Arjen Lenstra | Academic Influence

Arjen Lenstra's AcademicInfluence.com Rankings

Arjen Lenstra

Mathematics

#1381

World Rank

#2288

Historical Rank

Number Theory

#64

World Rank

#94

Historical Rank

Measure Theory

#1723

World Rank

#2117

Historical Rank

mathematics Degrees

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Mathematics

Arjen Lenstra's Degrees

PhD Mathematics University of Amsterdam
Masters Mathematics University of Amsterdam

Why Is Arjen Lenstra Influential?

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According to Wikipedia, Arjen Klaas Lenstra is a Dutch mathematician, cryptographer and computational number theorist. He is a professor emeritus from the École Polytechnique Fédérale de Lausanne where he headed of the Laboratory for Cryptologic Algorithms.

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Arjen Lenstra's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Factoring polynomials with rational coefficients (1982) (4126)
Selecting Cryptographic Key Sizes (2000) (1160)
Factorization of a 768-Bit RSA Modulus (2010) (487)
The Development of the Number Field Sieve (1993) (304)
The XTR Public Key System (2000) (279)
Short Chosen-Prefix Collisions for MD5 and the Creation of a Rogue CA Certificate (2009) (224)
Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities (2007) (194)
Algorithms in Number Theory (1991) (189)
Factorization of RSA-140 Using the Number Field Sieve (1999) (179)
Factorization of a 512-Bit RSA Modulus (2000) (176)
The number field sieve (1990) (173)
Chinese Remaindering Based Cryptosystems in the Presence of Faults (1999) (157)
Ron was wrong, Whit is right (2012) (152)
Factoring multivariate polynomials over finite fields (1983) (151)
ECRYPT yearly report on algorithms and keysizes (2009) (143)
Unbelievable Security. Matching AES Security Using Public Key Systems (2001) (134)
VSH, an Efficient and Provable Collision Resistant Hash Function (2006) (127)
Factoring by Electronic Mail (1990) (125)
The factorization of the ninth Fermat number (1993) (111)
The Magic Words are Squeamish Ossifrage (1994) (108)
Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers (1984) (102)
Memo on RSA signature generation in the presence of faults (1996) (100)
MD5 considered harmful today, creating a rogue CA certificate (2008) (99)
On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography (2009) (99)
Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables (2000) (97)
A World Wide Number Field Sieve Factoring Record: On to 512 Bits (1996) (94)
Public Keys (2012) (89)
Generating RSA Moduli with a Predetermined Portion (1998) (87)
Factoring With Two Large Primes (1990) (85)
A random zoo: sloth, unicorn, and trx (2015) (84)
Implementation of a New Primality Test (1985) (84)
Hard Equality Constrained Integer Knapsacks (2002) (81)
Integer Factoring (2000) (73)
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction (2012) (73)
Factoring Estimates for a 1024-Bit RSA Modulus (2003) (71)
Colliding X.509 Certificates (2005) (67)
Some Remarks on Lucas-Based Cryptosystems (1995) (64)
On the Possibility of Constructing Meaningful Hash Collisions for Public Keys (2005) (63)
A Kilobit Special Number Field Sieve Factorization (2007) (62)
Speeding Up XTR (2001) (59)
Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances (1999) (56)
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions (2002) (56)
Factorization of polynomials (1984) (55)
Analysis and Optimization of the TWINKLE Factoring Device (2000) (54)
Analysis of Bernstein's Factorization Circuit (2002) (52)
Factoring polynominals over algebraic number fields (1983) (51)
Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems Over Finite Fields (1997) (51)
NFS with Four Large Primes: An Explosive Experiment (1995) (50)
Key Improvements to XTR (2000) (49)
A Key Escrow System with Warrant Bounds (1995) (48)
Lattice sieving and trial division (1994) (43)
