Lambda Coordinates for Binary Elliptic Curves

  • Thomaz Oliveira
  • Julio López
  • Diego F. Aranha
  • Francisco Rodríguez-Henríquez
Conference paper

DOI: 10.1007/978-3-642-40349-1_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8086)
Cite this paper as:
Oliveira T., López J., Aranha D.F., Rodríguez-Henríquez F. (2013) Lambda Coordinates for Binary Elliptic Curves. In: Bertoni G., Coron JS. (eds) Cryptographic Hardware and Embedded Systems - CHES 2013. CHES 2013. Lecture Notes in Computer Science, vol 8086. Springer, Berlin, Heidelberg

Abstract

In this work we present the λ-coordinates, a new system for representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and timing results of our software implementation over the field \(\mathbb{F}_{2^{254}}\). As a result, we improve speed records for protected/unprotected single/multi-core software implementations of random-point elliptic curve scalar multiplication at the 128-bit security level. When implemented on a Sandy Bridge 3.4GHz Intel Xeon processor, our software is able to compute a single/multi-core unprotected scalar multiplication in 72,300 and 47,900 clock cycles, respectively; and a protected single-core scalar multiplication in 114,800 cycles. These numbers improve by around 2% on the newer Core i7 2.8GHz Ivy Bridge platform.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Thomaz Oliveira
    • 1
  • Julio López
    • 2
  • Diego F. Aranha
    • 3
  • Francisco Rodríguez-Henríquez
    • 1
  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico
  2. 2.Institute of ComputingUniversity of CampinasBrazil
  3. 3.Department of Computer ScienceUniversity of BrasíliaBrazil

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