Accurate estimates of the data complexity and success probability for various cryptanalyses

Céline Blondeau (1) , Benoît Gérard (1) , Jean-Pierre Tillich (1)

1 SECRET - Security, Cryptology and Transmissions

Many attacks on encryption schemes rely on statistical considerations using plaintext/ciphertext pairs to find some information on the key. We provide here simple formulae for estimating the data complexity and the success probability which can be applied to a lot of different scenarios (differential cryptanalysis, linear cryptanalysis, truncated differential cryptanalysis, etc.). Our work does not rely here on Gaussian approximation which is not valid in every setting but use instead a simple and general approximation of the binomial distribution and asymptotic expansions of the beta distribution.

Mots clés: statistical cryptanalysis; success probability; data complexity

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Céline Blondeau, Benoît Gérard, Jean-Pierre Tillich. Accurate estimates of the data complexity and success probability for various cryptanalyses. Designs, Codes and Cryptography, 2011, 59 (1-3), pp.3-34. ⟨10.1007/s10623-010-9452-2⟩. ⟨hal-00610101⟩