Joseph H. Silverman

Joseph H. Silverman's AcademicInfluence.com Rankings

Joseph H. Silverman

Mathematics

#220

World Rank

#489

Historical Rank

#103

USA Rank

Measure Theory

#346

World Rank

#520

Historical Rank

#148

USA Rank

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Mathematics

Why Is Joseph H. Silverman Influential?

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According to Wikipedia, Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography. Biography Joseph Silverman received an Sc.B. from Brown University in 1977 and a Ph.D. from Harvard University in 1982 under the direction of John Tate. He taught at M.I.T. and at Boston University before taking a position at Brown in 1988.

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Joseph H. Silverman'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

The arithmetic of elliptic curves (1986) (2560)
Advanced Topics in the Arithmetic of Elliptic Curves (1994) (1950)
NTRU: A Ring-Based Public Key Cryptosystem (1998) (1654)
The Arithmetic of Dynamical Systems (2007) (654)
Diophantine Geometry: An Introduction (2000) (482)
Rational Points on Elliptic Curves (1992) (346)
NTRUSIGN: Digital Signatures Using the NTRU Lattice (2003) (279)
Canonical heights on varieties with morphisms (1993) (258)
An introduction to mathematical cryptography (2008) (228)
Heights and the specialization map for families of abelian varieties. (1983) (190)
A Friendly Introduction to Number Theory (1996) (178)
Wieferich's criterion and the abc-conjecture (1988) (177)
Rational periodic points of rational functions (1994) (172)
NSS: An NTRU Lattice-Based Signature Scheme (2001) (132)
Computing heights on elliptic curves (1988) (128)
The difference between the Weil height and the canonical height on elliptic curves (1990) (128)
The Impact of Decryption Failures on the Security of NTRU Encryption (2003) (127)
Choosing Parameters for NTRUEncrypt (2017) (124)
Periodic points, multiplicities, and dynamical units. (1995) (118)
The space of rational maps on P^1 (1996) (114)
Optimizations for NTRU (2001) (107)
Rational points on K3 surfaces: A new canonical height (1991) (107)
Lower bounds for height functions (1984) (101)
Elliptic Curve Discrete Logarithms and the Index Calculus (1998) (100)
Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3 (2005) (93)
The space of rational maps on $\mathbb{P}^1$ (1998) (93)
Integer points, Diophantine approximation, and iteration of rational maps (1993) (90)
NTRU in Constrained Devices (2001) (87)
Cryptography and Lattices (2001) (86)
The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem (2000) (84)
Arithmetic distance functions and height functions in diophantine geometry (1987) (81)
Analysis of the Xedni Calculus Attack (2000) (78)
Lower bound for the canonical height on elliptic curves (1981) (78)
Heights and Elliptic Curves (1986) (73)
A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves. (1987) (72)
Fast Multiplication in Finite Fields GF(2N) (1999) (71)
NAEP: Provable Security in the Presence of Decryption Failures (2003) (69)
Bielliptic curves and symmetric products (1991) (65)
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties (2012) (64)
Moduli Spaces and Arithmetic Dynamics (2012) (62)
On the rank of an elliptic surface (1998) (61)
Random small Hamming weight products with applications to cryptography (2003) (60)
Uniform bounds for the number of solutions to Yn = f(X) (1986) (55)
Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space (2011) (54)
The S-unit equation over function fields (1984) (52)
Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta’s Conjecture for Blowups (2004) (51)
Timing Attacks on NTRUEncrypt Via Variation in the Number of Hash Calls (2007) (48)
Primitive divisors in arithmetic dynamics (2007) (48)
The number of elliptic curves over ℚ with conductorNwith conductorN (1996) (45)
Polynomial Rings and Efficient Public Key Authentication II (2001) (42)
Practical Signatures from the Partial Fourier Recovery Problem (2014) (41)
The Theory of Height Functions (1986) (41)
Current trends and open problems in arithmetic dynamics (2018) (40)
Geometric and arithmetic properties of the Hénon map (1994) (40)
Integer Points on Curves of Genus 1 (1983) (39)
Integral Points in Arithmetic Progression on y2=x(x2−n2) (2000) (39)
Addendum to “Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties" (2013) (37)
An inequality relating the regulator and the discriminant of a number field (1984) (37)
A lower bound for the canonical height on abelian varieties over abelian extensions (2003) (36)
Examples of dynamical degree equals arithmetic degree (2012) (35)
