Left-to-Right Optimal Signed-Binary Representation of a Pair of Integers

Authors:
Xiaoyu Ruan;Rajendra S. Katti
Affiliations:
IEEE;IEEE
Venue:
IEEE Transactions on Computers
Year:
2005

Citing 3
Cited 5

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Abstract

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. In this paper, 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.