Authors:
Pratik Poddar
;
Achin Bansal
and
Bernard Menezes
Affiliation:
Indian Institute of Technology - Bombay, India
Keyword(s):
Elliptic Curve Cryptography, Scalar Multiplication, near-Factorization, NAF, Window NAF, Koblitz Curves.
Related
Ontology
Subjects/Areas/Topics:
Applied Cryptography
;
Cryptographic Techniques and Key Management
;
Data Engineering
;
Databases and Data Security
;
Information and Systems Security
;
Network Security
;
Wireless Network Security
Abstract:
Elliptic curve scalar multiplication ( [k]P where k is an integer and P is a point on the elliptic curve) is widely used in encryption and signature generation. In this paper, we explore a factorization-based approach called Near-Factorization that can be used in conjunction with existing optimization techniques such as Window NAF (Non Adjacent Form). We present a performance model of Near-Factorization and validate model results with those from a simulation. We compare Near-Factorization with wNAF for a range of scalar sizes, window sizes, divisor lengths and Hamming weights of divisor. The use of Near-Factorization with wNAF results in a considerable reduction in the effective Hamming weight of the scalar and a reduction in overall computation cost for Koblitz curves.