An algorithm for exact division
Journal of Symbolic Computation
Finite Field Multiplier Using Redundant Representation
IEEE Transactions on Computers
Analysis of the Weil Descent Attack of Gaudry, Hess and Smart
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Random number generators with period divisible by a Mersenne prime
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Efficient bit-parallel multipliers over finite fields GF(2m)
Computers and Electrical Engineering
Hi-index | 0.00 |
In this article we introduce redundant trinomials to represent elements of finite fields of characteristic 2. This paper develops applications to cryptography, especially based on elliptic and hyperelliptic curves. After recalling well-known techniques to perform efficient arithmetic in extensions of $\mathbb{F}_2$, we describe redundant trinomial bases and discuss how to implement them efficiently. They are well suited to build $\mathbb{F}_{2^n}$ when no irreducible trinomial of degree n exists. Depending on n∈[2,10000] tests with NTL show that, in this case, improvements for squaring and exponentiation are respectively up to 45% and 25%. More attention is given to extension degrees relevant for curve-based cryptography. For this range, a scalar multiplication can be sped up by a factor up to 15%.