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Lenstra, Arjen K.

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Author ID: lenstra.arjen-k Recent zbMATH articles by "Lenstra, Arjen K."
Published as: Lenstra, Arjen K.; Lenstra, A. K.; Lenstra, Arjen
External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Documents Indexed: 96 Publications since 1980, including 5 Books
all top 5

Co-Authors

20 single-authored
11 Kleinjung, Thorsten
8 Lenstra, Hendrik W. jun.
7 Aardal, Karen I.
6 Bos, Joppe W.
6 Dodson, Bruce A.
6 Manasse, Mark S.
6 Verheul, Eric R.
5 Leyland, Paul C.
5 Montgomery, Peter Lawrence
4 de Weger, Benne
4 Hurkens, Cor A. J.
4 Lovász, László
3 Osvik, Dag Arne
3 Pollard, John M.
3 Shamir, Adi
3 Stam, Martijn
3 Stevens, Marc
3 te Riele, Herman
3 Zimmermann, Paul
2 Aoki, Kazumaro
2 Augier, Maxime
2 Bixby, Robert E.
2 Bosma, Wieb
2 Cavallar, Stefania Hedwig
2 Dixon, Brandon
2 Franke, Jens
2 Hughes, James P.
2 Lenstra, Jan Karel
2 Lioen, Walter M.
2 Muffett, Alec
2 Rinnooy Kan, Alexander Hendrik George
2 Shparlinski, Igor E.
2 Smeltink, Job W.
2 Thomé, Emmanuel
2 Tromer, Eran
2 Wansbeek, Tom J.
2 Wesolowski, Benjamin
2 Yacobi, Yacov
1 Appelbaum, Jacob
1 Atkins, Derek R.
1 Bernstein, Daniel Julius
1 Bleichenbacher, Daniel
1 Cohen, Henri
1 Contini, Scott
1 Cowie, James
1 de Weger, Benjamin M. M.
1 Denny, Thomas F.
1 Diem, Claus
1 Dodsons, Bruce
1 Elkenbracht-Huizing, Reina-Marije
1 Garay, Juan A.
1 Gaudry, Pierrick
1 Gélin, Alexandre
1 Gilchrist, Jeff
1 Golliver, Roger A.
1 Graff, Michael
1 Granger, Robert A.
1 Guillerm, Gérard
1 Joye, Marc
1 Junod, Pascal
1 Kaihara, Marcelo E.
1 Kannan, Ravindran
1 Karlov, Alexandre
1 Kortsmit, Wil
1 Kruppa, Alexander
1 Laih, Chi-Sung
1 Mambo, Masahiro
1 Marchand, Joël
1 McCurley, Kevin S.
1 Mercier, Hugues
1 Miele, Andrea
1 Molnar, David
1 Morain, François
1 Page, Dan
1 Page, Daniel R.
1 Peralta, René C.
1 Priplata, Christine
1 Putnam, Chris
1 Putnam, Craig
1 Quisquater, Jean-Jacques
1 Smart, Nigel P.
1 Smeets, Ionica
1 Sotirov, Alexander
1 Stahlke, Colin
1 Steinfeld, Ron
1 Timofeev, Andrey V.
1 Tomlinson, Jim
1 van der Hulst, Marc-Paul
1 van Emde Boas, Peter
1 Voss, Tim
1 Wachter, Christophe
1 Wagstaff, Sam
1 Winkler, Peter M.
1 Yen, Sung-Ming
1 Zayer, Jörg
1 Zumbrägel, Jens

Publications by Year

Citations contained in zbMATH Open

74 Publications have been cited 1,160 times in 917 Documents Cited by Year
Factoring polynomials with rational coefficients. Zbl 0488.12001
Lenstra, A. K.; Lenstra, H. W. jun.; Lovász, László
557
1982
The development of the number field sieve. Zbl 0777.00017
Lenstra, A. K. (ed.); Lenstra, H. W. jun. (ed.)
47
1993
Factoring multivariate polynomials over finite fields. Zbl 0577.12013
Lenstra, A. K.
33
1985
Selecting cryptographic key sizes. Zbl 1006.94020
Lenstra, Arjen K.; Verheul, Eric R.
30
2001
Factorization of a 768-bit RSA modulus. Zbl 1196.11167
Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul
28
2010
Algorithms in number theory. Zbl 0900.68250
Lenstra, A. K.; Lenstra, H. W. jun.
25
1990
Factoring multivariate polynomials over algebraic number fields. Zbl 0636.12005
Lenstra, Arjen K.
