Fast software implementation of binary elliptic curve cryptography

Manuel Bluhm, Shay Gueron

Research output: Contribution to journalArticlepeer-review


This paper presents an efficient and side-channel-protected software implementation of scalar multiplication for the standard National Institute of Standards and Technology (NIST) and Standards for Efficient Cryptography Group binary elliptic curves. The enhanced performance is achieved by leveraging Intel’s AVX architecture and utilizing the pclmulqdq processor instruction. The fast carry-less multiplication is further used to speed up the reduction on the Haswell platform. For the five NIST curves over $$GF(2^m)$$GF(2m) with $$m$$m$$\in $$∈$$\{163,233,283,409,571\}$${163,233,283,409,571}, the resulting scalar multiplication implementation is about 5–12 times faster than that of OpenSSL-1.0.1e, enhancing the ECDHE and ECDSA algorithms significantly.

Original languageEnglish
Pages (from-to)215-226
Number of pages12
JournalJournal of Cryptographic Engineering
Issue number3
StatePublished - 10 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


  • Binary elliptic curve
  • Binary field arithmetic
  • Mul&add
  • Pclmulqdq
  • Scalar multiplication
  • Side-channel protection

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications


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