Scalar multiplication for twisted Edwards curves using the extended double-base number system

Abstract

This paper analyzes the problem of speeding up single-scalar multiplication of a recently introduced type of elliptic curve, so-called ``twisted Edwards curve", and also presents a new construction of addition chains using the extended double-base number system. Our method uses the Fibonacci sequence. It was found through numerical investigation that our double-base chains can save time, compared with other methods in previous work.