Highly regular m-ary powering ladders

Abstract

This paper describes new exponentiation algorithms with applications to cryptography. The proposed algorithms can be seen as m-ary generalizations of the so-called Montgomery ladder. Both left-to-right and right-to-left versions are presented. Similarly to Montgomery ladder, the proposed algorithms always repeat the same instructions in the same order, without inserting dummy operations, and so offer a natural protection against certain implementation attacks. Moreover, as they are available in any radix m and in any scan direction, the proposed algorithms offer improved performance and greater flexibility. © 2009 Springer-Verlag Berlin Heidelberg.