SOME PROPERTIES OF VECTORIAL ADDITION CHAINS

Abstract

The concept of the shortest vectorial addition chains is considered to be an optimal approach for computing a monomial Pi(i=1)(p)x(i)(ni) with the minimum number of multiplications. In this paper, some properties of the shortest vectorial addition chain are presented. Furthermore, an approach to achieve the shortest chains in some special cases is proposed. The correctness of these properties and the optimality of this approach are also shown.