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The common computation in elliptic curve cryptography (ECC), aP + bQ, is performed by extending Shamir's method for the computation of the product of powers of two elements in a group. The complexity of computing aP + bQ is dependent on the joint weight of the binary expansion of positive integers a and b. We give a method of finding a minimum joint weight signed-binary representation of a pair of integers. Our method examines the integers a and b from left to right, thereby making the conversion to signed-binary form compatible with Shamir's method. This reduces the memory required to perform the computation of aP + bQ.
Date of Publication: Feb. 2005