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Representations of polynomials, algorithms and lower bounds
Computational complexity is the study of the resources — time, memory, …— needed to algorithmically solve a problem. Within these settings, algebraic complexity theory... -
Algorithmic Number Theory and Applications to the Cryptanalysis of Cryptograp...
The integer factorization and discrete logarithm problems are cornerstones of several public-key cryptography algorithms. In the realm of algorithms targeted at... -
A History of Galois fields
This paper stresses a specific line of development of the notion of finite field, from Évariste Galois's 1830 ''Note sur la théorie des nombres,'' and Camille Jordan's... -
Selecting polynomials for the Function Field Sieve
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Some contributions at the study of Laurent series with coefficients in a fini...
This thesis looks at the interplay of three important domains: combinatorics on words, theory of finite-state automata and number theory. More precisely, we show how... -
Modular Composition Modulo Triangular Sets and Applications
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On the tensor rank of multiplication in any extension of $\F_2$
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Fast algorithms for computing isogenies between elliptic curves
We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm... -
Algorithms of discrete logarithm in finite fields
In this thesis we study at length the discrete logarithm problem in finite fields. In the first part, we focus on the notion of smoothness and on ECM, the fastest... -
On some questions related to the Gauss conjecture for function fields
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Arithmetic, Geometry and Coding Theory
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Parametrizing the moduli space of curves and applications to smooth plane qua...
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On hyperquadratic continued fractions in power series fields over a finite field
The first part of this note is a short introduction on continued fraction expansions for certain algebraic power series. In the last part, as an illustration, we... -
Hyperquadratic continued fractions over a finite field of odd characteristic ...
International audience
