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 $$a \,\text {mod}\,b$$ from bit shifts, multiplications and additions in $$\mathbb {Z}$$. 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 scientiae, as safe as using randomly generated composite moduli.