25
1987
The number field sieve. Zbl 0806.11065
Lenstra, A. K.; Lenstra, H. W. jun.; Manasse, M. S.; Pollard, J. M.
23
1993
The XTR public key system. Zbl 0995.94538
Lenstra, Arjen K.; Verheul, Eric R.
23
2000
Solving a system of linear Diophantine equations with lower and upper bounds on the variables. Zbl 1073.90528
Aardal, Karen; Hurkens, Cor A. J.; Lenstra, Arjen K.
19
2000
Factoring polynomials over algebraic number fields. Zbl 0539.68030
Lenstra, A. K.
17
1983
The factorization of the ninth Fermat number. Zbl 0792.11055
Lenstra, A. K.; Lenstra, H. W. jun.; Manasse, M. S.; Pollard, J. M.
17
1993
VSH, an efficient and provable collision-resistant hash function. Zbl 1140.94331
Contini, Scott; Lenstra, Arjen K.; Steinfeld, Ron
17
2006
Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. Zbl 0654.12001
Kannan, R.; Lenstra, A. K.; Lovász, László
17
1988
Chosen-prefix collisions for MD5 and colliding X.509 certificates for different identities. Zbl 1141.94374
Stevens, Marc; Lenstra, Arjen; de Weger, Benne
14
2007
Unbelievable security. Zbl 1062.94550
Lenstra, Arjen K.
13
2001
Short chosen-prefix collisions for MD5 and the creation of a rogue CA certificate. Zbl 1252.94098
Stevens, Marc; Sotirov, Alexander; Appelbaum, Jacob; Lenstra, Arjen; Molnar, David; Osvik, Dag Arne; de Weger, Benne
12
2009
Hard equality constrained integer knapsacks. Zbl 1082.90066
Aardal, Karen; Lenstra, Arjen K.
11
2004
Implementation of a new primality test. Zbl 0608.10001
Cohen, H.; Lenstra, A. K.
11
1987
Market split and basis reduction: towards a solution of the Cornuéjols-Dawande instances. Zbl 1040.90023
Aardal, K.; Bixby, R. E.; Hurkens, C. A. J.; Lenstra, A. K.; Smeltink, J. W.
11
2000
Generating RSA moduli with a predetermined portion. Zbl 0930.94023
Lenstra, Arjen K.
10
1998
Hard equality constrained integer knapsacks. Zbl 1049.90042
Aardal, Karen; Lenstra, Arjen K.
10
2002
Factoring multivariate integral polynomials. Zbl 0985.12500
Lenstra, A. K.
9
1984
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction. Zbl 1276.94008
Bos, Joppe W.; Kaihara, Marcelo E.; Kleinjung, Thorsten; Lenstra, Arjen K.; Montgomery, Peter L.
8
2012
Some remarks on Lucas-based cryptosystems. Zbl 0877.94029
Bleichenbacher, Daniel; Bosma, Wieb; Lenstra, Arjen K.
8
1995
Factoring polynomials with rational coefficients. Zbl 0477.68043
Lenstra, A. K.; Lenstra, H. W. jun.; Lovász, László
7
1982
Public keys. Zbl 1296.94127
Lenstra, Arjen K.; Hughes, James P.; Augier, Maxime; Bos, Joppe W.; Kleinjung, Thorsten; Wachter, Christophe
7
2012
Solving a linear diophantine equation with lower and upper bounds on the variables. Zbl 0910.90216
Aardal, Karen; Hurkens, Cor; Lenstra, Arjen K.
7
1998
A kilobit special number field sieve factorization. Zbl 1153.11344
Aoki, Kazumaro; Franke, Jens; Kleinjung, Thorsten; Lenstra, Arjen K.; Osvik, Dag Arne
7
2007
Computation of a 768-bit prime field discrete logarithm. Zbl 1411.11135
Kleinjung, Thorsten; Diem, Claus; Lenstra, Arjen K.; Priplata, Christine; Stahlke, Colin
6
2017
Integer factoring. Zbl 0964.11057
Lenstra, Arjen K.
6
2000
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
6
2000
Multi-exponentiation. Zbl 0815.94009
Yen, S.-M.; Laih, C.-S.; Lenstra, A. K.
6
1994
Efficient subgroup exponentiation in quadratic and sixth degree extensions. Zbl 1020.94525
Stam, Martijn; Lenstra, Arjen K.
6
2002
The magic words are squeamish ossifrage. (Extended abstract). Zbl 0877.94026
Atkins, Derek; Graff, Michael; Lenstra, Arjen K.; Leyland, Paul C.
