Abstract. The Gallant-Lambert-Vanstone (GLV) method is a very efcient technique for accelerating point multiplication on elliptic curves with eciently computable endomorphisms. G...
We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural ...
The joint sparse form (JSF) for the non-adjacent form (NAF) representation of two large integers a and b, was proposed by Solinas. Then Ciet extended it to the -JSF for the -NAF r...
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isog...
A cryptographic pairing evaluates as an element of a finite extension field, and the evaluation itself involves a considerable amount of extension field arithmetic. It is recogn...