On the Security Bounds for Block Ciphers Without Whitening Key Addition Against Integral Distinguishers

At ASIACRYPT 2021, Phil Hebborn et al., developed a powerful theory for block ciphers against integral distinguishers under the assumption of independent round keys and a whitening key XORed with the full state. Nevertheless, for certain block ciphers, say SIMON and Simeck, a whitening key is not part of their design. In this paper, we provide an improved theory on the resistance of integral distinguishers, which can be applied to block ciphers without a whitening key addition. As an illustration, we apply our arguments to SIMON32 and Simeck32 and obtain tight security bounds for them against integral distinguishers. To the best of our knowledge, this is the first time that the truly tight security bounds against integral distinguishers are derived for both ciphers.