5
1995
Two lines least squares. Zbl 0495.62071
Lenstra, A. K.; Lenstra, J. K.; Kan, A. H. G. Rinnooy; Wansbeek, T. J.
5
1982
A general number field sieve implementation. Zbl 0806.11069
Bernstein, Daniel J.; Lenstra, A. K.
5
1993
Factoring with two large primes. Zbl 0806.11070
Lenstra, A. K.; Manasse, M. S.
5
1994
Factoring estimates for a 1024-bit RSA modulus. Zbl 1205.11129
Lenstra, Arjen; Tromer, Eran; Shamir, Adi; Kortsmit, Wil; Dodson, Bruce; Hughes, James; Leyland, Paul
5
2003
On the use of the negation map in the Pollard rho method. Zbl 1260.11080
Bos, Joppe W.; Kleinjung, Thorsten; Lenstra, Arjen K.
5
2010
Mersenne factorization factory. Zbl 1306.11098
Kleinjung, Thorsten; Bos, Joppe W.; Lenstra, Arjen K.
5
2014
Lattices and factorization of polynomials. Zbl 0477.12002
Lenstra, A. K.
4
1981
Lattices and factorization of polynomials over algebraic number fields. Zbl 0541.68018
Lenstra, A. K.
4
1982
Selecting cryptographic key sizes. (Extended abstract). Zbl 0972.94502
Lenstra, Arjen K.; Verheul, Eric R.
4
2000
On the possibility of constructing meaningful hash collisions for public keys. Zbl 1127.94349
Lenstra, Arjen; de Weger, Benne
4
2005
The history of the LLL-algorithm. In collaboration with Arjen Lenstra, Hendrik Lenstra, László Lovász, and Peter van Emde Boas. Zbl 1230.11002
Smeets, Ionica; Lenstra, Arjen; Lenstra, Hendrik; Lovász, László; Van Emde Boas, Peter
4
2010
Speeding up XTR. Zbl 1062.94553
Stam, Martijn; Lenstra, Arjen K.
4
2001
Fast and rigorous factorization under the generalized Riemann hypothesis. Zbl 0669.10012
Lenstra, A. K.
4
1988
An overview of the XTR public key system. Zbl 0986.94029
Lenstra, Arjen K.; Verheul, Eric R.
4
2001
A key escrow system with warrant bounds. Zbl 0868.94031
Lenstra, Arjen K.; Winkler, Peter; Yacobi, Yacov
3
1995
Massively parallel elliptic curve factoring. Zbl 0811.11078
Dixon, B.; Lenstra, A. K.
3
1993
Market split and basis reduction: Towards a solution of the Cornuéjols-Dawande instances. Zbl 0948.90108
Aardal, Karen; Bixby, Robert E.; Hurkens, Cor A. J.; Lenstra, Arjen K.; Smeltink, Job W.
3
1999
A world wide number field sieve factoring record: On to 512 bits. Zbl 1028.11500
Cowie, James; Dodson, Bruce; Elkenbracht-Huizing, R. Marije; Lenstra, Arjen K.; Montgomery, Peter L.; Zayer, Jörg
3
1996
Discrete logarithm variants of VSH. Zbl 1295.94103
Lenstra, Arjen K.; Page, Daniel; Stam, Martijn
2
2006
Factoring with two large primes. Zbl 0779.11061
Lenstra, Arjen K.; Manasse, Mark S.
2
1991
Chinese remaindering based cryptosystems in the presence of faults. Zbl 0935.94021
Joye, Marc; Lenstra, Arjen K.; Quisquater, Jean-Jacques
2
1999
Factoring integers using SIMD sieves. Zbl 0951.94513
Dixon, B.; Lenstra, A. K.
2
1994
Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields. Zbl 0989.94509
Lenstra, Arjen K.
2
1997
Factorization of RSA-140 using the number field sieve. Zbl 0971.94008
Cavallar, Stefania; Dodson, Bruce; Lenstra, Arjen; Leyland, Paul; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Zimmermann, Paul
2
1999
Factoring multivariate polynomials over algebraic number fields. Zbl 0568.12001
Lenstra, Arjen K.
2
1984
Using the cloud to determine key strengths. Zbl 1295.94093
Kleinjung, Thorsten; Lenstra, Arjen K.; Page, Dan; Smart, Nigel P.
1
2012
Twin RSA. Zbl 1126.94332
Lenstra, Arjen K.; de Weger, Benjamin M. M.
1
2005
Chosen-prefix collisions for MD5 and applications. Zbl 1271.94023
Stevens, Marc; Lenstra, Arjen K.; de Weger, Benne
1
2012
Primality testing. Zbl 0743.11071
Lenstra, Arjen K.
1
1990
NFS with four large primes: an explosive experiment. Zbl 0883.11054
Dodson, Bruce; Lenstra, Arjen K.
1
1995
Factorization of polynomials. Zbl 0464.12009
Lenstra, A. K.
1
1980
An implementation of the elliptic curve integer factorization method. Zbl 0830.11047
Bosma, Wieb; Lenstra, Arjen K.
1
1995
Lattice sieving and trial division. Zbl 0838.11080
Golliver, Roger A.; Lenstra, Arjen K.; McCurley, Kevin S.
1
1994
Analysis and optimization of the twinkle factoring device. Zbl 1082.94525
Lenstra, Arjen K.; Shamir, Adi
1
2000
Key improvements to XTR. Zbl 0974.94016
Lenstra, Arjen K.; Verheul, Eric R.
1
2000
Factorization of polynomials by transcendental evaluation. Zbl 0577.68057
van der Hulst, Marc-Paul; Lenstra, Arjen K.
1
1985
MPQS with three large primes. Zbl 1058.11069
Leyland, Paul; Lenstra, Arjen; Dodson, Bruce; Muffett, Alec; Wagstaff, Sam
1
2002
Fast irreducibility and subgroup membership testing in XTR. Zbl 0991.94042
Lenstra, Arjen K.; Verheul, Eric R.
1
2001
Trustworthy public randomness with sloth, unicorn, and trx. Zbl 1428.94083
Lenstra, Arjen K.; Wesolowski, Benjamin
1
2017
Computation of a 768-bit prime field discrete logarithm. Zbl 1411.11135
Kleinjung, Thorsten; Diem, Claus; Lenstra, Arjen K.; Priplata, Christine; Stahlke, Colin
6
2017
Trustworthy public randomness with sloth, unicorn, and trx. Zbl 1428.94083
Lenstra, Arjen K.; Wesolowski, Benjamin
1
2017
Mersenne factorization factory. Zbl 1306.11098
Kleinjung, Thorsten; Bos, Joppe W.; Lenstra, Arjen K.
5
2014
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction. Zbl 1276.94008
Bos, Joppe W.; Kaihara, Marcelo E.; Kleinjung, Thorsten; Lenstra, Arjen K.; Montgomery, Peter L.
8
2012
Public keys. Zbl 1296.94127
Lenstra, Arjen K.; Hughes, James P.; Augier, Maxime; Bos, Joppe W.; Kleinjung, Thorsten; Wachter, Christophe
7
2012
Using the cloud to determine key strengths. Zbl 1295.94093
Kleinjung, Thorsten; Lenstra, Arjen K.; Page, Dan; Smart, Nigel P.
1
2012
Chosen-prefix collisions for MD5 and applications. Zbl 1271.94023
Stevens, Marc; Lenstra, Arjen K.; de Weger, Benne
1
2012
Factorization of a 768-bit RSA modulus. Zbl 1196.11167
Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul
28
2010
On the use of the negation map in the Pollard rho method. Zbl 1260.11080
Bos, Joppe W.; Kleinjung, Thorsten; Lenstra, Arjen K.
5
2010
The history of the LLL-algorithm. In collaboration with Arjen Lenstra, Hendrik Lenstra, László Lovász, and Peter van Emde Boas. Zbl 1230.11002
Smeets, Ionica; Lenstra, Arjen; Lenstra, Hendrik; Lovász, László; Van Emde Boas, Peter
4
2010
Short chosen-prefix collisions for MD5 and the creation of a rogue CA certificate. Zbl 1252.94098
Stevens, Marc; Sotirov, Alexander; Appelbaum, Jacob; Lenstra, Arjen; Molnar, David; Osvik, Dag Arne; de Weger, Benne
12
2009
Chosen-prefix collisions for MD5 and colliding X.509 certificates for different identities. Zbl 1141.94374
Stevens, Marc; Lenstra, Arjen; de Weger, Benne
14
2007
A kilobit special number field sieve factorization. Zbl 1153.11344
Aoki, Kazumaro; Franke, Jens; Kleinjung, Thorsten; Lenstra, Arjen K.; Osvik, Dag Arne
7
2007
VSH, an efficient and provable collision-resistant hash function. Zbl 1140.94331
Contini, Scott; Lenstra, Arjen K.; Steinfeld, Ron
17
2006
Discrete logarithm variants of VSH. Zbl 1295.94103
Lenstra, Arjen K.; Page, Daniel; Stam, Martijn
2
2006
On the possibility of constructing meaningful hash collisions for public keys. Zbl 1127.94349
Lenstra, Arjen; de Weger, Benne
4
2005
Twin RSA. Zbl 1126.94332
Lenstra, Arjen K.; de Weger, Benjamin M. M.
