Arithmetic and geometric structures in cryptography
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We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...
The discrete logarithm problem (DLP) in finite fields of small characteristic recently enjoyed a dramatic series of breakthrough results and computational records, with its (heuristic) complexity dropping from subexponential to quasi-polynomial. While thes ...
Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algor ...
We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...
A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...
We present a Petrov-Galerkin reduced basis (RB) approximation for the parameterized Stokes equation. Our method, which relies on a reduced solution space and a parameter-dependent test space, is shown to be stable (in the sense of Babuska) and algebraicall ...
In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. U ...
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane g : X -> P-1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P-1). As a consequence, we prove t ...
We establish sharp upper and lower bounds for the number of rational points of bounded anticanonical height on a smooth bihomogeneous threefold defined over Q and of bidegree (1, 2). These bounds are in agreement with Manin's conjecture. ...
We propose a simple deterministic test for deciding whether or not a non-zero element a∈F2n or F3n is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...
