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Researches on generation of Montgomery form elliptic curve

Zeng Guo-ping

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Abstract

This paper analyzes the O-K-S algorithm1 in detail and gives an improved algorithm. The improved algo-rithm generate a Montgomery-form elliptic curve,whose cofactor is exactly 4 and which can prevent the timing-attack over a Mersenne prime finite field. Furthermore,the early-abort strategy and pseudo-random method are used to effec-tively improve the generation speed of these elliptic curves.

About this research paper

What this paper is about

This paper analyzes the O-K-S algorithm1 in detail and gives an improved algorithm. The improved algo-rithm generate a Montgomery-form elliptic curve,whose cofactor is exactly 4 and which can prevent the timing-attack over a Mersenne prime finite field. Furthermore,the early-abort strategy and pseudo-random method are used to effec-tively improve the generation speed of these elliptic curves.

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Available abstract

This paper analyzes the O-K-S algorithm1 in detail and gives an improved algorithm. The improved algo-rithm generate a Montgomery-form elliptic curve,whose cofactor is exactly 4 and which can prevent the timing-attack over a Mersenne prime finite field. Furthermore,the early-abort strategy and pseudo-random method are used to effec-tively improve the generation speed of these elliptic curves.

Key concepts: Computer science, Curve25519, Mersenne prime, Elliptic curve, Prime (order theory), Elliptic curve point multiplication, Algorithm, Elliptic curve cryptography

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