Edlyn Teske

A Taxonomy of Pairing-Friendly Elliptic Curves

Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairing-based cryptographic systems. Such “pairing-friendly” curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses all of the constructions of pairing-friendly elliptic curves currently existing in the literature. We also include new constructions of pairing-friendly curves that improve on the previously known constructions for certain embedding degrees. Finally, for all embedding degrees up to 50, we provide recommendations as to which pairing-friendly curves to choose to best satisfy a variety of performance and security requirements.

On random walks for Pollard's RHO method

We consider Pollards rho method for discrete logarithm computation. Usually, in the analysis of its running time the assumption is made that a random walk in the underlying group is simulated. We show that this assumption does not hold for the walk originally suggested by Pollard: its performance is worse than in the random case. We study alternative walks that can be efficiently applied to compute discrete logarithms. We introduce a class of walks that lead to the same performance as expected in the random case. We show that this holds for arbitrarily large prime group orders, thus making Pollards rho method for prime group orders about 20% faster than before.

Analysis of the Xedni Calculus Attack

AbstractThe xedni calculus attack on the elliptic curve discrete logarithm problem (ECDLP) involves lifting points from the finite field

On Some Attacks on Multi-prime RSA

{\mathbb{F}}_p

A space efficient algorithm for group structure computation

to the rational numbers

Explict bounds and heuristics on class numbers in hyperelliptic function fields

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