Short−output universal hash functions and their use in fast and secure message authentication

Abstract

Message authentication codes usually require the underlining universal hash functions to have a long output so that the successful probability of forging messages is low enough for cryptographic purposes. To take advantage of fast operation on word-size parameters in modern processors, long-output universal hashing schemes can be securely constructed by concatenating several instances of short-output primitives. In this paper, we describe a new method for short-output universal hash function termed digest() suitable for very fast software implementation and applicable to secure message authentication. The method possesses a higher level of security relative to other well-studied short-output universal hashing schemes. Suppose that the universal hash output is fixed at one word of b bits, then the collision probability of ours is 2^1-b compared to 6 * 2^-b of MMH, whereas 2^-b/2 of NH within UMAC is far away from optimality. In addition to message authentication codes, we show how short-output universal hashing is applicable to manual authentication protocols where universal hash keys are used in a very different and interesting way.