1
2005
Hard equality constrained integer knapsacks. Zbl 1082.90066
Aardal, Karen; Lenstra, Arjen K.
11
2004
Factoring estimates for a 1024-bit RSA modulus. Zbl 1205.11129
Lenstra, Arjen; Tromer, Eran; Shamir, Adi; Kortsmit, Wil; Dodson, Bruce; Hughes, James; Leyland, Paul
5
2003
Hard equality constrained integer knapsacks. Zbl 1049.90042
Aardal, Karen; Lenstra, Arjen K.
10
2002
Efficient subgroup exponentiation in quadratic and sixth degree extensions. Zbl 1020.94525
Stam, Martijn; Lenstra, Arjen K.
6
2002
MPQS with three large primes. Zbl 1058.11069
Leyland, Paul; Lenstra, Arjen; Dodson, Bruce; Muffett, Alec; Wagstaff, Sam
1
2002
Selecting cryptographic key sizes. Zbl 1006.94020
Lenstra, Arjen K.; Verheul, Eric R.
30
2001
Unbelievable security. Zbl 1062.94550
Lenstra, Arjen K.
13
2001
Speeding up XTR. Zbl 1062.94553
Stam, Martijn; Lenstra, Arjen K.
4
2001
An overview of the XTR public key system. Zbl 0986.94029
Lenstra, Arjen K.; Verheul, Eric R.
4
2001
Fast irreducibility and subgroup membership testing in XTR. Zbl 0991.94042
Lenstra, Arjen K.; Verheul, Eric R.
1
2001
The XTR public key system. Zbl 0995.94538
Lenstra, Arjen K.; Verheul, Eric R.
23
2000
Solving a system of linear Diophantine equations with lower and upper bounds on the variables. Zbl 1073.90528
Aardal, Karen; Hurkens, Cor A. J.; Lenstra, Arjen K.
19
2000
Market split and basis reduction: towards a solution of the Cornuéjols-Dawande instances. Zbl 1040.90023
Aardal, K.; Bixby, R. E.; Hurkens, C. A. J.; Lenstra, A. K.; Smeltink, J. W.
11
2000
Integer factoring. Zbl 0964.11057
Lenstra, Arjen K.
6
2000
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
6
2000
Selecting cryptographic key sizes. (Extended abstract). Zbl 0972.94502
Lenstra, Arjen K.; Verheul, Eric R.
4
2000
Analysis and optimization of the twinkle factoring device. Zbl 1082.94525
Lenstra, Arjen K.; Shamir, Adi
1
2000
Key improvements to XTR. Zbl 0974.94016
Lenstra, Arjen K.; Verheul, Eric R.
1
2000
Market split and basis reduction: Towards a solution of the Cornuéjols-Dawande instances. Zbl 0948.90108
Aardal, Karen; Bixby, Robert E.; Hurkens, Cor A. J.; Lenstra, Arjen K.; Smeltink, Job W.
3
1999
Chinese remaindering based cryptosystems in the presence of faults. Zbl 0935.94021
Joye, Marc; Lenstra, Arjen K.; Quisquater, Jean-Jacques
2
1999
Factorization of RSA-140 using the number field sieve. Zbl 0971.94008
Cavallar, Stefania; Dodson, Bruce; Lenstra, Arjen; Leyland, Paul; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Zimmermann, Paul
2
1999
Generating RSA moduli with a predetermined portion. Zbl 0930.94023
Lenstra, Arjen K.
10
1998
Solving a linear diophantine equation with lower and upper bounds on the variables. Zbl 0910.90216
Aardal, Karen; Hurkens, Cor; Lenstra, Arjen K.
7
1998
Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields. Zbl 0989.94509
Lenstra, Arjen K.
2
1997
A world wide number field sieve factoring record: On to 512 bits. Zbl 1028.11500
Cowie, James; Dodson, Bruce; Elkenbracht-Huizing, R. Marije; Lenstra, Arjen K.; Montgomery, Peter L.; Zayer, Jörg
3
1996
Some remarks on Lucas-based cryptosystems. Zbl 0877.94029
Bleichenbacher, Daniel; Bosma, Wieb; Lenstra, Arjen K.
8
1995
The magic words are squeamish ossifrage. (Extended abstract). Zbl 0877.94026
Atkins, Derek; Graff, Michael; Lenstra, Arjen K.; Leyland, Paul C.
5
1995
A key escrow system with warrant bounds. Zbl 0868.94031
Lenstra, Arjen K.; Winkler, Peter; Yacobi, Yacov
3
1995
NFS with four large primes: an explosive experiment. Zbl 0883.11054
Dodson, Bruce; Lenstra, Arjen K.
1
1995
An implementation of the elliptic curve integer factorization method. Zbl 0830.11047
Bosma, Wieb; Lenstra, Arjen K.
1
1995
Multi-exponentiation. Zbl 0815.94009
Yen, S.-M.; Laih, C.-S.; Lenstra, A. K.
6
1994
Factoring with two large primes. Zbl 0806.11070
Lenstra, A. K.; Manasse, M. S.
5
1994
Factoring integers using SIMD sieves. Zbl 0951.94513
Dixon, B.; Lenstra, A. K.
2
1994
Lattice sieving and trial division. Zbl 0838.11080
Golliver, Roger A.; Lenstra, Arjen K.; McCurley, Kevin S.
1
1994
The development of the number field sieve. Zbl 0777.00017
Lenstra, A. K.; Lenstra, H. W. jun.
47
1993
The number field sieve. Zbl 0806.11065
Lenstra, A. K.; Lenstra, H. W. jun.; Manasse, M. S.; Pollard, J. M.
23
1993
The factorization of the ninth Fermat number. Zbl 0792.11055
Lenstra, A. K.; Lenstra, H. W. jun.; Manasse, M. S.; Pollard, J. M.
17
1993
A general number field sieve implementation. Zbl 0806.11069
Bernstein, Daniel J.; Lenstra, A. K.
5
1993
Massively parallel elliptic curve factoring. Zbl 0811.11078
Dixon, B.; Lenstra, A. K.
3
1993
Factoring with two large primes. Zbl 0779.11061
Lenstra, Arjen K.; Manasse, Mark S.
2
1991
Algorithms in number theory. Zbl 0900.68250
Lenstra, A. K.; Lenstra, H. W. jun.
25
1990
Primality testing. Zbl 0743.11071
Lenstra, Arjen K.
1
1990
Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. Zbl 0654.12001
Kannan, R.; Lenstra, A. K.; Lovász, László
17
1988
Fast and rigorous factorization under the generalized Riemann hypothesis. Zbl 0669.10012
Lenstra, A. K.
4
1988
Factoring multivariate polynomials over algebraic number fields. Zbl 0636.12005
Lenstra, Arjen K.
25
1987
Implementation of a new primality test. Zbl 0608.10001
Cohen, H.; Lenstra, A. K.
11
1987
Factoring multivariate polynomials over finite fields. Zbl 0577.12013
Lenstra, A. K.
33
1985
Factorization of polynomials by transcendental evaluation. Zbl 0577.68057
van der Hulst, Marc-Paul; Lenstra, Arjen K.
1
1985
Factoring multivariate integral polynomials. Zbl 0985.12500
Lenstra, A. K.
9
1984
Factoring multivariate polynomials over algebraic number fields. Zbl 0568.12001
Lenstra, Arjen K.
2
1984
Factoring polynomials over algebraic number fields. Zbl 0539.68030
Lenstra, A. K.
17
1983
Factoring polynomials with rational coefficients. Zbl 0488.12001
Lenstra, A. K.; Lenstra, H. W. jun.; Lovász, László
557
1982
Factoring polynomials with rational coefficients. Zbl 0477.68043
Lenstra, A. K.; Lenstra, H. W. jun.; Lovász, László
7
1982
Two lines least squares. Zbl 0495.62071
Lenstra, A. K.; Lenstra, J. K.; Kan, A. H. G. Rinnooy; Wansbeek, T. J.
5
1982
Lattices and factorization of polynomials over algebraic number fields. Zbl 0541.68018
Lenstra, A. K.
4
1982
Lattices and factorization of polynomials. Zbl 0477.12002
Lenstra, A. K.
4
1981
Factorization of polynomials. Zbl 0464.12009
Lenstra, A. K.
