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Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Publications associées (42)

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On isogeny classes of Edwards curves over finite fields

Robert Granger

We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is isogeno ...

Elsevier2012

Compute-and-Forward: Harnessing Interference Through Structured Codes

Michael Christoph Gastpar

Abstract—Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea ...

Institute of Electrical and Electronics Engineers2011

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

We focus on a specific class of curves that can be parametrized using a finite number of variables in two dimensions. The corresponding indicator plane, which is a binary image, has infinite bandwidth and can not be sampled and perfectly reconstructed with ...

2011

Efficient SIMD Arithmetic Modulo a Mersenne Number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementa ...

IEEE2011

Efficient SIMD arithmetic modulo a Mersenne number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...

IEEE Computer Soc Press2011

Sur la méthode de Buser-Silhol pour l'uniformisation des surfaces de Riemann hyperelliptiques

Grégoire Aubry

The Uniformization Theorem due to Koebe and Poincaré implies that every compact Riemann surface of genus greater or equal to 2 can be endowed with a metric of constant curvature – 1. On the other hand, a compact Riemann surface is a complex algebraic curve ...

EPFL2010

On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

Robert Granger, Martijn Stam

The value of the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using this simple observation, we transfer techniques recently developed for torus-based cryptography to pairing-based cryptography, r ...

2006

On Small Degree Extension Fields in Cryptology

Robert Granger

This thesis studies the implications of using public key cryptographic primitives that are based in, or map to, the multiplicative group of finite fields with small extension degree. A central observation is that the multiplicative group of extension field ...

PhD dissertation, University of Bristol, UK, February 20062006

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Michaël Unser, Thierry Blu

We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accoun ...

IEEE2006

Finite fields And Error-Correcting Codes

Nelly Burrin

After introducing the concept of finite fields and their properties, we look algebraic constructions of error correcting codes. ...

2006