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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... -
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... -
Self-dual skew codes and factorization of skew polynomials
International audience -
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... -
Algebraic varieties and function fields over a finite field
Nous nous intéressons au nombre de points rationnels des variétés algébriques projectives sur un corps fini. Nous déterminons notamment la fonction zêta (et plus...
