On the Construction of Short Addition-Subtraction Chains and their Applications

The problem of computing effciently, such that and are known to be very interesting, specially when is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method.