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Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three

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Executive Summary

Elliptic curve cryptosystems, proposed independently by Neal Koblitz and Victor Miller are more and more widespread in everyday-life applications. The core operation of elliptic curve cryptosystems is the scalar multiplication on elliptic curves. There are numerous investigations of fast and regular scalar multiplication on elliptic curves over large prime field or binary field. In this paper, the authors propose an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic three. This method is based on full signed ternary expansion of a scalar to be multiplied. The cost per bit of this algorithm is lower than that of all previous ones.

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