathematical relationship connecting the ke ...
s and
slide attack
The slide attack is a form of cryptanalysis designed to deal with the prevailing idea that even weak ciphers can become very strong by increasing the number of rounds, which can ward off a differential attack. The slide attack works in such a way ...
s, many modern ciphers use more elaborate key schedules to generate an "expanded key" from which round keys are drawn. Some ciphers, such as
Rijndael (AES) and
Blowfish
Tetraodontidae is a family of primarily marine and estuarine fish of the order Tetraodontiformes. The family includes many familiar species variously called pufferfish, puffers, balloonfish, blowfish, blowies, bubblefish, globefish, swellfis ...
, use the same operations as those used in the data path of the cipher algorithm for their key expansion, sometimes initialized with some "
nothing-up-my-sleeve numbers". Other ciphers, such as
RC5, expand keys with functions that are somewhat or completely different from the encryption functions.
Notes
Knudsen and Mathiassen (2004) give some experimental evidence that indicate that the key schedule plays a part in providing strength against
linear
Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
and
differential cryptanalysis. For toy
Feistel cipher
In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering research ...
s, it was observed that those with complex and well-designed key schedules can reach a uniform distribution for the probabilities of
differentials and
linear hulls faster than those with poorly designed key schedules.
References
* Lars R. Knudsen and John Erik Mathiassen
On the Role of Key Schedules in Attacks on Iterated Ciphers ESORICS 2004, pp322–334.
* Uri Blumenthal and Steven M. Bellovin
A Better Key Schedule for DES-like Ciphers Proceedings of PRAGOCRYPT '96.
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Cryptographic algorithms