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Arithmetic and geometric structures in cryptography

Publications associées (192)

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On the security of 1024-bit RSA and 160-bit elliptic curve cryptography

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Marcelo Kaihara

Meeting the requirements of NIST’s new cryptographic standard ‘Suite B Cryptography’ means phasing out usage of 1024-bit RSA and 160-bit Elliptic Curve Cryptography (ECC) by the year 2010. This write-up comments on the vulnerability of these systems to an ...

2009

Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynom ...

2009

Explicit construction of self-dual integral normal bases for the square-root of the inverse different

Erik Jarl Pickett

Let K be a finite extension of Q(p), let L/K be a finite abelian Galois extension of odd degree and let D-L be the valuation ring of L. We define A(L/K) to be the unique fractional D-L-ideal with square equal to the inverse different of L/K. For p an odd p ...

2009

Conformational analysis of nucleic acids revisited: Curves

John Maddocks, Daiva Petkeviciute

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algori ...

Oxford University Press2009

Foncteurs de Mackey projectifs

This work deals with the study of projective Mackey functors. Mackey functors are algebraic structures with operations which behave like induction, restriction and conjugation in group representation theory. These objects have properties which generalize m ...

EPFL2008

Applications of a theorem of Singerman about Fuchsian groups

Hugo Parlier

Assume that we have a (compact) Riemann surface S, of genus greater than 2, with S = D/Gamma, where D is the complex unit disc and Gamma is a surface Fuchsian group. Let us further consider that S has an automorphism group G in such a way that the orbifold ...

2008

On the essential dimension of cyclic p-groups

Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have edℚ(ℤ/8ℤ)=4, a result which ...

Springer-Verlag2008

Adaptive Filters

Ali H. Sayed

Adaptive filtering is a topic of immense practical and theoretical value, having applications in areas ranging from digital and wireless communications to biomedical systems. This book enables readers to gain a gradual and solid introduction to the subject ...

John Wiley & Sons2008

On Hermitian Pfister Forms

Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamen ...

2008

Ate Pairing on Hyperelliptic Curves

Robert Granger

In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up t ...

Springer-Verlag Berlin Heidelberg2007