Fast Software Implementation of Binary Elliptic Curve Cryptography

Manuel Bluhm; Shay Gueron

Paper 2013/741

Fast Software Implementation of Binary Elliptic Curve Cryptography

Manuel Bluhm and Shay Gueron

Abstract

This paper presents an efficient and side channel protected software implementation of point multiplication for the standard NIST and SECG binary elliptic curves. The enhanced performance is achieved by improving the Lòpez-Dahab/Montgomery method at the algorithmic level, and by leveraging Intel's AVX architecture and the pclmulqdq processor instruction at the coding level. The fast carry-less multiplication is further used to speed up the reduction on the newest Haswell platforms. For the five NIST curves over $GF(2^m)$ with $m$ $\in$ $\{163,233,283,409,571\}$, the resulting point multiplication implementation is about 6 to 12 times faster than that of OpenSSL-1.0.1e, enhancing the ECDHE and ECDSA algorithms significantly.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Contact author(s): shay @ math haifa ac il
History: 2013-11-17: received
Short URL: https://ia.cr/2013/741
License: CC BY

BibTeX

@misc{cryptoeprint:2013/741,
      author = {Manuel Bluhm and Shay Gueron},
      title = {Fast Software Implementation of Binary Elliptic Curve Cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/741},
      year = {2013},
      url = {https://eprint.iacr.org/2013/741}
}