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Faugère, Jean-Charles

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Author ID: faugere.jean-charles Recent zbMATH articles by "Faugère, Jean-Charles"
Published as: Faugère, Jean-Charles; Faugere, Jean-Charles; Faugère, Jean Charles; Faugère, J. C.
Documents Indexed: 96 Publications since 1993, including 2 Books
all top 5

Co-Authors

4 single-authored
40 Perret, Ludovic
8 Renault, Guénaël
8 Spaenlehauer, Pierre-Jean
7 Albrecht, Martin R.
7 Safey El Din, Mohab
6 Berthomieu, Jérémy
6 Bettale, Luk
5 Bender, Matías R.
5 Tsigaridas, Elias P.
4 Otmani, Ayoub
4 Svartz, Jules
4 Tillich, Jean-Pierre
3 Bardet, Magali
3 Basiri, Abdolali
3 Boyer, Brice
3 Cid, Carlos Frederico
3 de Portzamparc, Frédéric
3 Fitzpatrick, Robert
3 Huot, Louise
3 Joux, Antoine
3 Verron, Thibaut
2 Augot, Daniel
2 Cazals, Frédéric
2 Coron, Jean-Sébastien
2 Eder, Christian
2 Enge, Andreas
2 Farshim, Pooya
2 Gaudry, Pierrick
2 Gligoroski, Danilo
2 Gürel, Nicolas
2 Liang, Ye
2 Mou, Chenqi
2 Pouget, Marc
2 Rouillier, Fabrice
2 Salvy, Bruno
2 Zeitoun, Rina
1 Améndola, Carlos
1 Ars, Gwénolé
1 Beullens, Ward
1 Bi, Jingguo
1 Bonnard, Bernard
1 Bouillaguet, Charles
1 Bourgeois, Gerald
1 Chakraborty, Olive
1 Dullien, Thomas
1 Fouque, Pierre-Alain
1 Gauthier-Umaña, Valérie
1 Gianni, Patrizia M.
1 Gomez-Perez, Domingo
1 Goyet, Christopher
1 Gutierrez, Jaime
1 Hering, Milena
1 Herold, Gottfried
1 Imai, Hideki
1 Jacquemard, Alain
1 Kawazoe, Mitsuru
1 Kotsireas, Ilias S.
1 Koussa, Eliane
1 Lachartre, Sylvian
1 Lazard, Daniel
1 Levy-dit-Vehel, Françoise
1 Lin, Dongdai
1 Loidl, Hans-Wolfgang
1 Lubicz, David
1 Macario-Rat, Gilles
1 Mantzaflaris, Angelos
1 Marinier, Raphaël
1 Martani, Fayssal
1 Monagan, Michael B.
1 Mora, Teo
1 Nguyen, Phong Q.
1 Ødegård, Rune Steinsmo
1 Patarin, Jacques
1 Pena, Marta Conde
1 Petit, Christophe
1 Phan, Jeff
1 Rahmany, Sajjad
1 Robert, Damien
1 Samardjiska, Simona
1 Sturmfels, Bernd
1 Sugita, Makoto
1 Thomae, Enrico
1 Todo, Yosuke
1 Treger, Joana
1 Vitse, Vanessa
1 von zur Gathen, Joachim
1 Wallet, Alexandre
1 Wang, Tianze
1 Xagawa, Keita

Publications by Year

Citations contained in zbMATH Open

78 Publications have been cited 920 times in 513 Documents Cited by Year
A new efficient algorithm for computing Gröbner bases \((F_4)\). Zbl 0930.68174
Faugère, Jean-Charles
194
1999
Efficient computation of zero-dimensional Gröbner bases by change of ordering. Zbl 0805.13007
Faugère, J. C.; Gianni, P.; Lazard, D.; Mora, T.
161
1993
A new efficient algorithm for computing Gröbner bases without reduction to zero \((F_5)\). Zbl 1072.68664
Faugère, Jean-Charles
120
2002
Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. Zbl 1122.94371
Faugère, Jean-Charles; Joux, Antoine
54
2003
FGb: a library for computing Gröbner bases. Zbl 1294.68156
Faugère, Jean-Charles
19
2010
On the complexity of the \(F_5\) Gröbner basis algorithm. Zbl 1328.68319
Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno
16
2015
Algebraic cryptanalysis of McEliece variants with compact keys. Zbl 1280.94051
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; Tillich, Jean-Pierre
16
2010
Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases. Zbl 1237.13052
Faugère, Jean-Charles; Rahmany, Sajjad
14
2009
A distinguisher for high-rate McEliece cryptosystems. Zbl 1364.94536
Faugère, Jean-Charles; Gauthier-Umaña, Valérie; Otmani, Ayoub; Perret, Ludovic; Tillich, Jean-Pierre
13
2013
Hybrid approach for solving multivariate systems over finite fields. Zbl 1183.94021
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
13
2009
Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Zbl 1307.13031
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
12
2013
Comparison between XL and Gröbner basis algorithms. Zbl 1094.94024
Ars, Gwénolé; Faugère, Jean-Charles; Imai, Hideki; Kawazoe, Mitsuru; Sugita, Makoto
11
2004
Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity. Zbl 1226.13017
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
11
2011
Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices. Zbl 1323.68596
Faugère, Jean-Charles; Mou, Chenqi
10
2011
Cryptanalysis of MinRank. Zbl 1183.94033
Faugère, Jean-Charles; Levy-dit-Vehel, Françoise; Perret, Ludovic
10
2008
Improving the complexity of index calculus algorithms in elliptic curves over binary fields. Zbl 1290.94070
Faugère, Jean-Charles; Perret, Ludovic; Petit, Christophe; Renault, Guénaël
10
2012
Sub-cubic change of ordering for Gröbner basis: a probabilistic approach. Zbl 1325.68277
Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël
9
2014
On the complexity of the BKW algorithm on LWE. Zbl 1331.94051
Albrecht, Martin R.; Cid, Carlos; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic
9
2015
Critical points and Gröbner bases: the unmixed case. Zbl 1308.68171
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
8
2012
Moment varieties of Gaussian mixtures. Zbl 1361.13017
Améndola, Carlos; Faugère, Jean-Charles; Sturmfels, Bernd
7
2016
Lazy modulus switching for the BKW algorithm on LWE. Zbl 1335.94025
Albrecht, Martin R.; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic
7
2014
A survey on signature-based algorithms for computing Gröbner bases. Zbl 1412.68306
Eder, Christian; Faugère, Jean-Charles
7
2017
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. Zbl 1321.68529
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
7
2010
Cryptanalysis of \(2r^-\) schemes. Zbl 1161.94397
Faugère, Jean-Charles; Perret, Ludovic
7
2006
Using symmetries in the index calculus for elliptic curves discrete logarithm. Zbl 1320.94063
Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël
7
2014
On the complexity of the generalized MinRank problem. Zbl 1302.13026
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
7
2013
On the complexity of solving quadratic Boolean systems. Zbl 1255.65090
Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno; Spaenlehauer, Pierre-Jean
7
2013
The arithmetic of Jacobian groups of superelliptic cubics. Zbl 1094.14049
Basiri, Abdolali; Enge, Andreas; Faugère, Jean-Charles; Gürel, Nicolas
6
2005
Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of \(N\) vortices in the plane. Zbl 1323.68597
Faugère, Jean-Charles; Svartz, Jules
6
2012
Implementing the arithmetic of \(C_{3,4}\) curves. Zbl 1148.14304
Basiri, Abdolali; Enge, Andreas; Faugère, Jean-Charles; Gürel, Nicolas
6
2004
Implicit factoring with shared most significant and middle bits. Zbl 1271.11117
Faugère, Jean-Charles; Marinier, Raphaël; Renault, Guénaël
6
2010
Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences. Zbl 1346.68269
Berthomieu, Jérémy; Boyer, Brice; Faugère, Jean-Charles
5
2015
On the complexity of computing Gröbner bases for quasi-homogeneous systems. Zbl 1360.68930
Faugère, Jean-Charles; Safey El Din, Mohab; Verron, Thibaut
5
2013
Gröbner bases of ideals invariant under a commutative group: the non-modular case. Zbl 1360.68931
Faugere, Jean-Charles; Svartz, Jules
5
2013
Finding all the solutions of cyclic 9 using Gröbner basis techniques. Zbl 1030.68112
Faugère, Jean-Charles
5
2001
Sparse FGLM algorithms. Zbl 1404.13031
Faugère, Jean-Charles; Mou, Chenqi
5
2017
Solving polynomial systems over finite fields: improved analysis of the hybrid approach. Zbl 1323.68583
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
5
2012
An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography. Zbl 1175.12004
Faugère, Jean-Charles; Perret, Ludovic
5
2009
Cryptanalysis of multivariate and odd-characteristic HFE variants. Zbl 1291.94058
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
5
2011
Structural cryptanalysis of McEliece schemes with compact keys. Zbl 1361.94039
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre
4
2016
On enumeration of polynomial equivalence classes and their application to MPKC. Zbl 1251.94033
Lin, Dongdai; Faugère, Jean-Charles; Perret, Ludovic; Wang, Tianze
4
2012
Polly cracker, revisited. Zbl 1227.94025
Albrecht, Martin R.; Farshim, Pooya; Faugère, Jean-Charles; Perret, Ludovic
4
2011
Symmetrized summation polynomials: using small order torsion points to speed up elliptic curve index calculus. Zbl 1326.94092
Faugère, Jean-Charles; Huot, Louise; Joux, Antoine; Renault, Guénaël; Vitse, Vanessa
4
2014
Decomposition of generic multivariate polynomials. Zbl 1321.68530
Faugère, Jean-Charles; von zur Gathen, Joachim; Perret, Ludovic
4
2010
Artificial discontinuities of single-parametric Gröbner bases. Zbl 1211.13019
Faugère, Jean-Charles; Liang, Ye
4
2011
Practical cryptanalysis of the identification scheme based on the isomorphism of polynomial with one secret problem. Zbl 1291.94062
Bouillaguet, Charles; Faugère, Jean-Charles; Fouque, Pierre-Alain; Perret, Ludovic
4
2011
Polynomial equivalence problems: algorithmic and theoretical aspects. Zbl 1140.94337
Faugère, Jean-Charles; Perret, Ludovic
4
2006
A superfast randomized algorithm to decompose binary forms. Zbl 1361.68300
Bender, Matías R.; Faugère, Jean-Charles; Perret, Ludovic; Tsigaridas, Elias
3
2016
Computing modular correspondences for abelian varieties. Zbl 1247.14046
Faugère, Jean-Charles; Lubicz, David; Robert, Damien
3
2011
The implicit structure of ridges of a smooth parametric surface. Zbl 1112.65013
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
3
2006
On the decoding of binary cyclic codes with the Newton identities. Zbl 1174.94023
Augot, Daniel; Bardet, Magali; Faugère, Jean-Charles
3
2009
Algebraic cryptanalysis of curry and flurry using correlated messages. Zbl 1281.94023
Faugère, Jean-Charles; Perret, Ludovic
3
2010
Folding alternant and Goppa codes with non-trivial automorphism groups. Zbl 1359.94876
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre
2
2016
Sparse Gröbner bases: the unmixed case. Zbl 1325.68278
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean; Svartz, Jules
2
2014
Attacking (EC)DSA given only an implicit hint. Zbl 1327.94043
Faugère, Jean-Charles; Goyet, Christopher; Renault, Guénaël
2
2013
Guessing linear recurrence relations of sequence tuplesand P-recursive sequences with linear algebra. Zbl 1362.13026
Berthomieu, Jérémy; Faugère, Jean-Charles
2
2016
Determinantal sets, singularities and application to optimal control in medical imagery. Zbl 1362.13031
Bonnard, Bernard; Faugère, Jean-Charles; Jacquemard, Alain; Safey El Din, Mohab; Verron, Thibaut
2
2016
GBLA: Gröbner basis linear algebra package. Zbl 1361.13014
Boyer, Brice; Eder, Christian; Faugère, Jean-Charles; Lachartre, Sylvian; Martani, Fayssal
2
2016
Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences. Zbl 1453.68222
Berthomieu, Jérémy; Boyer, Brice; Faugère, Jean-Charles
2
2017
Polynomial-time algorithms for quadratic isomorphism of polynomials: the regular case. Zbl 1338.94064
Berthomieu, Jérémy; Faugère, Jean-Charles; Perret, Ludovic
2
2015
Practical cryptanalysis of a public-key encryption scheme based on new multivariate quadratic assumptions. Zbl 1288.94049
Albrecht, Martin R.; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic; Todo, Yosuke; Xagawa, Keita
2
2014
On the relation between the MXL family of algorithms and Gröbner basis algorithms. Zbl 1237.13051
Albrecht, Martin R.; Cid, Carlos; Faugère, Jean-Charles; Perret, Ludovic
2
2012
Changing the ordering of Gröbner bases with LLL: case of two variables. Zbl 1072.68645
Basiri, Abdolali; Faugère, Jean-Charles
2
2003
Cryptanalysis of the TRMS signature scheme of PKC’05. Zbl 1142.94333
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
2
2008
Algebraic cryptanalysis of the PKC ’2009 algebraic surface cryptosystem. Zbl 1271.94018
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean
2
2010
Pivoting in extended rings for computing approximate Gröbner bases. Zbl 1252.68356
Faugère, Jean-Charles; Liang, Ye
2
2011
Ridges and umbilics of polynomial parametric surfaces. Zbl 1167.53004
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
2
2008
High order derivatives and decomposition of multivariate polynomials. Zbl 1237.68255
Faugère, Jean-Charles; Perret, Ludovic
2
2009
Cryptanalysis of the hidden matrix cryptosystem. Zbl 1285.94059
Faugère, Jean-Charles; Joux, Antoine; Perret, Ludovic; Treger, Joana
2
2010
Factoring \(N=p^rq^s\) for large \(r\) and \(s\). Zbl 1334.11091
Coron, Jean-Sébastien; Faugère, Jean-Charles; Renault, Guénaël; Zeitoun, Rina
1
2016
Polly cracker, revisited. Zbl 1405.94039
Albrecht, Martin R.; Faugère, Jean-Charles; Farshim, Pooya; Herold, Gottfried; Perret, Ludovic
1
2016
Computing small certificates of inconsistency of quadratic fewnomial systems. Zbl 1361.13016
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean; Svartz, Jules
1
2016
Rounding and chaining LLL: finding faster small roots of univariate polynomial congruences. Zbl 1335.11102
Bi, Jingguo; Coron, Jean-Sébastien; Faugère, Jean-Charles; Nguyen, Phong Q.; Renault, Guénaël; Zeitoun, Rina
1
2014
A polynomial-time key-recovery attack on MQQ cryptosystems. Zbl 1345.94059
Faugère, Jean-Charles; Gligoroski, Danilo; Perret, Ludovic; Samardjiska, Simona; Thomae, Enrico
1
2015
Algebraic cryptanalysis of a quantum money scheme: the noise-free case. Zbl 1345.94084
Pena, Marta Conde; Faugère, Jean-Charles; Perret, Ludovic
1
2015
Symmetry theorems for the Newtonian 4- and 5-body problems with equal masses. Zbl 1087.70504
Faugère, Jean-Charles; Kotsireas, Ilias
1
1999
Algebraic attack against variants of McEliece with Goppa polynomial of a special form. Zbl 1306.94051
Faugère, Jean-Charles; Perret, Ludovic; de Portzamparc, Frédéric
1
2014
Algebraic precomputations in differential and integral cryptanalysis. Zbl 1295.94006
Albrecht, Martin; Cid, Carlos; Dullien, Thomas; Faugère, Jean-Charles; Perret, Ludovic
1
2011
A survey on signature-based algorithms for computing Gröbner bases. Zbl 1412.68306
Eder, Christian; Faugère, Jean-Charles
7
2017
Sparse FGLM algorithms. Zbl 1404.13031
Faugère, Jean-Charles; Mou, Chenqi
5
2017
Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences. Zbl 1453.68222
Berthomieu, Jérémy; Boyer, Brice; Faugère, Jean-Charles
2
2017
Moment varieties of Gaussian mixtures. Zbl 1361.13017
Améndola, Carlos; Faugère, Jean-Charles; Sturmfels, Bernd
7
2016
Structural cryptanalysis of McEliece schemes with compact keys. Zbl 1361.94039
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre
4
2016
A superfast randomized algorithm to decompose binary forms. Zbl 1361.68300
Bender, Matías R.; Faugère, Jean-Charles; Perret, Ludovic; Tsigaridas, Elias
3
2016
Folding alternant and Goppa codes with non-trivial automorphism groups. Zbl 1359.94876
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; de Portzamparc, Frédéric; Tillich, Jean-Pierre
2
2016
Guessing linear recurrence relations of sequence tuplesand P-recursive sequences with linear algebra. Zbl 1362.13026
Berthomieu, Jérémy; Faugère, Jean-Charles
2
2016
Determinantal sets, singularities and application to optimal control in medical imagery. Zbl 1362.13031
Bonnard, Bernard; Faugère, Jean-Charles; Jacquemard, Alain; Safey El Din, Mohab; Verron, Thibaut
2
2016
GBLA: Gröbner basis linear algebra package. Zbl 1361.13014
Boyer, Brice; Eder, Christian; Faugère, Jean-Charles; Lachartre, Sylvian; Martani, Fayssal
2
2016
Factoring \(N=p^rq^s\) for large \(r\) and \(s\). Zbl 1334.11091
Coron, Jean-Sébastien; Faugère, Jean-Charles; Renault, Guénaël; Zeitoun, Rina
1
2016
Polly cracker, revisited. Zbl 1405.94039
Albrecht, Martin R.; Faugère, Jean-Charles; Farshim, Pooya; Herold, Gottfried; Perret, Ludovic
1
2016
Computing small certificates of inconsistency of quadratic fewnomial systems. Zbl 1361.13016
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean; Svartz, Jules
1
2016
On the complexity of the \(F_5\) Gröbner basis algorithm. Zbl 1328.68319
Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno
16
2015
On the complexity of the BKW algorithm on LWE. Zbl 1331.94051
Albrecht, Martin R.; Cid, Carlos; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic
9
2015
Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences. Zbl 1346.68269
Berthomieu, Jérémy; Boyer, Brice; Faugère, Jean-Charles
5
2015
