## Abstract

We present an architecture level optimization technique called divide-and-concatenate based on two observations: 1) the area of an array multiplier and its associated data path decreases quadratically and their delay decreases linearly as their operand size is reduced and 2) in universal hash functions and their associated message authentication codes, two one-way hash functions are equivalent if they have the same collision probability property. In the proposed approach, we divide a 2ω-bit data path (with collision probability 2^{-2ω}) into two w-bit data paths (each with collision probability 2^{-ω}) and concatenate their results to construct an equivalent 2ω-bit data path (with a collision probability 2^{-2ω}). We applied this technique on NH universal hash, a universal hash function that uses multiplications and additions. We implemented the straightforward 32-bit pipelined NH universal hash data path and the divide-and-concatenate architecture that uses four equivalent 8-bit divide-and-concatenate NH universal hash data paths on a Xilinx Virtex II XC2VP7-7 field programmable gate array (FPGA) device. This divide-and- concatenate architecture yielded a 94% increase in throughput with only 40% hard-ware overhead. Finally, the implementation of universal message authentication code (UMAC) with collision probability 2^{-32} using the divide-and-concatenate NH hash as a building block yielded a throughput of 79.2 Gb/s with only 3840 Virtex II XC2VP7-7 FPGA slices.

Original language | English (US) |
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Article number | 1705615 |

Pages (from-to) | 1831-1839 |

Number of pages | 9 |

Journal | IEEE Journal on Selected Areas in Communications |

Volume | 24 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2006 |

## Keywords

- Divide-and-concatenate
- Performance optimization
- Universal hash functions
- Universal message authentication code (UMAC)

## ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering