An Improved wNAF Scalar-Multiplication Algorithm With Low Computational Complexity by Using Prime Precomputation

To reduce the computational complexity of scalar multiplication, an improved wNAF scalar-multiplication algorithm is proposed by using prime precomputation. It replaces odd number with prime number in the precomputation stage, and makes up the difference between prime and odd by building the tiny multi-base chains. Thanks to the proposed algorithm, the computational complexity, the cost of precomputation and the creation time of addition chains are all reduced. Compared with the wNAF, the computational complexity and the running speed are optimized by 28.37% and 77.38% respectively at the fittest case. Also, lower computational complexity and higher running speed are outstanding features of the introduced algorithm than other existing algorithms.