Polynomial-time algorithms for quadratic isomorphism of polynomials: the regular case. Zbl 1338.94064
Berthomieu, Jérémy; Faugère, Jean-Charles; Perret, Ludovic
2
2015
A polynomial-time key-recovery attack on MQQ cryptosystems. Zbl 1345.94059
Faugère, Jean-Charles; Gligoroski, Danilo; Perret, Ludovic; Samardjiska, Simona; Thomae, Enrico
1
2015
Algebraic cryptanalysis of a quantum money scheme: the noise-free case. Zbl 1345.94084
Pena, Marta Conde; Faugère, Jean-Charles; Perret, Ludovic
1
2015
Sub-cubic change of ordering for Gröbner basis: a probabilistic approach. Zbl 1325.68277
Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël
9
2014
Lazy modulus switching for the BKW algorithm on LWE. Zbl 1335.94025
Albrecht, Martin R.; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic
7
2014
Using symmetries in the index calculus for elliptic curves discrete logarithm. Zbl 1320.94063
Faugère, Jean-Charles; Gaudry, Pierrick; Huot, Louise; Renault, Guénaël
7
2014
Symmetrized summation polynomials: using small order torsion points to speed up elliptic curve index calculus. Zbl 1326.94092
Faugère, Jean-Charles; Huot, Louise; Joux, Antoine; Renault, Guénaël; Vitse, Vanessa
4
2014
Sparse Gröbner bases: the unmixed case. Zbl 1325.68278
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean; Svartz, Jules
2
2014
Practical cryptanalysis of a public-key encryption scheme based on new multivariate quadratic assumptions. Zbl 1288.94049
Albrecht, Martin R.; Faugère, Jean-Charles; Fitzpatrick, Robert; Perret, Ludovic; Todo, Yosuke; Xagawa, Keita
2
2014
Rounding and chaining LLL: finding faster small roots of univariate polynomial congruences. Zbl 1335.11102
Bi, Jingguo; Coron, Jean-Sébastien; Faugère, Jean-Charles; Nguyen, Phong Q.; Renault, Guénaël; Zeitoun, Rina
1
2014
Algebraic attack against variants of McEliece with Goppa polynomial of a special form. Zbl 1306.94051
Faugère, Jean-Charles; Perret, Ludovic; de Portzamparc, Frédéric
1
2014
A distinguisher for high-rate McEliece cryptosystems. Zbl 1364.94536
Faugère, Jean-Charles; Gauthier-Umaña, Valérie; Otmani, Ayoub; Perret, Ludovic; Tillich, Jean-Pierre
13
2013
Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Zbl 1307.13031
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
12
2013
On the complexity of the generalized MinRank problem. Zbl 1302.13026
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
7
2013
On the complexity of solving quadratic Boolean systems. Zbl 1255.65090
Bardet, Magali; Faugère, Jean-Charles; Salvy, Bruno; Spaenlehauer, Pierre-Jean
7
2013
On the complexity of computing Gröbner bases for quasi-homogeneous systems. Zbl 1360.68930
Faugère, Jean-Charles; Safey El Din, Mohab; Verron, Thibaut
5
2013
Gröbner bases of ideals invariant under a commutative group: the non-modular case. Zbl 1360.68931
Faugere, Jean-Charles; Svartz, Jules
5
2013
Attacking (EC)DSA given only an implicit hint. Zbl 1327.94043
Faugère, Jean-Charles; Goyet, Christopher; Renault, Guénaël
2
2013
Improving the complexity of index calculus algorithms in elliptic curves over binary fields. Zbl 1290.94070
Faugère, Jean-Charles; Perret, Ludovic; Petit, Christophe; Renault, Guénaël
10
2012
Critical points and Gröbner bases: the unmixed case. Zbl 1308.68171
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
8
2012
Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of \(N\) vortices in the plane. Zbl 1323.68597
Faugère, Jean-Charles; Svartz, Jules
6
2012
Solving polynomial systems over finite fields: improved analysis of the hybrid approach. Zbl 1323.68583
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
5
2012
On enumeration of polynomial equivalence classes and their application to MPKC. Zbl 1251.94033
Lin, Dongdai; Faugère, Jean-Charles; Perret, Ludovic; Wang, Tianze
4
2012
On the relation between the MXL family of algorithms and Gröbner basis algorithms. Zbl 1237.13051
Albrecht, Martin R.; Cid, Carlos; Faugère, Jean-Charles; Perret, Ludovic
2
2012
Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity. Zbl 1226.13017
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
11
2011
Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices. Zbl 1323.68596
Faugère, Jean-Charles; Mou, Chenqi
10
2011
Cryptanalysis of multivariate and odd-characteristic HFE variants. Zbl 1291.94058
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
5
2011
Polly cracker, revisited. Zbl 1227.94025
Albrecht, Martin R.; Farshim, Pooya; Faugère, Jean-Charles; Perret, Ludovic
4
2011
Artificial discontinuities of single-parametric Gröbner bases. Zbl 1211.13019
