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This paper presents efficient formulas to compute Miller doubling and Miller addition utilizing degree-3 twists on curves with j-invariant 0 written in Hessian form. We give the formulas for both odd...
In this paper high-speed hardware architectures of point multiplication based on Montgomery ladder algorithm for binary Edwards and generalized Hessian curves in Gaussian normal basis are presented. C...
This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77M per bit for 256-bit variable-base single-scalar multiplication when curve...
In this article we present how we can use fast Fp2 multiplication to speed-up arithmetic on elliptic curves. We use parallel computations for multiplication in Fp2 which is not much slower than mult...
We describe a hashing function from the elements of the finite field $\F_q$ into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fiber...
In this paper, we present a new addition operation on Hessian curves with low cost. It can be applied to resist the side channel attacks for scalar multiplication, and also can be used to compute pr...

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