On the Success Probability of χ2-attack on RC6

Knudsen and Meier applied the χ2-attack to RC6. The χ2-attack can be used for both distinguishing attacks and key recovery attacks. Up to the present, the success probability of key recovery attack in any χ2attack has not been evaluated theoretically without any assumption of experimental results. In this paper, we discuss the success probability of key recovery attack in χ2-attack and give the theorem that evaluates the success probability of a key recovery attack without any assumption of experimental approximation, for the first time. We make sure the accuracy of our theorem by demonstrating it on both 4-round RC6 without post-whitening and 4-round RC6-8. We also evaluate the security of RC6 theoretically and show that a variant of the χ2-attack is faster than an exhaustive key search for the 192-bit-key and 256-bit-key RC6 with up to 16 rounds. As a result, we succeed in answering such an open question that a variant of the χ2-attack can be used to attack RC6 with 16 or more rounds.