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 ...

, impossible differential cryptanalysis is a form of differential cryptanalysis for block ciphers. While ordinary differential cryptanalysis tracks differences that propagate through the cipher with greater than expected

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

, impossible differential cryptanalysis exploits differences that are impossible (having probability 0) at some intermediate

state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * ''Our S ...

of the cipher algorithm.

Lars Knudsen Lars Ramkilde Knudsen (born 21 February 1962) is a Danish researcher in cryptography, particularly interested in the design and analysis of block ciphers, hash functions and message authentication codes (MACs). Academic After some early work ...

appears to be the first to use a form of this attack, in the 1998 paper where he introduced his

AES candidate The Advanced Encryption Standard (AES), the symmetric block cipher ratified as a standard by National Institute of Standards and Technology of the United States (NIST), was chosen using a process lasting from 1997 to 2000 that was markedly more ...

DEAL A deal, or deals may refer to: Places United States * Deal, New Jersey, a borough * Deal, Pennsylvania, an unincorporated community * Deal Lake, New Jersey Elsewhere * Deal Island (Tasmania), Australia * Deal, Kent, a town in England * Deal, ...

. The first presentation to attract the attention of the cryptographic community was later the same year at the rump session of CRYPTO '98, in which

Eli Biham Eli Biham ( he, אלי ביהם) is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion - Israel Institute of Technology Computer Science department. Starting from October 2008 and till 2013, Biham was the dean of t ...

, Alex Biryukov, and

Adi Shamir Adi Shamir ( he, עדי שמיר; born July 6, 1952) is an Israeli cryptographer. He is a co-inventor of the Rivest–Shamir–Adleman (RSA) algorithm (along with Ron Rivest and Len Adleman), a co-inventor of the Feige–Fiat–Shamir identifi ...

introduced the name "impossible differential" and used the technique to break 4.5 out of 8.5 rounds of

IDEA In common usage and in philosophy, ideas are the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophers have considered ideas to be a fundamental ontological category of bei ...

and 31 out of 32 rounds of the

NSA The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collecti ...

-designed cipher Skipjack. This development led cryptographer

Bruce Schneier Bruce Schneier (; born January 15, 1963) is an American cryptographer, computer security professional, privacy specialist, and writer. Schneier is a Lecturer in Public Policy at the Harvard Kennedy School and a Fellow at the Berkman Klein Cente ...

to speculate that the NSA had no previous knowledge of impossible differential cryptanalysis. The technique has since been applied to many other ciphers:

Khufu and Khafre In cryptography, Khufu and Khafre are two block ciphers designed by Ralph Merkle in 1989 while working at Xerox's Palo Alto Research Center. Along with Snefru, a cryptographic hash function, the ciphers were named after the Egyptian Pharaohs Khuf ...

, E2, variants of

Serpent Serpent or The Serpent may refer to: * Snake, a carnivorous reptile of the suborder Serpentes Mythology and religion * Sea serpent, a monstrous ocean creature * Serpent (symbolism), the snake in religious rites and mythological contexts * Serp ...

MARS Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...

Twofish In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization. T ...

, Rijndael,

CRYPTON In cryptography, CRYPTON is a symmetric block cipher submitted as a candidate for the Advanced Encryption Standard (AES). It is very efficient in hardware implementations and was designed by Chae Hoon Lim of Future Systems Inc. The CRYPTON al ...

Zodiac The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The pat ...

Hierocrypt-3 In cryptography, Hierocrypt-L1 and Hierocrypt-3 are block ciphers created by Toshiba in 2000. They were submitted to the NESSIE project, but were not selected. Both algorithms were among the cryptographic techniques recommended for Japanese gove ...

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 ...

, XTEA, Mini-AES,

ARIA In music, an aria ( Italian: ; plural: ''arie'' , or ''arias'' in common usage, diminutive form arietta , plural ariette, or in English simply air) is a self-contained piece for one voice, with or without instrumental or orchestral accompa ...

Camellia ''Camellia'' (pronounced or ) is a genus of flowering plants in the family Theaceae. They are found in eastern and southern Asia, from the Himalayas east to Japan and Indonesia. There are more than 220 described species, with some controv ...

, and

SHACAL-2 SHACAL-1 (originally simply SHACAL) is a 160-bit block cipher based on SHA-1, and supports keys from 128-bit to 512-bit. SHACAL-2 is a 256-bit block cipher based upon the larger hash function SHA-256. Both SHACAL-1 and SHACAL-2 were selected fo ...

. Biham, Biryukov and Shamir also presented a relatively efficient specialized method for finding impossible differentials that they called a ''miss-in-the-middle'' attack. This consists of finding "two events with probability one, whose conditions cannot be met together."

References

Further reading