A Formula That Generates Hash Collisions

Abstract: We present an explicit formula that produces hash collisions for the Merkle-Damg{\aa}rd construction. The formula works for arbitrary choice of message block and irrespective of the standardized constants used in hash functions, although some padding schemes may cause the formula to fail. This formula bears no obvious practical implications because at least one of any pair of colliding messages will have length double exponential in the security parameter. However, due to ambiguity in existing definitions of collision resistance, this formula arguably breaks the collision resistance of some hash functions.