Gary Carter

Twisted Edwards Curves Revisited

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 wide range of applications. Notably, the new addition algorithm uses

Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes

8\mathrm{\textbf{M}}

New formulae for efficient elliptic curve arithmetic

for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use

Strengthening the Key Schedule of the AES

9\mathrm{\textbf{M}} + 1\mathrm{\textbf{S}}

Jacobi Quartic Curves Revisited

. It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to

Efficient Methods for Generating MARS-Like S-Boxes

2\mathrm{\textbf{M}}

Key Schedules of Iterative Block Ciphers

. This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

An exploration of affine group laws for elliptic curves

Recent advances are reported in the use of heuristic optimisation for the design of cryptographic mappings. The genetic algorithm (GA) is adapted for the design of regular substitution boxes (s-boxes) with relatively high nonlinearity and low autocorrelation. We discuss the selection of suitable GA parameters, and in particular we introduce an effective technique for breeding s-boxes. This assimilation operation, produces a new s-box which is a simple and natural compromise between the properties of two dissimilar parent s-boxes. Our results demonstrate that assimilation provides rapid convergence to good solutions. We present an analysis comparing the relative effectiveness of including a local optimisation procedure at various stages of the GA. Our results show that these algorithms find cryptographically strong s-boxes faster than exhaustive search.

The security of fixed versus random elliptic curves in cryptography

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobiquartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (9M+4S) and Hessian (8M+6S+1d) forms. We show that Hessian tripling costs 6M+4C+1d for Hessian curves defined over a field of characteristic 3. We discuss an alternative way of choosing the base point in successive squaring based scalar multiplication algorithms. Using this technique, we improve the latest mixed-addition formulae for Jacobi-intersection (10M+2S+1d), Hessian (5M+6S) and Edwards (9M+1S+ 1d+4a) forms. We discuss the significance of these optimizations for elliptic curve cryptography.

DESV-1: A Variation of the Data Encryption Standard (DES)

In this paper we present practical guidelines for designing secure block cipher key schedules. In particular we analyse the AES key schedule and discuss its security properties both from a theoretical viewpoint, and in relation to published attacks exploiting weaknesses in its key schedule. We then propose and analyse an efficient and more secure key schedule.