Paper 2014/852
Faster ECC over $\mathbb{F}_{2^{521}-1}$
Robert Granger and Michael Scott
Abstract
In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime $2^{521} - 1$. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST's (and SECG's) curve P-521 requires 1,073,000 cycles, while on the recently proposed Edwards curve E-521 it requires just 943,000 cycles. As a comparison, on the same architecture openSSL's ECDH speed test for curve P-521 requires 1,319,000 cycles. Furthermore, our code was written entirely in C and so is robust across different platforms. The basic observation behind these speedups is that the form of the modulus allows one to multiply residues with as few word-by-word multiplications as is needed for squaring, while incurring very little overhead from extra additions, in contrast to the usual Karatsuba methods.
Note: This version now has cache-safe implementation timings.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- A minor revision of an IACR publication in PKC 2015
- Keywords
- elliptic curve cryptographyperformanceP-521E-521Edwards curvesgeneralised repunit primes
- Contact author(s)
- robbiegranger @ gmail com
- History
- 2015-03-23: revised
- 2014-10-22: received
- See all versions
- Short URL
- https://ia.cr/2014/852
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/852,
author = {Robert Granger and Michael Scott},
title = {Faster {ECC} over $\mathbb{F}_{2^{521}-1}$},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/852},
year = {2014},
url = {https://eprint.iacr.org/2014/852}
}