1
1980
all top 5

Cited by 1,383 Authors

17 Shparlinski, Igor E.
12 Sarkar, Santanu
11 Buchmann, Johannes A.
9 Lenstra, Arjen K.
9 Lenstra, Hendrik W. jun.
9 Peng, Liqiang
8 Pohst, Michael E.
8 Schnorr, Claus Peter
8 Takayasu, Atsushi
8 Yasuda, Masaya
7 Bernstein, Daniel Julius
7 Futa, Yuichi
7 Kunihiro, Noboru
7 Lu, Yao
7 Shidama, Yasunari
7 van Hoeij, Mark
7 von zur Gathen, Joachim
6 Gutierrez, Jaime
6 Hu, Lei
6 Kaltofen, Erich L.
6 Nitaj, Abderrahmane
6 Susilo, Willy
5 de Weger, Benjamin M. M.
5 Hauenstein, Jonathan D.
5 Joux, Antoine
5 Kleinjung, Thorsten
5 Klüners, Jürgen
5 Lee, Hyangsook
5 Maitra, Subhamoy
5 Mossinghoff, Michael J.
5 Smart, Nigel P.
5 Steinfeld, Ron
5 Takagi, Tsuyoshi
5 Thomé, Emmanuel
4 Aono, Yoshinori
4 Barbulescu, Razvan
4 Cai, Jin-Yi
4 Cheon, Jung Hee
4 Cornuéjols, Gérard P.
4 Costello, Craig
4 Gaál, István
4 Galbraith, Steven D.
4 Grigor’ev, Dmitriĭ Yur’evich
4 Hanrot, Guillaume
4 Harase, Shin
4 Khadir, Omar
4 Kogure, Jun
4 Krishnamoorthy, Bala
4 Lercier, Reynald
4 Lim, Seongan
4 Menezes, Alfred J.
4 Naccache, David
4 Nguyen, Phong Q.
4 Panario, Daniel
4 Pethő, Attila
4 Peyrin, Thomas
4 Plantard, Thomas
4 Rojas, J. Maurice
4 Schneider, Michael
4 Shamir, Adi
4 Silverberg, Alice
4 Stehlé, Damien
4 te Riele, Herman
4 Trudgian, Timothy S.
4 Venkatesan, Ramarathnam
4 Wang, Baocang
4 Wang, Huaxiong
4 Wu, Qiang
4 Wu, Wenyuan
3 Aardal, Karen I.
3 Abu Salem, Fatima K.
3 Akhavi, Ali
3 Avendano, Martin
3 Bai, Shi
3 Belabas, Karim
3 Bellare, Mihir
3 Boneh, Dan
3 Bremner, Murray R.
3 Brent, Richard Peirce
3 Chen, Jingwei
3 Chen, Yi-Chou
3 De Loera, Jesús A.
3 Duquesne, Sylvain
3 Feng, Yong
3 Fischlin, Marc
3 García-Escudero, Luis Angel
3 Gaudry, Pierrick
3 Gérard, Yan
3 Ghammam, Loubna
3 Gorla, Elisa
3 Granger, Robert A.
3 Hare, Kevin G.
3 Heninger, Nadia
3 Howgrave-Graham, Nick A.
3 Hu, Yupu
3 Ibeas, Álvar
3 Ivanyos, Gábor
3 Izu, Tetsuya
3 Kim, Minkyu
3 Koblitz, Neal I.
...and 1,283 more Authors
all top 5

Cited in 201 Serials

91 Mathematics of Computation
53 Journal of Symbolic Computation
46 Designs, Codes and Cryptography
37 Theoretical Computer Science
28 Journal of Cryptology
22 Journal of Number Theory
20 Experimental Mathematics
17 Journal of Mathematical Cryptology
16 Discrete Applied Mathematics
16 Journal of Computer and System Sciences
11 Journal de Théorie des Nombres de Bordeaux
10 Information Processing Letters
10 Journal of Complexity
10 Linear Algebra and its Applications
10 Computational Complexity
10 LMS Journal of Computation and Mathematics
9 Applied Mathematics and Computation
9 Information and Computation
9 Advances in Mathematics of Communications
8 Journal of Computational and Applied Mathematics
8 Finite Fields and their Applications
7 Computers & Mathematics with Applications
7 Information Sciences
7 Applicable Algebra in Engineering, Communication and Computing
7 Formalized Mathematics
6 Combinatorica
6 Mathematical Programming. Series A. Series B
6 Journal of High Energy Physics
5 The Mathematical Intelligencer
5 Journal of Algebra
5 Journal of Combinatorial Theory. Series A
5 Journal of Global Optimization
5 International Journal of Computer Mathematics
5 Journal of Discrete Mathematical Sciences & Cryptography
5 Discrete Optimization
4 Bulletin of the Australian Mathematical Society
4 Discrete Mathematics
4 Journal of Soviet Mathematics
4 Monatshefte für Mathematik
4 Operations Research Letters
4 Algorithmica
4 Annals of Operations Research
4 Japan Journal of Industrial and Applied Mathematics
4 RAIRO. Informatique Théorique et Applications
4 Journal of Mathematical Sciences (New York)
4 Foundations of Computational Mathematics
4 Journal of Applied Mathematics and Computing
4 Cryptography and Communications
3 Computing
3 Mathematics of Operations Research
3 Acta Applicandae Mathematicae
3 Journal of Automated Reasoning
3 SIAM Journal on Discrete Mathematics
