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Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output. In the case of a block cipher, it refers to a set of techniques for tracing differences through the network of transformations, discovering where the cipher exhibits non-random behaviour, and exploiting such properties to recover the secret key.
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Origins of differential cryptanalysis
The discovery of differential cryptanalysis is generally attributed to Eli Biham and Adi Shamir in the late 1980s, who published a number of attacks against various block ciphers and hash functions, including a theoretical weakness in the Data Encryption Standard (DES). It was noted that DES is surprisingly resilient to differential cryptanalysis, in the sense that even small modifications to the algorithm would make it much more susceptible; this suggested that the designers at IBM knew of this in the 1970s. In 1994, a member of the original IBM DES team, Don Coppersmith, published a paper stating that differential cryptanalysis was known to IBM as early as 1974, and that defending against differential cryptanalysis had been a design goal
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Within IBM, differential cryptanalysis was known as the "T-attack"[, or "Tickle attack"][Matt Blaze, sci.crypt, 15 August 1996, Re: Reverse engineering and the Clipper chip"].
While DES was designed with resistance to differential cryptanalysis in mind, other contemporary ciphers proved to be vulnerable. An early target for the attack was the FEAL block cipher. The original proposed version with four rounds (FEAL-4) can be broken using only eight chosen plaintexts, and even a 31-round version of FEAL is susceptible to the attack.
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A description of the attack
Differential cryptanalysis is usually a chosen plaintext attack, meaning that the attacker must be able to obtain encrypted ciphertexts for some set of plaintexts of his choosing. The scheme can successfully cryptanalyze DES with an effort on the order 247 chosen plaintexts. There are, however, extensions that would allow a known plaintext or even a ciphertext-only attack. The basic method uses pairs of plaintext related by a constant difference; difference can be defined in several ways, but the eXclusive OR (XOR) operation is usual. The attacker then computes the differences of the corresponding ciphertexts, hoping to detect statistical patterns in their distribution. In the basic attack, one particular ciphertext difference is expected to be especially frequent; in this way, the cipher can be distinguished from random. More sophisticated variations allow the key to be recovered faster than exhaustive search.
For any particular cipher, the input difference must be carefully selected if the attack is to be successful. An analysis of the algorithm's internals is undertaken; the standard method is to trace a path of highly probable differences through the various stages of encryption, termed a differential characteristic.
Since differential cryptanalysis became public knowledge, it has become a basic concern of cipher designers. New designs are expected to be accompanied by evidence that the algorithm is resistant to this attack, and many, including the Advanced Encryption Standard, have been proven secure against the attack.
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Specialized types
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See also
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