Errata To Sound Hashing Modes Of Arbitrary Functions, Permutations, And Block Ciphers

In ToSC 2018(4), Daemen et al. performed an in-depth investigation of sound hashing modes based on arbitrary functions, permutations, or block ciphers. However, for the case of invertible primitives, there is a glitch. In this errata, we formally fix this glitch by adding an extra term to the security bound, q/2(b-n), where q is query complexity, b the width of the permutation or the block size of the block cipher, and n the size of the hash digest. For permutations that are wider than two times the chaining value this term is negligible. For block cipher based hashing modes where the block size is close to the digest size, the term degrades the security significantly.