Faugère, Jean-Charles; Liang, Ye
4
2011
Practical cryptanalysis of the identification scheme based on the isomorphism of polynomial with one secret problem. Zbl 1291.94062
Bouillaguet, Charles; Faugère, Jean-Charles; Fouque, Pierre-Alain; Perret, Ludovic
4
2011
Computing modular correspondences for abelian varieties. Zbl 1247.14046
Faugère, Jean-Charles; Lubicz, David; Robert, Damien
3
2011
Pivoting in extended rings for computing approximate Gröbner bases. Zbl 1252.68356
Faugère, Jean-Charles; Liang, Ye
2
2011
Algebraic precomputations in differential and integral cryptanalysis. Zbl 1295.94006
Albrecht, Martin; Cid, Carlos; Dullien, Thomas; Faugère, Jean-Charles; Perret, Ludovic
1
2011
FGb: a library for computing Gröbner bases. Zbl 1294.68156
Faugère, Jean-Charles
19
2010
Algebraic cryptanalysis of McEliece variants with compact keys. Zbl 1280.94051
Faugère, Jean-Charles; Otmani, Ayoub; Perret, Ludovic; Tillich, Jean-Pierre
16
2010
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. Zbl 1321.68529
Faugère, Jean-Charles; El Din, Mohab Safey; Spaenlehauer, Pierre-Jean
7
2010
Implicit factoring with shared most significant and middle bits. Zbl 1271.11117
Faugère, Jean-Charles; Marinier, Raphaël; Renault, Guénaël
6
2010
Decomposition of generic multivariate polynomials. Zbl 1321.68530
Faugère, Jean-Charles; von zur Gathen, Joachim; Perret, Ludovic
4
2010
Algebraic cryptanalysis of curry and flurry using correlated messages. Zbl 1281.94023
Faugère, Jean-Charles; Perret, Ludovic
3
2010
Algebraic cryptanalysis of the PKC ’2009 algebraic surface cryptosystem. Zbl 1271.94018
Faugère, Jean-Charles; Spaenlehauer, Pierre-Jean
2
2010
Cryptanalysis of the hidden matrix cryptosystem. Zbl 1285.94059
Faugère, Jean-Charles; Joux, Antoine; Perret, Ludovic; Treger, Joana
2
2010
Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases. Zbl 1237.13052
Faugère, Jean-Charles; Rahmany, Sajjad
14
2009
Hybrid approach for solving multivariate systems over finite fields. Zbl 1183.94021
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
13
2009
An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography. Zbl 1175.12004
Faugère, Jean-Charles; Perret, Ludovic
5
2009
On the decoding of binary cyclic codes with the Newton identities. Zbl 1174.94023
Augot, Daniel; Bardet, Magali; Faugère, Jean-Charles
3
2009
High order derivatives and decomposition of multivariate polynomials. Zbl 1237.68255
Faugère, Jean-Charles; Perret, Ludovic
2
2009
Cryptanalysis of MinRank. Zbl 1183.94033
Faugère, Jean-Charles; Levy-dit-Vehel, Françoise; Perret, Ludovic
10
2008
Cryptanalysis of the TRMS signature scheme of PKC’05. Zbl 1142.94333
Bettale, Luk; Faugère, Jean-Charles; Perret, Ludovic
2
2008
Ridges and umbilics of polynomial parametric surfaces. Zbl 1167.53004
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
2
2008
Cryptanalysis of \(2r^-\) schemes. Zbl 1161.94397
Faugère, Jean-Charles; Perret, Ludovic
7
2006
Polynomial equivalence problems: algorithmic and theoretical aspects. Zbl 1140.94337
Faugère, Jean-Charles; Perret, Ludovic
4
2006
The implicit structure of ridges of a smooth parametric surface. Zbl 1112.65013
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
3
2006
The arithmetic of Jacobian groups of superelliptic cubics. Zbl 1094.14049
Basiri, Abdolali; Enge, Andreas; Faugère, Jean-Charles; Gürel, Nicolas
6
2005
Comparison between XL and Gröbner basis algorithms. Zbl 1094.94024
Ars, Gwénolé; Faugère, Jean-Charles; Imai, Hideki; Kawazoe, Mitsuru; Sugita, Makoto
11
2004
Implementing the arithmetic of \(C_{3,4}\) curves. Zbl 1148.14304
Basiri, Abdolali; Enge, Andreas; Faugère, Jean-Charles; Gürel, Nicolas
6
2004
Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. Zbl 1122.94371
Faugère, Jean-Charles; Joux, Antoine
54
2003
Changing the ordering of Gröbner bases with LLL: case of two variables. Zbl 1072.68645
Basiri, Abdolali; Faugère, Jean-Charles
2
2003
A new efficient algorithm for computing Gröbner bases without reduction to zero \((F_5)\). Zbl 1072.68664
Faugère, Jean-Charles
120
2002
Finding all the solutions of cyclic 9 using Gröbner basis techniques. Zbl 1030.68112
Faugère, Jean-Charles
5
2001
A new efficient algorithm for computing Gröbner bases \((F_4)\). Zbl 0930.68174
Faugère, Jean-Charles
194
1999
Symmetry theorems for the Newtonian 4- and 5-body problems with equal masses. Zbl 1087.70504
Faugère, Jean-Charles; Kotsireas, Ilias
1
1999
Efficient computation of zero-dimensional Gröbner bases by change of ordering. Zbl 0805.13007
Faugère, J. C.; Gianni, P.; Lazard, D.; Mora, T.
