AN IMPROVED WNAF ALGORITHM BASED ON PELL PRECOMPUTATION AND MIXED COORDINATE SYSTEM

To improve the efficiency of scalar multiplication, an improved wNAF algorithm is proposed by using Pell precomputation and mixed coordinates. The algorithm replaced odd number and prime number with Pell number in the precomputation stage, which reduced the number of point addition and double point operations. In the evaluation stage, a new mixed coordinate system strategy was introduced, which combined Affine Coordinate, Jacobian Coordinate and Modified Jacobian Coordinate, effectively reducing the number of modular inversion operations in the scalar multiplication algorithm. After experimental analysis, the average computational complexity of the enhanced wNAF algorithm under the PPMC scheme is reduced by 50%. Compared with existing algorithms, the enhanced algorithm proposed in this paper has lower computational complexity and higher scalar multiplication algorithm efficiency.