Divide-and-concatenate: an architecture-level optimization technique for universal hash functions

The authors present an architectural optimization technique called divide-and-concatenate for hardware architectures of universal hash functions based on three observations: 1) the area of a multiplier and associated data path decreases quadratically and their speeds increase gradually as their operand size is reduced; 2) multiplication is at the core of universal hash functions and multipliers consume most of the area of universal hash function hardware; and 3) two universal hash functions are equivalent if they have the same collision-probability property. In the proposed approach, the authors divide a 2w-bit data path (with collision probability 2^-2w) into two w-bit data paths (each with collision probability 2^-w), apply one message word to these two w-bit data paths and concatenate their results to construct an equivalent 2w-bit data path (with a collision probability 2^-2w). The divide-and-concatenate technique is complementary to all circuit-, logic-, and architecture-optimization techniques. The authors applied this technique on a linear congruential universal hash (LCH) family. When compared to the 100% overhead associated with duplicating a straightforward 32-bit LCH data path, the divide-and-concatenate approach that uses four equivalent 8-bit data paths yields a 101% increase in throughput with only 52% hardware overhead.