Attacks faster than brute-force
There are three attacks known that can break the full 16 rounds of DES with less complexity than a brute-force search: differential cryptanalysis (DC), linear cryptanalysis (LC), and Davies' attack. However, the attacks are theoretical and are unfeasible to mount in practice[citation needed]; these types of attack are sometimes termed certificational weaknesses.
Differential cryptanalysis was rediscovered in the late 1980s by Eli Biham and Adi Shamir; it was known earlier to both IBM and the NSA and kept secret. To break the full 16 rounds, differential cryptanalysis requires 249 chosen plaintexts.[26] DES was designed to be resistant to DC.
Linear cryptanalysis was discovered by Mitsuru Matsui, and needs 243 known plaintexts (Matsui, 1993); the method was implemented (Matsui, 1994), and was the first experimental cryptanalysis of DES to be reported. There is no evidence that DES was tailored to be resistant to this type of attack. A generalization of LC — multiple linear cryptanalysis — was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov and others. (2004); their analysis suggests that multiple linear approximations could be used to reduce the data requirements of the attack by at least a factor of 4 (that is, 241 instead of 243). A similar reduction in data complexity can be obtained in a chosen-plaintext variant of linear cryptanalysis (Knudsen and Mathiassen, 2000). Junod (2001) performed several experiments to determine the actual time complexity of linear cryptanalysis, and reported that it was somewhat faster than predicted, requiring time equivalent to 239–241 DES evaluations.
Improved Davies' attack: while linear and differential cryptanalysis are general techniques and can be applied to a number of schemes, Davies' attack is a specialized technique for DES, first suggested by Donald Davies in the eighties, and improved by Biham and Biryukov (1997). The most powerful form of the attack requires 250 known plaintexts, has a computational complexity of 250, and has a 51% success rate.
There have also been attacks proposed against reduced-round versions of the cipher, that is, versions of DES with fewer than 16 rounds. Such analysis gives an insight into how many rounds are needed for safety, and how much of a "security margin" the full version retains. Differential-linear cryptanalysis was proposed by Langford and Hellman in 1994, and combines differential and linear cryptanalysis into a single attack. An enhanced version of the attack can break 9-round DES with 215.8 known plaintexts and has a 229.2 time complexity (Biham and others, 2002).
