New methods for generating short addition chains

Power exponentiation is an important operation in modern cryptography. This operation carl be efficiently calculated using the concept of the addition chain. In this paper, two new systematic methods, a Run-length method and a Hybrid method, are proposed to generate a short addition chain. The perfo rmance of these two methods are theoretically analyzed and it is shown that the Hybrid method is more efficient and practical than known methods. The proposed methods can reduce the addition chain length by 8%, in the best ca se, compared to the Window method.