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Impossible differential cryptanalysis
 
 
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In cryptography
Cryptography

Cryptography is the practice and study of hiding information. In modern times cryptography is considered a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering....
, impossible differential cryptanalysis is a form of differential cryptanalysis
Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions....
 for block cipher
Block cipher

In cryptography, a block cipher is a symmetric key algorithm cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation....
s. While ordinary differential cryptanalysis tracks differences that propagate through the cipher with greater than expected probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
, impossible differential cryptanalysis exploits differences that are impossible
IMpossible

"IMpossible" is the second track from band Figurine 's second album, The Heartfelt. It was released in October 2001...
 (having probability 0) at some intermediate state
State (computer science)

In computer science and automata theory, a state is a unique configuration of information in a program or machine. It is a concept that occasionally extends into some forms of systems programming such as Lexical analysiss and parsers....
 of the cipher algorithm.

Lars Knudsen
Lars Knudsen

Lars Ramkilde Knudsen is a Denmark researcher in cryptography, particularly interested in the design and cryptanalysis of block ciphers, cryptographic hash function and message authentication codes ....
 appears to be the first to use a form of this attack, in the 1998 paper where he introduced his AES candidate
Advanced Encryption Standard process

The Advanced Encryption Standard , the block cipher ratified as a standard by National Institute of Standards and Technology of the United States , was chosen using a process markedly more open and transparent than its predecessor, the aging Data Encryption Standard ....
, DEAL
Deal

Deal may refer to:* Deal , an automobile built in Jonesville, Michigan, from 1905 to 1911* Deal, Kent, a town in Kent, England* Deal, New Jersey, a Borough in Monmouth County, New Jersey, United States...
.






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In cryptography
Cryptography

Cryptography is the practice and study of hiding information. In modern times cryptography is considered a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering....
, impossible differential cryptanalysis is a form of differential cryptanalysis
Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions....
 for block cipher
Block cipher

In cryptography, a block cipher is a symmetric key algorithm cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation....
s. While ordinary differential cryptanalysis tracks differences that propagate through the cipher with greater than expected probability
Probability

Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t...
, impossible differential cryptanalysis exploits differences that are impossible
IMpossible

"IMpossible" is the second track from band Figurine 's second album, The Heartfelt. It was released in October 2001...
 (having probability 0) at some intermediate state
State (computer science)

In computer science and automata theory, a state is a unique configuration of information in a program or machine. It is a concept that occasionally extends into some forms of systems programming such as Lexical analysiss and parsers....
 of the cipher algorithm.

Lars Knudsen
Lars Knudsen

Lars Ramkilde Knudsen is a Denmark researcher in cryptography, particularly interested in the design and cryptanalysis of block ciphers, cryptographic hash function and message authentication codes ....
 appears to be the first to use a form of this attack, in the 1998 paper where he introduced his AES candidate
Advanced Encryption Standard process

The Advanced Encryption Standard , the block cipher ratified as a standard by National Institute of Standards and Technology of the United States , was chosen using a process markedly more open and transparent than its predecessor, the aging Data Encryption Standard ....
, DEAL
Deal

Deal may refer to:* Deal , an automobile built in Jonesville, Michigan, from 1905 to 1911* Deal, Kent, a town in Kent, England* Deal, New Jersey, a Borough in Monmouth County, New Jersey, United States...
. The first presentation to attract the attention of the cryptographic community was later the same year at the rump session of CRYPTO
Crypto

Crypto can refer to:In security systems and military intelligence:*Cryptography, the practice and study of hiding information.*Cryptanalysis, the study of methods for obtaining the meaning of encrypted information...
 '98, in which Eli Biham
Eli Biham

Eli Biham is an Israeli cryptographer and Cryptanalysis, currently a professor at the Technion Israeli Institute of Technology Computer Science department....
, Alex Biryukov
Alex Biryukov

Alex Biryukov is a cryptographer, currently an assistant professor at the University of Luxembourg. His notable work includes the design of the stream cipher LEX , as well as the cryptanalysis of numerous cryptographic primitives....
, and Adi Shamir
Adi Shamir

Adi Shamir is an Israeli cryptography. He was one of the inventors of the RSA algorithm , one of the inventors of the Feige-Fiat-Shamir Identification Scheme , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer science....
 introduced the name "impossible differential" and used the technique to break 4.5 out of 8.5 rounds of IDEA
International Data Encryption Algorithm

In cryptography, the International Data Encryption Algorithm is a block cipher designed by Xuejia Lai and James Massey of ETH Zurich and was first described in 1991....
 and 31 out of 32 rounds of the NSA
National Security Agency

The National Security Agency/Central Security Service is a Cryptology Intelligence agency of the Federal government of the United States, administered as part of the United States Department of Defense....
-designed cipher Skipjack
Skipjack (cipher)

In cryptography, Skipjack is a block cipher — an algorithm for encryption — developed by the United States National Security Agency ....
. This development led noted cryptographer Bruce Schneier
Bruce Schneier

Bruce Schneier is an American cryptographer, computer security specialist, and writer. He is the author of several books on computer security and cryptography, and is the founder and chief technology officer of BT Counterpane, formerly Counterpane Internet Security, Inc....
 to speculate that the NSA had no previous knowledge of impossible differential cryptanalysis. The technique has since been applied to many other ciphers, including Khufu and Khafre
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....
, E2
E2 (cipher)

In cryptography, E2 is a block cipher which was created in 1998 by Nippon Telegraph and Telephone and submitted to the AES competition.Like other AES candidates, E2 operates on blocks of 128 bits, using a key of 128, 192, or 256 bits....
, variants of Serpent
Serpent (cipher)

Serpent is a symmetric key block cipher which was a finalist in the Advanced Encryption Standard process, where it came second to Rijndael. Serpent was designed by Ross Anderson, Eli Biham, and Lars Knudsen....
, MARS, Twofish
Twofish

In cryptography, Twofish is a Symmetric-key algorithm 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 process, but was not selected for standardisation....
, Rijndael, CRYPTON
CRYPTON

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

In cryptography, Zodiac is a block cipher designed in 2000 by Chang-Hyi Lee for the Korean firm SoftForum.Zodiac uses a 16-round Feistel cipher structure with key whitening....
, Hierocrypt-3, TEA
Tiny Encryption Algorithm

In cryptography, the Tiny Encryption Algorithm is a block cipher notable for its simplicity of description and implementation . It was designed by David Wheeler and Roger Needham of the Cambridge University Computer Laboratory; it was first presented at the Fast Software Encryption workshop in Leuven in 1994, and first published in the pro...
, XTEA
XTEA

In cryptography, XTEA is a block cipher designed to correct weaknesses in Tiny Encryption Algorithm. The cipher's designers were David Wheeler and Roger Needham of the University of Cambridge Computer Laboratory, and the algorithm was presented in an unpublished technical report in 1997 ....
, Mini-AES, ARIA
ARIA (cipher)

In cryptography, ARIA is a block cipher designed in 2003 by a large group of South Korean researchers. In 2004, the Korean Agency for Technology and Standards selected it as a standard cryptographic technique....
, Camellia
Camellia (cipher)

In cryptography, Camellia is a block cipher that has been evaluated favorably by several organisations, including the European Union's NESSIE project , and the Japanese CRYPTREC project ....
, and SHACAL-2.

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."

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