Addition Chains Algorithm Based on Fast Fourier Transform

Some algorithms for generating addition chains are discussed, Fast Fourier Transform is considered thoroughly, and then a new algorithm based on FFT is proposed to quickly generate addition chains. The new addition chains given by the FFT based algorithm consist lots of multiply 2 operations, which can generate the addition chains at the fastest speed and can make the addition chains shortest. The new addition chain is close to the shortest addition chain. Besides, the FFT based algorithm for addition chains can be parallel implemented to improve its efficiency. More important, this algorithm gives a new direction for the research and application of FFT algorithm.