Abstract
To improve the efficiency of scalar multiplication, a run-length addition chain of scalar was proposed. New scalar multiplication integrated with algorithms of direct computing 2Q+P, 2nR+S in field, sliding window algorithm and run-length algorithm. The addition chain length, storage and pre-computing would be decreased. Its efficiency has been enhanced about 53% than binary method, about 47.5% than NAF method, about 46.2% than run-length algorithm and about 42.2% than Windows method.
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