On arithmetical algorithms over finite fields
Journal of Combinatorial Theory Series A
Fast construction of irreducible polynomials over finite fields
Journal of Symbolic Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Modern computer algebra
Efficient computation of minimal polynomials in algebraic extensions of finite fields
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Challenges of symbolic computation: my favorite open problems
Journal of Symbolic Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Isomorphisms between Artin-Schreier towers
Mathematics of Computation
Computing l-Isogenies Using the p-Torsion
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Polynomial factorization over F2
Mathematics of Computation
Tellegen's principle into practice
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
An Elliptic Curve Trapdoor System
Journal of Cryptology
Change of order for bivariate triangular sets
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast Modular Composition in any Characteristic
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Fast fourier transform algorithms with applications
Fast fourier transform algorithms with applications
Fast arithmetics in artin-schreier towers over finite fields
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Faster multiplication in GF(2)[x]
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
A fast algorithm for the Fourier transform over finite fields and its VLSI implementation
IEEE Journal on Selected Areas in Communications
Fast algorithms for l-adic towers over finite fields
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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An Artin-Schreier tower over the finite field F"p is a tower of field extensions generated by polynomials of the form X^p-X-@a. Following Cantor and Couveignes, we give algorithms with quasi-linear time complexity for arithmetic operations in such towers. As an application, we present an implementation of Couveignes' algorithm for computing isogenies between elliptic curves using the p-torsion.