Paper 2015/785

Double-Speed Barrett Moduli

Rémi Géraud, Diana Maimut, and David Naccache


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 $a \bmod b$ from bit shifts, multiplications and additions in $\mathbb{Z}$. This allows building modular reduction at very marginal code or silicon costs by leveraging existing hardware or software multipliers. This paper presents a method allowing doubling 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 scientae, as safe as using randomly generated composite moduli.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
modular multiplication
Contact author(s)
david naccache @ ens fr
2015-08-07: received
Short URL
Creative Commons Attribution


      author = {Rémi Géraud and Diana Maimut and David Naccache},
      title = {Double-Speed Barrett Moduli},
      howpublished = {Cryptology ePrint Archive, Paper 2015/785},
      year = {2015},
      note = {\url{}},
      url = {}
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