Improbable Differential Attacks on Serpent using Undisturbed Bits

A recently introduced S-box evaluation criteria called undisturbed bits allow the attacker to construct longer truncated, impossible or improbable differentials. In this paper, we analyze the security of Serpent against impossible and improbable differential cryptanalysis for the first time and provide a 7-round improbable differential attack by using undisturbed bits of its S-boxes. Although these cryptanalytic techniques are discovered after Serpent was designed, our analysis shows that the cipher is secure against these kind of attacks. Moreover, it was shown that every 3 × 3 S-box contains undisturbed bits and a list of ciphers were provided whose 4 × 4 S-boxes contain undisturbed bits. In this study we provide undisturbed bits for larger S-boxes for the first time. Namely, the undisturbed bits for the 5 × 5 and 6 × 6 S-boxes of Fides and the 9 × 9 S-boxes of Kasumi and Misty