Optimal Use of Montgomery Multiplication on Smart Cards

Abstract

Montgomery multiplication is used to speed up modular multiplications involved in public-key cryptosystems. However, it requires conversion of parameters into N -residue representation. These additional pre-computations can be costly for low resource devices like smart cards. In this paper, we propose a new, more efficient method, suitable for smart card implementations of most of public-key cryptosystems. Our approach essentially consists in modifying the representation of the key and the algorithm embedded in smart card in order to take advantage of the Montgomery multiplication properties.