Linear cryptanalysis

In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis. The discovery is attributed to Mitsuru Matsui, who first applied the technique to the FEAL cipher (Matsui and Yamagishi, 1992). Subsequently, Matsui published an attack on the Data Encryption Standard (DES), eventually leading to the first experimental cryptanalysis of the cipher reported in the open community (Matsui, 1993; 1994). The attack on DES is not generally practical, requiring 2 known plaintexts. A variety of refinements to the attack have been suggested, including using multiple linear approximations or incorporating non-linear expressions, leading to a generalized partitioning cryptanalysis. Evidence of security against linear cryptanalysis is usually expected of new cipher designs. There are two parts to linear cryptanalysis. The first is to construct linear equations relating plaintext, ciphertext and key bits that have a high bias; that is, whose probabilities of holding (over the space of all possible values of their variables) are as close as possible to 0 or 1.