Computation of a 768-Bit Prime Field Discrete Logarithm (2017) (43)
Key Lengths Contribution to The Handbook of Information Security (2010) (42)
Factoring polynomials with integer coefficients (1982) (41)
Chosen-prefix collisions for MD5 and applications (2012) (41)
Factoring Multivariate Integral Polynomials (1983) (40)
Multi-exponentiation (cryptographic protocols) (1994) (40)
Cryptology and Computational Number Theory (1997) (40)
Market Split and Basis Reduction: Towards a Solution of the Cornue'jols-Dawande Instances (2000) (40)
Lattices and Factorization of Polynomials over Algebraic Number Fields (1982) (38)
An overview of the XTR public key system (2001) (35)
Factoring Multivariate Polynomials over Algebraic Number Fields (1984) (33)
On the Factorization of RSA-120 (1993) (31)
Trustworthy public randomness with sloth, unicorn, and trx (2017) (31)
On the Use of the Negation Map in the Pollard Rho Method (2010) (30)
Birthday Paradox (2005) (29)
Fast Irreducibility and Subgroup Membership Testing in XTR (2001) (28)
Factoring polynomials with rational coefficients : (preprint) (1982) (28)
Solving a Linear Diophantine Equation with Lower and Upper Bounds on the Variables (1998) (26)
Information Security Risk Assessment, Aggregation, and Mitigation (2004) (25)
Factoring Integers Using SIMD Sieves (1994) (24)
Efficient SIMD Arithmetic Modulo a Mersenne Number (2011) (22)
Using the Cloud to Determine Key Strengths (2012) (22)
Information Security Management System (2014) (21)
A heterogeneous computing environment to solve the 768-bit RSA challenge (2012) (20)
Security Observance throughout the Life-Cycle of Embedded Systems (2008) (19)
Mersenne Factorization Factory (2014) (18)
Factoring with two large primes (extended abstract) (1991) (17)
Predicting the winner of the 2008 US Presidential Elections using a Sony PlayStation 3 (2007) (16)
Iso/iec 27001 (2011) (16)
MPQS with Three Large Primes (2002) (16)
Fast and rigorous factorization under the generalized Riemann hypothesis (1987) (16)
Universal Security - From Bits and Mips to Pools, Lakes - and Beyond (2013) (15)
Massively Parallel Computing and Factoring (1992) (15)
Two Lines Least Squares (1982) (15)
Polynomial Factorization by Root Approximation (1984) (15)
Lattices and factorization of polynomials (1981) (14)
Target Collisions for MD5 and Colliding X.509 Certificates for Different Identities (2006) (14)
The Eurocrypt '92 Controversial Issue: Trapdoor Primes and Moduli (Panel) (1992) (14)
Further progress in hashing cryptanalysis (2005) (14)
An Implementation of the Elliptic Curve Integer Factorization Method (1995) (13)
Massively Parallel Elliptic Curve Factorin (1992) (13)
The History of the LLL-Algorithm (2010) (13)
Cofactorization on Graphics Processing Units (2014) (13)
Addendum: “The factorization of the ninth Fermat number” [Math. Comp. 61 (1993), no. 203, 319–349; MR1182953 (93k:11116)] (1995) (12)
Discrete Logarithm Variants of VSH (2006) (9)
Selective Forgery of RSA Signatures with Fixed-Pattern Padding (2002) (8)
Polynomial - time algorithms for the factorization of polynomials (1984) (8)
Twin RSA (2005) (8)
STEP-archival: Storage integrity and anti-tampering using data entanglement (2015) (7)
Generating Standard DSA Signatures Without Long Inversion (1996) (7)
Factorization of Polynominals by Transcendental Evaluation (1985) (6)
Parametrizations for Families of ECM-Friendly Curves (2017) (6)
Hard equality constrained integer knapsacks (Erratum) (2006) (6)
Efficient Identity Based Parameter Selection for Elliptic Curve Cryptosystems (1999) (6)
Supplement to Implementation of a New Primality Test (1987) (5)
Improving the Boneh-Franklin Traitor Tracing Scheme (2009) (5)
Topics in computational number theory inspired by Peter L. Montgomery (2017) (5)
Efficient Ephemeral Elliptic Curve Cryptographic Keys (2015) (5)
Creating a rogue CA certificate (2008) (5)
An algorithm for solving a diophantine equation with lower and upper bounds on the variables (1997) (4)
