Analysis of gradient statistical attack at block ciphers RC6, MARS, CAST-128

This work covers an experimental research of statistical methods in cryptoanalysis on the example of the block ciphers RC6, MARS and CAST-128. The offered gradient attack is based on the statistical test named “bookstack”. The described schemes and modifications of the attack allow to reduce complexity of finding a secret key in compare to earlier known types of attacks. Researches of efficiency of gradient statistical attack are conducted in this work, limits of its practical and theoretical applicability are shown (9 rounds of cipher RC6, 21 round of MARS and 4 rounds of CAST-128). Also in the work deduced analytical dependences between effectively attacked rounds and temporal and hardware complexity of attack. Besides, for ciphers RC6 and MARS it was developed the modifications of gradient attack, which considerably reduce time and operational complexity have been developed. Also in this work the method of definition optimal parameters of attack is shown; time complexity and its dependence on test and size parameters of a ciphertext are researched; theoretical requirements for the computing resources for realization of attack are shown.