Faster Software for Fast Endomorphisms

Families of fast elliptic curves from Q-curves

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the sameway asGallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducingQ-curves—curves over quadratic number fields without complex multiplication, butwith isogenies to their ...

Families of Fast Elliptic Curves from ℚ-curves

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducing Q-curves—curves over quadratic number fields without complex multiplication, but with isogenies to th...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms

As Koblitz curves were generalized to hyperelliptic Koblitz curves for faster point multiplication by Günter,et al [10], we extend the recent work of Gallant,et al [8] to hyperelliptic curves. So the extended method for speeding point multiplication applies to a much larger family of hyperelliptic curves over finite fields that have efficiently-computable endomorphisms. For this special family ...

Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms

The fundamental operation in elliptic curve cryptographic schemes is the multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves than previous such methods. For this s...