On arithmetical algorithms over finite fields
Journal of Combinatorial Theory Series A
Fast construction of irreducible polynomials over finite fields
Journal of Symbolic Computation
Arithmetic and factorization of polynomial over F2 (extended abstract)
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Finite fields
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
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
Tellegen's principle into practice
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
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 fourier transform algorithms with applications
Fast fourier transform algorithms with applications
Fast decomposition of polynomials with known Galois group
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Faster multiplication in GF(2)[x]
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
transalpyne: a language for automatic transposition
ACM Communications in Computer Algebra
transalpyne: a language for automatic transposition
ACM Communications in Computer Algebra
Fast arithmetics in Artin-Schreier towers over finite fields
Journal of Symbolic Computation
Algorithms for the universal decomposition algebra
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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An Artin-Schreier tower over the finite field Fp is a tower of field extensions generated by polynomials of the form Xp-X-α. 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.