Authors:
Yin Li
1
and
Christophe Negre
2
Affiliations:
1
Institute of Information Security, Shanghai jiaotong University, China
;
2
Team DALI/ELIAUS, University of Perpignan, France
Keyword(s):
Finite Field, Multiplication, Montgomery, Binomial residue representation.
Related
Ontology
Subjects/Areas/Topics:
Cryptographic Techniques and Key Management
;
Information and Systems Security
;
Public Key Crypto Applications
Abstract:
In this paper, we propose an extension of the algorithm proposed by Bajard, Imbert and Negre in (Bajar et al., 2006), refered as BIN algorithm. We use binomial residue representation of field elements instead of the Lagrange representation of (Bajar et al., 2006). Specifically, every elements in Fpk is represented by a set of residue modulo fixed binomials. We propose two versions of our algorithm, one in general form with a sub-quadratic complexity equal to O(k1.5 ) operations in Fp . The second one is optimized with the use of FFT. In this case the cost is O(k log(k)) operations in Fp . For fields GF ( pk ) suitable for elliptic curve cryptography our algorithm roughly improves the time delay of (Bajar et al., 2006) by 45%.