Abstract
Elliptic curve cryptography (ECC) is one of the most promising public-key techniques in terms of short key size and various crypto protocols. For this reason, many studies on the implementation of ECC on resource-constrained devices within a practical execution time have been conducted. To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC. A number of studies have proposed pre-computation and advanced scalar multiplication using a non-adjacent form (NAF) representation, and more sophisticated approaches have employed a width-w NAF representation and a modified pre-computation table. In this paper, we propose a new pre-computation method in which zero occurrences are much more frequent than in previous methods. This method can be applied to ordinary group scalar multiplication, but it requires large pre-computation table, so we combined the previous method with ours for practical purposes. This novel structure establishes a new feature that adjusts speed performance and table size finely, so we can customize the pre-computation table for our own purposes. Finally, we can establish a customized look-up table for embedded microprocessors.
Highlights
Elliptic curve cryptography (ECC) is a public-key cryptography based on the algebraic structure of elliptic curves over finite fields [1,2,3]
We propose an efficient method for fixed-point scalar multiplication, enhancing the method of Mohamed et al by constructing a novel look-up table structure
Released novel scalar multiplication by Mohamed et al reduced the number of addition operations using w-non-adjacent form (NAF) and a novel look-up table structure
Summary
Elliptic curve cryptography (ECC) is a public-key cryptography based on the algebraic structure of elliptic curves over finite fields [1,2,3]. The use of elliptic curves in cryptography was suggested independently by Koblitz [4] and Miller [5] in 1985. The short key size and various crypto protocols are available in ECC, which enable secure and robust communications. Scalar multiplication, which multiplies a secret scalar, k, with a point, P , on an elliptic curve, E(Fq ), resulting in the point, Q ∈ E(Fq ), is too expensive to compute on embedded microprocessors. For a fixed point, P , we can take advantage of pre-computation tables for scalar multiplication, which were proposed in 1992 [6]
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