A Collision Attack on a Double-Block-Length Compression Function Instantiated with 8-/9-Round AES-256

This paper presents the first non-trivial collision attack on the double-block-length compression function presented at FSE 2006 instantiated with round-reduced AES-256: f(0)(h(0)parallel to h(1), M)parallel to f(1)(h(0)parallel to h(1), M) such that f(0)(h0 parallel to h(1), M) = Eh(1)parallel to(M)(h(0))circle plus h(0), f(1)(h(0)parallel to h(1), M) = E-h1 parallel to(M)(h(0)circle plus c)circle plus h(0)circle plus c, where parallel to represents concatenation, E is AES-256 and c is a 16-byte nonzero constant. The proposed attack is a free-start collision attack using the rebound attack proposed by Mendel et al. The success of the proposed attack largely depends on the configuration of the constant c: the number of its non-zero bytes and their positions. For the instantiation with AES-256 reduced from 14 rounds to 8 rounds, it is effective if the constant c has at most four non-zero bytes at some specific positions, and the time complexity is 2(64) or 2(96). For the instantiation with AES-256 reduced to 9 rounds, it is effective if the constant c has four non-zero bytes at some specific positions, and the time complexity is 2(120). The space complexity is negligible in both cases.