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Implementing the Thull-Yap algorithm for computing Euclidean remainder sequences

François Morain
ISSAC2022, Jul 2022, Villeneuve-d’Ascq, France
Conference papers hal-03572271v2
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Solvability by Radicals from an Algorithmic Point of View

Guillaume Hanrot , François Morain
[Research Report] RR-4109, INRIA. 2001
Reports inria-00072522v1
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Fast algorithms for computing isogenies between elliptic curves

Alin Bostan , Bruno Salvy , Francois Morain , Eric Schost
[Research Report] 2006, pp.28
Reports inria-00091441v1
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Improving NFS for the Discrete Logarithm Problem in Non-prime Finite Fields

Razvan Barbulescu , Pierrick Gaudry , Aurore Guillevic , François Morain
EUROCRYPT 2015, Proceedings, Part {I}, Apr 2015, Sofia, Bulgaria. pp.129-155, ⟨10.1007/978-3-662-46800-5_6⟩
Conference papers hal-01112879v2

Factoring Safe Semiprimes with a Single Quantum Query

Frédéric Grosshans , Thomas Lawson , Benjamin Smith , François Morain
Preprints, Working Papers, ... hal-01229587v1
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Building Carmichael numbers with a large number of prime factors and generalization to other numbers

D. Guillaume , François Morain
[Research Report] RR-1741, INRIA. 1992
Reports inria-00076980v1

Algorithms for computing isogenies between elliptic curves

Reynald Lercier , François Morain
Computational Perspectives on Number Theory, 1995, Chicago, United States. pp.77-96
Conference papers hal-01102041v1
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Computing discrete logarithms in $GF(p^6)$

Laurent Grémy , Aurore Guillevic , François Morain , Emmanuel Thomé
Selected Areas in Cryptography – SAC 2017, Aug 2017, Ottawa, Canada. pp.85-105, ⟨10.1007/978-3-319-72565-9_5⟩
Conference papers hal-01624662v1

Computing isogenies between elliptic curves over $GF(p^n)$ using Couveignes's algorithm

Reynald Lercier , François Morain
Mathematics of Computation, 2000, 69 (229), pp.351-370. ⟨10.1090/S0025-5718-99-01081-9⟩
Journal articles hal-01102025v1
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Speeding up the discrete log computation on curves with automorphisms

Iwan Duursma , Pierrick Gaudry , François Morain
Asiacrypt, 1999, Singapour, Singapore. pp.103-121
Conference papers inria-00511639v1
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Discrete Logarithms

Aurore Guillevic , François Morain
Nadia El Mrabet; Marc Joye. Guide to pairing-based cryptography, CRC Press - Taylor and Francis Group, pp.42, 2016, 9781498729505
Book sections hal-01420485v2
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Discrete logarithm computations over finite fields using Reed-Solomon codes

Daniel Augot , François Morain
Preprints, Working Papers, ... hal-00672050v1
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Implementing the asymptotically fast version of the elliptic curve primality proving algorithm

François Morain
Preprints, Working Papers, ... hal-00004136v2
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BigNum : un module portable et efficace pour une arithmetique a precision arbitraire

Jean-Claude Herve , François Morain , David Salesin , Bernard Paul Serpette , Jean Vuillemin , et al.
[Rapport de recherche] RR-1016, INRIA. 1989
Reports inria-00075542v1

Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances

Reynald Lercier , François Morain
EUROCRYPT '95, May 1995, Saint-Malo, France. ⟨10.1007/3-540-49264-X_7⟩
Conference papers hal-01102046v1
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Breaking DLP in $GF(p^5)$ using 3-dimensional sieving

Laurent Grémy , Aurore Guillevic , François Morain
Preprints, Working Papers, ... hal-01568373v1
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Deterministic factoring with oracles

François Morain , Guénaël Renault , Benjamin Smith
Applicable Algebra in Engineering, Communication and Computing, 2021, ⟨10.1007/s00200-021-00521-8⟩
Journal articles hal-01715832v2

Building curves with arbitrary small MOV degree over finite prime fields

Régis Dupont , Andreas Enge , François Morain
Journal of Cryptology, 2005, 18 (2), pp.79-89
Journal articles inria-00386299v1
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Improvements to the number field sieve for non-prime finite fields

Razvan Barbulescu , Pierrick Gaudry , Aurore Guillevic , François Morain
Preprints, Working Papers, ... hal-01052449v5
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Computing cardinalities of Q-curve reductions over finite fields

François Morain , Charlotte Scribot , Benjamin Smith
LMS Journal of Computation and Mathematics, 2016, 19 (A), pp.15. ⟨10.1112/S1461157016000267⟩
Journal articles hal-01320388v3
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Modular curves over number fields and ECM

François Morain
Research in Number Theory, 2022
Journal articles hal-03606355v2
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Using the Charlap-Coley-Robbins polynomials for computing isogenies

François Morain
Preprints, Working Papers, ... hal-04009243v1

Factorization of a 512-bit RSA Modulus

Stefania Cavallar , Bruce Dodson , Arjen K. Lenstra , Walter Lioen , Peter L. Montgomery , et al.
International Conference on the Theory and Application of Cryptographic Techniques - EUROCRYPT 2000, May 2000, Bruges, Belgium. pp.1-18, ⟨10.1007/3-540-45539-6_1⟩
Conference papers inria-00099117v1
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Some factors of numbers of the form $b^n ± 1$ found using ECM with new classes of curves

François Morain
Preprints, Working Papers, ... hal-03437714v2
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Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts

Preda Mihailescu , François Morain , Eric Schost
Other publications inria-00130142v1

Solvability by radicals from an algorithmic point of view

Guillaume Hanrot , François Morain
International Symposium on Symbolic and Algebraic Computation - ISSAC'2001, 2001, London, Ontario, Canada, 18 p
Conference papers inria-00100542v1
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Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm

Pierrick Gaudry , François Morain
ISSAC '06: Proceedings of the 2006 international symposium on symbolic and algebraic computation, Jul 2006, Genoa, Italy, pp.109 - 115, ⟨10.1145/1145768.1145791⟩
Conference papers inria-00001009v1
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Solving discrete logarithms on a 170-bit MNT curve by pairing reduction

Aurore Guillevic , François Morain , Emmanuel Thomé
Selected Areas in Cryptography -- SAC 2016, Aug 2016, St. Johns, Newfoundland, Canada. pp.559-578, ⟨10.1007/978-3-319-69453-5_30⟩
Conference papers hal-01320496v2
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Computing the Charlap-Coley-Robbins modular polynomials

François Morain
Preprints, Working Papers, ... hal-03980413v1
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Edwards curves and CM curves

François Morain
Preprints, Working Papers, ... inria-00375427v1