Abstract. We describe a message authentication algorithm, UMAC, which can authenticate messages (in software, on contemporary machines) roughly an order of magnitude faster than current practice (e.g., HMAC-SHA1), and about twice as fast as times previously reported for the universal hash-function family MMH. To achieve such speeds, UMAC uses a new universal hash-function family, NH, and a design which allows effective exploitation of SIMD parallelism. The “cryptographic ” work of UMAC is done using standard primitives of the user’s choice, such as a block cipher or cryptographic hash function; no new heuristic primitives are developed here. Instead, the security of UMAC is rigorously proven, in the sense of giving exact and quantitatively strong results which demonstrate an inability to forge UMAC-authenticated messages assuming an inability to break the underlying cryptographic primitive. Unlike conventional, inherently serial MACs, UMAC is parallelizable, and will have ever-faster implementation speeds as machines offer up increasing amounts of parallelism. We envision UMAC as a practical algorithm for next-generation message authentication. 1

We introduce a new technique for constructing a family of universal hash functions.

There is a well-known class of message authentication systems guaranteeing that attackers will have a negligible chance of successfully forging a message. This paper shows how one of these systems can hash messages at extremely high speed -- much more quickly than previous systems at the same security level -- using IEEE floating-point arithmetic. This paper also presents a survey of the literature in a unified mathematical framework.

Abstract. This paper compares the parameters sizes and software performance of several recent constructions for universal hash functions: bucket hashing, polynomial hashing, Toeplitz hashing, division hashing, evaluation hashing, and MMH hashing. An objective comparison between these widely varying approaches is achieved by defining constructions that offer a comparable security level. It is also demonstrated how the security of these constructions compares favorably to existing MAC algorithms, the security of which is less understood. 1

This paper introduces two new ideas in the construction of fast universal hash functions geared towards the task of message authentication.

We present a cryptographic architecture optimization technique called divide-and-concatenate based on two observations: (i) the area of a multiplier and associated data path decreases exponentially and their speeds increase linearly as their operand size is reduced. (ii) in hash functions, message authentication codes and related cryptographic algorithms, two functions are equivalent if they have the same collision probability property. In the proposed approach we divide a 2w-bit data path (with collision probability 2 ) into two w-bit data paths (each with collision probability 2 ) and concatenate their results to construct an equivalent 2w-bit data path (with a collision probability 2 ). We applied this technique on NH hash, a universal hash function that uses multiplications and additions. When compared to the 100% overhead associated with duplicating a straightforward 32-bit pipelined NH hash data path, the divide-and-concatenate approach yields a 94% increase in throughput with only 40% hardware overhead. The NH hash associated message authentication code UMAC architecture with collision probability 2 that uses four equivalent 8-bit divide-and-concatenate NH hash data paths yields a throughput of 79.2 Gbps with only 3840 FPGA slices when implemented on a Xilinx XC2VP7-7 Field Programmable Gate Array (FPGA). 1. Motivation In the past, most cryptographic algorithms have been developed to run fast on general-purpose processors. More recently, dedicated cryptographic hardware is being developed and deployed to match the >10 Gbps wire speed requirements. In this paper we will investigate scalable hardware architectures for cryptographic algorithms.