161
1993
all top 5

Cited by 805 Authors

30 Faugère, Jean-Charles
17 Hashemi, Amir
12 Perret, Ludovic
10 Safey El Din, Mohab
9 Lin, Dongdai
9 Sun, Yao
8 Gerdt, Vladimir P.
8 Wang, Dingkang
7 Albrecht, Martin R.
7 Huang, Zhenyu
7 Kreuzer, Martin
7 M.-Alizadeh, Benyamin
7 Schost, Éric
6 Ding, Jintai
6 Martínez-Moro, Edgar
6 Mou, Chenqi
6 Semaev, Igor A.
6 Takagi, Tsuyoshi
6 Wang, Dongming
6 Yokoyama, Kazuhiro
5 Fouque, Pierre-Alain
5 Gao, Shuhong
5 Lecerf, Grégoire
5 Mourrain, Bernard
5 Sturmfels, Bernd
4 Borges-Quintana, Mijail
4 Borges Trenard, Miguel Ángel
4 Brickenstein, Michael
4 Caboara, Massimo
4 Gao, Xiaoshan
4 Gomez-Perez, Domingo
4 Hashimoto, Yasufumi
4 Henrion, Didier
4 Huang, Ming-Deh A.
4 Lazard, Daniel
4 Naldi, Simone
4 Petzoldt, Albrecht
4 Robbiano, Lorenzo
4 Robert, Damien
4 Rouillier, Fabrice
4 Tan, Chik How
4 Tsigaridas, Elias P.
4 van der Hoeven, Joris
4 Verron, Thibaut
4 Zinin, M. V.
3 Baena, John Bayron
3 Bardet, Magali
3 Basiri, Abdolali
3 Berthomieu, Jérémy
3 Blinkov, Yuri A.
3 Bouillaguet, Charles
3 Chen, Ming-shing
3 Clough, Crystal Lee
3 Dahan, Xavier
3 Davenport, James Harold
3 Dehghani Darmian, Mahdi
3 Emiris, Ioannis Z.
3 England, Matthew
3 Gaborit, Philippe
3 Galkin, V. V.
3 Gaudry, Pierrick
3 Gueye, Cheikh Thiecoumba
3 Gutnik, Sergey A.
3 Hu, Lei
3 Jia, Jianwei
3 Johansson, Thomas
3 Joux, Antoine
3 Klamti, Jean Belo
3 Kosters, Michiel
3 Kudo, Momonari
3 Lau, Terry Shue Chien
3 Liu, Jinhui
3 Lu, Yao
3 Lubicz, David
3 Lundqvist, Samuel
3 Mehta, Dhagash
3 Moreno Maza, Marc
3 Niu, Wei
3 Noro, Masayuki
3 Oliveira, Thomaz
3 Otmani, Ayoub
3 Peng, Liqiang
3 Perry, John Edward
3 Renault, Guénaël
3 Rodríguez-Henríquez, Francisco
3 Sakurai, Kouichi
3 Sala, Massimiliano
3 Sarychev, Vasily A.
3 Thomas, Rekha R.
3 Tillich, Jean-Pierre
3 Vaccon, Tristan
3 Yang, Bo-Yin
3 Yasuda, Masaya
3 Yeo, Sze Ling
2 Abbott, John A.
2 Adj, Gora
2 Améndola, Carlos
2 Ars, Gwénolé
2 Aubry, Philippe
2 Barreto, Paulo S. L. M.
...and 705 more Authors
all top 5

Cited in 111 Serials

99 Journal of Symbolic Computation
28 Designs, Codes and Cryptography
21 Mathematics in Computer Science
19 Finite Fields and their Applications
16 Journal of Mathematical Cryptology
15 Mathematics of Computation
15 Applicable Algebra in Engineering, Communication and Computing
14 Programming and Computer Software
13 Theoretical Computer Science
12 Advances in Mathematics of Communications
9 Journal of Cryptology
9 Journal of Systems Science and Complexity
7 Journal of Pure and Applied Algebra
7 Advances in Applied Mathematics
7 Foundations of Computational Mathematics
6 Journal of Algebra
6 Journal of Complexity
5 Science China. Mathematics
4 Journal of Computational and Applied Mathematics
4 LMS Journal of Computation and Mathematics
4 Journal of High Energy Physics
4 Cryptography and Communications
3 Automatica
3 Computer Aided Geometric Design
3 Japan Journal of Industrial and Applied Mathematics
3 International Journal of Algebra and Computation
3 Linear Algebra and its Applications
3 Annals of Mathematics and Artificial Intelligence
3 Journal of Algebra and its Applications
2 Communications in Algebra
2 Journal of Mathematical Analysis and Applications
2 Mathematics and Computers in Simulation
2 Bulletin of the Iranian Mathematical Society
2 Discrete & Computational Geometry
2 SIAM Journal on Discrete Mathematics
2 International Journal of Foundations of Computer Science
2 Celestial Mechanics and Dynamical Astronomy
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 Experimental Mathematics
2 Journal of Mathematical Sciences (New York)
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Revista Matemática Complutense
2 JSIAM Letters
2 Pacific Journal of Mathematics for Industry
2 SIAM Journal on Applied Algebra and Geometry
1 International Journal of Modern Physics A
