Linear cryptanalysis, a Known-Plaintext Attack, for symmetric block cipher works by constructing linear approximations of the non-linear components of the cipher. The only component which introduces non-linearity in the symmetric block cipher is an S-box. Using classical computing algorithms, the best known solution to find a linear approximation of a non-linear function, in this case an S-box, requires 𝑶(𝟐 𝒏 ) queries to the S-box and 𝑶(𝟐 𝟐𝒏+𝒎) time-complexity, where 𝒏 is the input size of the S-box and 𝒎 is the output size. In this paper, a quantum algorithm is presented which can produce best linear approximations of a non-linear S-box using only 𝑶(𝟐 𝒎) queries to S-box with 𝑶(𝒏𝟐 𝒎) time-complexity. The proposed algorithm shows a significant improvement over the classical algorithm. Correctness proof of the proposed quantum algorithm is presented along with an example.
Non-Linear Approximations in Linear Cryptanalysis