Constructing trapdoor primes for the proposed DSS (1991) (4)
Factoring Integers Using the Web and the Number Field Sieve (1995) (4)
Recent developments in cryptography (2001) (4)
Compact incremental Gaussian Elimination over Z/2Z (1988) (3)
Computation of a 30750-Bit Binary Field Discrete Logarithm (2020) (3)
STeP-Archival: Storage Integrity and Tamper Resistance Using Data Entanglement (2018) (3)
User impersonation in key certification schemes (1993) (3)
Lattices and factorization of polynomials : (preprint) (1981) (2)
Selecting Cryptographic Key Sizes ! Extended Abstract (2000) (2)
Trust , and public entropy : a unicorn hunt (2016) (2)
Computational methods in public key cryptology (2002) (2)
General purpose integer factoring (2017) (2)
Towards a Structural Secure Design Process (2010) (2)
Fast massively parallel modular arithmetic (1993) (2)
Using the Cloud to Determine Key Strengths - Triennial Update (2018) (2)
Proceedings of the 10th international conference on Information Security (2007) (2)
Efficient committed oblivious transfer of bit strings (2007) (2)
Securing the Net - The Fruits of Incompetence (1996) (2)
On the Amount of Sieving in Factorization Methods (2004) (2)
The Magic Words Are Squeamish Ossifrage (Extended Abstract) (2007) (2)
Systolic Montgomery multiplication (1992) (2)
Smoothness Probability (2005) (1)
Progress in Cryptology – INDOCRYPT 2017 (2017) (1)
Information Integrity (2011) (1)
Factoring Multivariate Polynomials over Finite Fields (Extended Abstract) (1983) (1)
Uses of Randomness in Algorithms and Protocols (Joe Kilian) (1993) (0)
Cryptanalysis of Widely-used Hash Function Standards and Beyond (2012) (0)
Factoring multivariate integral polynomials II: (preprint) (1983) (0)
Factoring multivariate integral polynomials, II (1983) (0)
Addendum: The Factorization of the Ninth Fermat Number (1995) (0)
BIOS Basic Input Output System (2011) (0)
Biometric Cryptosystem (2009) (0)
Massively parallel number crunching at EPFL version 1 , July 29 , 2010 (2010) (0)
Two lines least squares : (preprint) (1981) (0)
Information Security. Proceedings 10th International Conference, ISC 2007 (2007) (0)
Polynomial factorization and lattices in the very early 1980s (2007) (0)
The three pillars of cryptography (2008) (0)
Automated IS risk assessment and aggregation (2004) (0)
Entries related to integer factoring (2004) (0)
— Summary — Evaluation of complexity of the sieving step of the general number ﬁeld sieve (2018) (0)
Segment and Strong Segment LLL-Reduction of Lattice Bases (2002) (0)
Massively parallel number crunching at EPFL (2009) (0)
An Attack Bound for Small Multiplicative Inverse of φ ( N ) mod e with a Composed Prime Sum p + q Using Sublattice Based Techniques (2018) (0)
Securing the net (1996) (0)
Polynomial factorization and lattices in the very early 1980 s Perspectives of an early user of lattice basis reduction (2007) (0)
ECC vs. RSA (2015) (0)
L Notation (2011) (0)
ON MULTIDIMENSIONAL DIOPHANTINE APPROXIMATION OF ALGEBRAIC NUMBERS (2015) (0)
Reportrapport Factorization of a 512--bit Rsa Modulus Factorization of a 5122bit Rsa Modulus (0)
Preface (2004) (0)
Journal of Cryptology: Preface (2004) (0)
The three pillars of cryptology (2008) (0)
Experts onthullen zwakke plek in internetbeveiliging : YouTube film (2008) (0)
Latt ice s ieving and trial divis ion (0)
An Explosive Experiment (2002) (0)
Patent nonsense and the joined keys lemma (2011) (0)
Viewpoint: Network Security - Elusive, Essential (1996) (0)
Subgroup Cryptosystems (2005) (0)
Identity Proof (2011) (0)
Computational number theory (2001) (0)
On the Security of Lenstra's Variant of DSA without Long Inversions (2001) (0)
A recent algorithm for the factorization of polynomials (1985) (0)
The bank card (2013) (0)
A heterogeneous computing environment to solve the 768-bit RSA challenge (2010) (0)

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