This paper introduces fast algorithms for performing group operations on twisted Edwards
curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a …

Abstract Modern Graphics Processing Units (GPU) have reached a dimension with respect
to performance and gate count exceeding conventional Central Processing Units (CPU) by …

This paper presents new speed records for arithmetic on a large family of elliptic curves with
cofactor 3: specifically, 8.77 M 8.77 M per bit for 256-bit variable-base single-scalar …

This paper considers a generalized form for Hessian curves. The family of generalized
Hessian curves covers more isomorphism classes of elliptic curves. Over a finite field F_q, it …

We propose a new unified point compression format for Edwards, Twisted Edwards and
Montgomery curves over large-characteristic fields, which effectively divides the curve's …

This paper reports record-setting performance for the elliptic-curve method of integer
factorization: for example, 926.11 curves/second for ECM stage 1 with B 1= 8192 for 280-bit …

In this thesis we use isogenies between ordinary elliptic curves for the construction of new
cryptographic schemes. The thesis is organized into an introductory chapter followed by …

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic
curves, y 2= dx 4+ 2 ax 2+ 1. With recent bandwidth-efficient proposals, the arithmetic on …

This paper sets new speed records for ECM, the elliptic-curve method of factorization, on
several different hardware platforms: GPUs (specifically the NVIDIA GTX), x86 CPUs with …

Elliptic curves are very often used in the cryptographic protocol design due to their memory
efficiency and useful features, such as the bilinear pairing support. However, in many …