Double-Speed Barrett Moduli

Modular multiplication and modular reduction are the atomic constituents of most public-key cryptosystems. Amongst the numerous algorithms for performing these operations, a particularly elegant method was proposed by Barrett. This method builds the operation a mod b from bit shifts, multiplications and additions in Z. This allows to build modular reduction at very marginal code or silicon costs by leveraging existing hardware or software multipliers. This paper presents a method allowing to double the speed of Barrett’s algorithm by using specific composite moduli. This is particularly useful for lightweight devices where such an optimization can make a difference in terms of power consumption, cost and processing time. The generation of composite moduli with a predetermined portion is a well-known technique and the use of such moduli is considered, in statu scientiæ, as safe as using randomly generated composite moduli.