Maozhi Xu

The Weight Distributions of Cyclic Codes and Elliptic Curves

Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications. The determination of the weight distributions of such codes is an open problem. Generally, the weight distributions of cyclic codes are difficult to determine. Utilizing a class of elliptic curves, this paper determines the weight distributions of dual codes of q-ary cyclic codes with two zeros for a few more cases, where q is an odd prime power.

Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0

The Gallant–Lambert–Vanstone (GLV) method is a very efficient technique for accelerating point multiplication on elliptic curves with efficiently computable endomorphisms. Galbraith et al. (J Cryptol 24(3):446–469, 2011) showed that point multiplication exploiting the 2-dimensional GLV method on a large class of curves over

A note on cyclic codes from APN functions

{\mathbb{F}_{p^2}}

Constructing vectorial Boolean functions with high algebraic immunity based on group decomposition

was faster than the standard method on general elliptic curves over

A class of elliptic curves in edwards form

{\mathbb{F}_{p}}

Security analysis of a TESLA-based homomorphic MAC scheme for authentication in P2P live streaming system

, and left as an open problem to study the case of 4-dimensional GLV on special curves (e.g., j (E) = 0) over