3 Bulletin of the American Mathematical Society. New Series
3 Journal of Systems Science and Complexity
3 International Journal of Number Theory
3 Groups, Complexity, Cryptology
3 Prikladnaya Diskretnaya Matematika
2 Mathematical Notes
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Moscow University Mathematics Bulletin
2 Rocky Mountain Journal of Mathematics
2 Chaos, Solitons and Fractals
2 Journal of Geometry and Physics
2 Manuscripta Mathematica
2 Mathematische Annalen
2 Mathematics and Computers in Simulation
2 Numerical Functional Analysis and Optimization
2 Operations Research
2 SIAM Journal on Computing
2 Transactions of the American Mathematical Society
2 Advances in Applied Mathematics
2 Annals of Pure and Applied Logic
2 Computer Aided Geometric Design
2 Journal of the American Mathematical Society
2 The Journal of Supercomputing
2 European Journal of Operational Research
2 SIAM Journal on Optimization
2 Combinatorics, Probability and Computing
2 Journal of Difference Equations and Applications
2 Journal of Geodesy
2 Mathematical Problems in Engineering
2 The Ramanujan Journal
2 Abstract and Applied Analysis
2 Journal of Combinatorial Optimization
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Integers
2 Algebraic & Geometric Topology
2 Journal of Algebra and its Applications
2 Science in China. Series F
2 International Journal of Parallel, Emergent and Distributed Systems
2 Journal of Zhejiang University. Science A
2 SIAM Journal on Imaging Sciences
2 Mathematical Programming Computation
2 Science China. Mathematics
2 JSIAM Letters
2 Matematicheskie Voprosy Kriptografii
1 American Mathematical Monthly
1 Artificial Intelligence
1 Computer Physics Communications
...and 101 more Serials
all top 5

Cited in 54 Fields

418 Number theory (11-XX)
332 Information and communication theory, circuits (94-XX)
263 Computer science (68-XX)
88 Numerical analysis (65-XX)
78 Algebraic geometry (14-XX)
72 Operations research, mathematical programming (90-XX)
64 Field theory and polynomials (12-XX)
37 Commutative algebra (13-XX)
37 Quantum theory (81-XX)
32 Combinatorics (05-XX)
23 Linear and multilinear algebra; matrix theory (15-XX)
20 Group theory and generalizations (20-XX)
19 Mathematical logic and foundations (03-XX)
15 Convex and discrete geometry (52-XX)
9 Functions of a complex variable (30-XX)
9 Special functions (33-XX)
9 Dynamical systems and ergodic theory (37-XX)
9 Probability theory and stochastic processes (60-XX)
8 Statistics (62-XX)
7 Manifolds and cell complexes (57-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Ordinary differential equations (34-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Geometry (51-XX)
5 Statistical mechanics, structure of matter (82-XX)
4 Associative rings and algebras (16-XX)
4 Difference and functional equations (39-XX)
4 Approximations and expansions (41-XX)
4 Relativity and gravitational theory (83-XX)
3 History and biography (01-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Nonassociative rings and algebras (17-XX)
3 Real functions (26-XX)
3 Sequences, series, summability (40-XX)
3 Biology and other natural sciences (92-XX)
3 Systems theory; control (93-XX)
2 General and overarching topics; collections (00-XX)
2 Potential theory (31-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Partial differential equations (35-XX)
2 Functional analysis (46-XX)
2 Operator theory (47-XX)
2 Differential geometry (53-XX)
2 Geophysics (86-XX)
1 General algebraic systems (08-XX)
1 \(K\)-theory (19-XX)
1 Topological groups, Lie groups (22-XX)
1 Measure and integration (28-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral transforms, operational calculus (44-XX)
1 Integral equations (45-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Algebraic topology (55-XX)
1 Global analysis, analysis on manifolds (58-XX)

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