Paper 2014/427

Fast point multiplication algorithms for binary elliptic curves with and without precomputation

Thomaz Oliveira, Diego F. Aranha, Julio López, and Francisco Rodríguez-Henríquez


In this paper we introduce new methods for computing constant-time variable-base point multiplications over the Galbraith-Lin-Scott (GLS) and the Koblitz families of elliptic curves. Using a left-to-right double-and-add and a right-to-left halve-and-add Montgomery ladder over a GLS curve, we present some of the fastest timings yet reported in the literature for point multiplication. In addition, we combine these two procedures to compute a multi-core protected scalar multiplication. Furthermore, we designed for the first time a regular $\tau$-adic scalar expansion for Koblitz curves. As a result, using the regular recoding approach, we set the speed record for a single constant-time point multiplication on standardized binary elliptic curves at the $128$-bit security level.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
binary elliptic curvesscalar multiplicationsoftware implementation
Contact author(s)
thomaz figueiredo @ gmail com
2014-07-31: last of 2 revisions
2014-06-06: received
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Creative Commons Attribution


      author = {Thomaz Oliveira and Diego F.  Aranha and Julio López and Francisco Rodríguez-Henríquez},
      title = {Fast point multiplication algorithms for binary elliptic curves with and without precomputation},
      howpublished = {Cryptology ePrint Archive, Paper 2014/427},
      year = {2014},
      note = {\url{}},
      url = {}
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