Efficient and secure elliptic curve point multiplication using double-base chains

Abstract

In this paper, we propose a efficient and secure point multiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled double-base number system (DBNS). The speed-ups are the results of fewer point additions and improved formulae for point triplings and quadruplings in both even and odd characteristic. Our algorithms can be protected against simple and differential side-channel analysis by using side-channel atomicity and classical randomization techniques. Our numerical experiments show that our approach leads to speed-ups compared to windowing methods, even with window size equal to 4, and other SCA resistant algorithms. © International Association for Cryptologic Research 2005.