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2009•Unpublished venueRequires access

Research on Fast Arithmetic of Elliptic Curve over GF(3~m)

Lei Feng-yu

Open publisher page 1 citations

Abstract

The arithmetic on supersingular and non-supersingular elliptic curve over GF(3m) were researched,and computational formulas of point addition,2P,3P and 3kP in affine coordinate were given and confirmed.Based on these,a new 3kP recursive algorithm was proposed which was prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication was high.Furthermore,we proposed a new variable length sliding window base-3 wr NAF scalar multiplication algorithm which can reduce the cost of tripling points needed in kP computation.

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What this paper is about

The arithmetic on supersingular and non-supersingular elliptic curve over GF(3m) were researched,and computational formulas of point addition,2P,3P and 3kP in affine coordinate were given and confirmed.Based on these,a new 3kP recursive algorithm was proposed which was prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication was high.Furthermore,we proposed a new variable length sliding window base-3 wr NAF scalar multiplication algorithm which can reduce the cost of tripling points needed in kP computation.

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Available abstract

The arithmetic on supersingular and non-supersingular elliptic curve over GF(3m) were researched,and computational formulas of point addition,2P,3P and 3kP in affine coordinate were given and confirmed.Based on these,a new 3kP recursive algorithm was proposed which was prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication was high.Furthermore,we proposed a new variable length sliding window base-3 wr NAF scalar multiplication algorithm which can reduce the cost of tripling points needed in kP computation.

Key concepts: Scalar multiplication, Tripling-oriented Doche–Icart–Kohel curve, Elliptic curve, Elliptic curve point multiplication, Affine transformation, Computer science, Computation, Arithmetic

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