Optimized Approach for Computing Multi-base Chains

As a generalization of double base chains, multi-base number system were very suitable for efficient computation of scalar multiplications of elliptic curves because of shorter representation length and less Hamming weight. Thus it is needed to search efficient multi-base chains. We considered settings with different computing cost of point operations and introduced an optimized tree-based method for searching multi-base chains. Experimental results show that compared with NAF, greedy algorithm and tree based computing double base chain method, applying the multi-base representation returned by our proposed algorithms, the scalar computing costs reduced by 22%, 12.9%, 10.6% respectively on prime elliptic curves and 20.2%, 11.5%, 9.7% on binary elliptic curves.