We apply the Cocks-Pinch method to obtain pairing-friendly composite order groups with prescribed embedding degree associated to ordinary elliptic curves, and we show that new security issues arise in the composite order setting.

This study investigates geometrical non-linear analysis of composite circular cylindrical shells under external pressure over part of their surfaces and also shells subjected to combined axial compression and triangular external pressure. Donnell non-linear shell theory along with first order shear deformation theory (FOSD) are adopted in the analysis. In the case of combined axial compression ...

We compare the method of Weil descent for solving the ECDLP, over extensions fields of composite degree in characteristic two, against the standard method of parallelised Pollard rho. We give details of a theoretical and practical comparison and then use this to analyse the difficulty of actually solving the ECDLP for curves of the size needed in practical cryptographic systems. We show that co...

The Elliptic Curve Discrete Logarithm Problem(ECDLP) is known to be an exponential time problem except the cases of smooth curves, supersingular curves and anomalous curves. Recently, several new methods to solve ECDLP on a prime eld were proposed. All of them try to solve ECDLP on a prime eld by lifting a given elliptic curve to low rank elliptic curves de ned over the rationals. In this exten...

| Damage detection using guided Lamb waves is an important tool in Structural health Monitoring. In this paper, we outline a method of obtaining Lamb wave modes in composite structures using two dimensional Spectral Finite Elements. Using this approach, Lamb wave dispersion curves are obtained for laminated composite structures with different fibre orientation. These propagating Lamb wave modes...

In a series of papers, D. Gordon and C. Pomerance demonstrated that pseudoprimes on elliptic curves behave in many ways very similar to pseudoprimes related to Lucas sequences. In this paper we give an answer to a challenge that was posted by D. Gordon in 1989. The challenge was to either prove that a certain composite N ≡ 1 mod 4 did not exist, or to explicitly calculate such a number. In this...

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...