Abstract
This paper introduces the Frobenius endomorphism on the the binary Edwards elliptic curves proposed by Bernstein, Lange and Farashahi in 2008 and by Diao and Lubicz (2010). To speed up the scalar multiplication on binary Edwards curves, we use the GLV method combined with the Frobenius endomorphism over the curve.
Highlights
This paper introduces the Frobenius endomorphism on the the binary Edwards elliptic curves proposed by Bernstein, Lange and Farashahi in 2008 and by Diao and Lubicz (2010)
To speed up the scalar multiplication on binary Edwards curves, we use the GLV method combined with the Frobenius endomorphism over the curve
We introduce the Frobenius endomorphism for the Edwards model proposed by Diao and Lubicz (2010)
Summary
Edwards introduced a new elliptic curve model. This model, called Edwards curves later, gain more interest and is widely investigated during the last six years. We defined and study the Frobenius endomorphism over the Edwards elliptic curves model on a field of characteristic 2. It’s well known that such an endomorphism can be used to derive fast algorithm to perform scalar multiplication over elliptic curves. We recall some basic notions on Edwards curves and Frobenius endomorphism. We give the expression of the group law and the birational equivalence between elliptic curves in Edwards model and elliptic curves in Weierstrass model when considering a finite field of characteristic 2.
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