Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

TL;DR

This paper introduces a new algorithm that accelerates scalar multiplication and pairing computations on elliptic curves, enhancing efficiency for cryptographic applications by reducing the number of field multiplications needed.

Contribution

The authors propose an algorithm that reduces field multiplications in elliptic curve operations, improving scalar multiplication and pairing evaluation speeds over existing methods.

Findings

Scalar multiplication speed improved by up to 8.5%.

Weil and Tate pairing computations are up to 7.8% faster.

Applications include faster multiple scalar multiplication and factorization methods.

Abstract

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8 % to 8.5 % over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8 %.