1 Bulletin of the Australian Mathematical Society
1 Computers & Mathematics with Applications
1 International Journal of Control
1 Information Processing Letters
1 Journal of Computational Physics
1 Journal of Mathematical Physics
1 Linear and Multilinear Algebra
1 Mathematical Methods in the Applied Sciences
1 Mathematical Notes
1 Moscow University Mathematics Bulletin
1 Periodica Mathematica Hungarica
1 Problems of Information Transmission
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 Annals of the Institute of Statistical Mathematics
1 Applied Mathematics and Computation
1 BIT
1 Compositio Mathematica
1 Geometriae Dedicata
1 Information Sciences
1 Journal of Combinatorial Theory. Series A
1 Journal of Economic Theory
1 Proceedings of the American Mathematical Society
1 Results in Mathematics
1 SIAM Journal on Computing
1 Cryptologia
1 European Journal of Combinatorics
1 Acta Applicandae Mathematicae
1 Algorithmica
1 Mathematical and Computer Modelling
1 Formal Aspects of Computing
1 Multidimensional Systems and Signal Processing
1 Discrete Mathematics and Applications
1 Numerical Algorithms
1 European Journal of Operational Research
1 SIAM Journal on Optimization
1 Applied Mathematics. Series B (English Edition)
1 Annales Mathématiques Blaise Pascal
1 Journal of Combinatorial Designs
1 Bulletin des Sciences Mathématiques
1 Reliable Computing
1 Computer Science Journal of Moldova
1 Multibody System Dynamics
1 Mathematical Methods of Operations Research
1 Mechanism and Machine Theory
1 Discrete Dynamics in Nature and Society
1 Journal of Discrete Mathematical Sciences & Cryptography
1 Journal of the European Mathematical Society (JEMS)
1 Computational Geosciences
1 Qualitative Theory of Dynamical Systems
1 Journal of Applied Mathematics and Computing
1 Journal of Intelligent and Fuzzy Systems
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Science in China. Series F
1 The European Physical Journal C. Particles and Fields
...and 11 more Serials
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Cited in 46 Fields

240 Commutative algebra (13-XX)
210 Computer science (68-XX)
183 Information and communication theory, circuits (94-XX)
96 Algebraic geometry (14-XX)
88 Number theory (11-XX)
44 Numerical analysis (65-XX)
34 Quantum theory (81-XX)
30 Field theory and polynomials (12-XX)
19 Combinatorics (05-XX)
18 Linear and multilinear algebra; matrix theory (15-XX)
11 Operations research, mathematical programming (90-XX)
10 Ordinary differential equations (34-XX)
10 Biology and other natural sciences (92-XX)
9 Order, lattices, ordered algebraic structures (06-XX)
9 Associative rings and algebras (16-XX)
8 Dynamical systems and ergodic theory (37-XX)
8 Statistics (62-XX)
8 Systems theory; control (93-XX)
7 Mechanics of particles and systems (70-XX)
6 Partial differential equations (35-XX)
4 Nonassociative rings and algebras (17-XX)
4 Functions of a complex variable (30-XX)
4 Several complex variables and analytic spaces (32-XX)
4 Approximations and expansions (41-XX)
4 Operator theory (47-XX)
4 Convex and discrete geometry (52-XX)
3 Mathematical logic and foundations (03-XX)
2 Topological groups, Lie groups (22-XX)
2 Special functions (33-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Manifolds and cell complexes (57-XX)
2 Probability theory and stochastic processes (60-XX)
2 Relativity and gravitational theory (83-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 History and biography (01-XX)
1 General algebraic systems (08-XX)
1 Group theory and generalizations (20-XX)
1 Real functions (26-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral transforms, operational calculus (44-XX)
1 Geometry (51-XX)
1 Algebraic topology (55-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Geophysics (86-XX)

Citations by Year