International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Gary McGuire

Publications

Year
Venue
Title
2013
CRYPTO
2009
EPRINT
A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem
This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields $GF(p)$. We use this processor to compare a new algorithm for point addition and point doubling operations on the twisted Edwards curves, against a current standard algorithm in use, namely the Double-and-Add. Secure power analysis versions of both algorithms are also examined and compared. The algorithms are implemented on an FPGA, and the speed, area and power performance of each are then evaluated for various modes of circuit operation using parallel processing. To the authors' knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields $GF(p)$.
2008
EPRINT
CM construction of genus 2 curves with p-rank 1
We present an algorithm for constructing cryptographic hyperelliptic curves of genus $2$ and $p$-rank $1$, using the CM method. We also present an algorithm for constructing such curves that, in addition, have a prescribed small embedding degree. We describe the algorithms in detail, and discuss other aspects of $p$-rank 1 curves too, including the reduction of the class polynomials modulo $p$.
2007
EPRINT
Quadratic Almost Perfect Nonlinear Functions With Many Terms
We introduce a new infinite family of multiterm functions that are APN on $GF(2^{2k})$ for odd $k$.