Variation of periods modulo p in arithmetic dynamics (2007) (34)
Amicable Pairs and Aliquot Cycles for Elliptic Curves (2009) (33)
THE AVERAGE RANK OF AN ALGEBRAIC FAMILY OF ELLIPTIC CURVES (1998) (33)
Title: Estimated Breaking times for Ntru Lattices (1999) (33)
Ntru: a Public Key Cryptosystem (1999) (33)
Dynamics of projective morphisms having identical canonical heights (2007) (33)
S-INTEGER POINTS ON ELLIPTIC CURVES (1995) (33)
Sur le nombre de points de torsion rationnels sur une courbe elliptique (1999) (32)
A lower bound for the canonical height on elliptic curves over abelian extensions (2003) (31)
Exceptional Units and Numbers of Small Mahler Measure (1995) (31)
Variation of the Canonical Height On Elliptic-Surfaces II:: Local Analyticity Properties (1994) (31)
The sign of an elliptic divisibility sequence (2004) (30)
Invertibility in Truncated Polynomial Rings (1998) (29)
p-adic properties of division polynomials and elliptic divisibility sequences (2004) (29)
Nonarchimedean Green functions and dynamics on projective space (2007) (28)
Variation of the Canonical Height On Elliptic Surfaces III: Global Boundedness Properties (1994) (28)
Performance Improvements and a Baseline Parameter Generation Algorithm for NTRUSign (2005) (28)
Transcript Secure Signatures Based on Modular Lattices (2014) (28)
On the Linear Complexity of the Naor–Reingold Pseudo-random Function from Elliptic Curves (2001) (28)
Taxicabs and sums of two cubes (1993) (25)
Arithmetic and Dynamical Degrees on Abelian Varieties (2015) (24)
IEEE P1363.1 Draft 10: Draft Standard for Public Key Cryptographic Techniques Based on Hard Problems over Lattices. (2008) (24)
Representations of integers by binary forms and the rank of the Mordell-Weil group (1983) (24)
Computing canonical heights with little (or no) factorization (1997) (24)
Small Salem Numbers, Exceptional Units, and Lehmer's Conjecture (1996) (23)
Variation of the canonical height on elliptic surfaces I: Three examples. (1992) (23)
Divisibility of the Specialization Map for Families of Elliptic Curves (1985) (23)
Computing rational points on rank 1 elliptic curves via L-series and canonical heights (1999) (23)
The Markoff equation X2 + Y2 + Z2 = aXYZ over quadratic imaginary fields (1990) (22)
VARIATIONS ON A THEME OF ROMANOFF (1996) (21)
On the independence of Heegner points associated to distinct quadratic imaginary fields (2005) (21)
Uniform estimates for primitive divisors in elliptic divisibility sequences (2012) (21)
Weierstrass equations and the minimal discriminant of an elliptic curve (1984) (20)
Primitive Divisors, Dynamical Zsigmondy Sets, and Vojta's Conjecture (2012) (20)
The rank of elliptic surfaces in unramified abelian towers (2003) (19)
Integer points and the rank of Thue elliptic curves (1982) (19)
ON THE RANK OF ELLIPTIC CURVES (1999) (18)
ON THE RANK OF ELLIPTIC CURVES (1999) (18)
Wraps, Gaps, and Lattice Constants (2001) (18)
A Uniform Bound for Rational Points on Twists of a Given Curve (1993) (18)
Rational Points on Certain Families of Curves of Genus at Least 2 (1987) (17)
Terms in elliptic divisibility sequences divisible by their indices (2010) (17)
Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups (2018) (16)
Computing the canonical height on K3 surfaces (1996) (16)
A Local-Global Criterion for Dynamics on P^1 (2008) (16)
The Catalan equation over function fields (1982) (16)
A Bound For The Mordell-Weil Rank Of An Elliptic Surface After A Cyclic Base Extension (1998) (16)
Protecting NTRU Against Chosen Ciphertext and Reaction Attacks (2000) (16)
Fully Homomorphic Encryption from the Finite Field Isomorphism Problem (2018) (15)
Integral points on curves and surfaces (1989) (15)
Elliptic Carmichael Numbers and Elliptic Korselt Criteria (2011) (15)
Polynomial Rings and Eecient Public Key Authentication (2007) (14)
On the distribution of integer points on curves of genus zero (2000) (14)
ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS (2011) (14)
FINITE RAMIFICATION FOR PREIMAGE FIELDS OF POSTCRITICALLY FINITE MORPHISMS (2015) (14)
Common divisors of a n − 1 and b n − 1 over function fields (2004) (13)
NSS : The NTRU Signature Scheme (2000) (13)
On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture (2011) (13)
Height Estimates for Equidimensional Dominant Rational Maps (2009) (13)
MMSAT: A Scheme for Multimessage Multiuser Signature Aggregation (2020) (12)
Lifting and Elliptic Curve Discrete Logarithms (2009) (12)
The Neron-Tate height on elliptic curves (1982) (12)
Common divisors of an − 1 and bn − 1 over function fields (2004) (12)
The field of definition for dynamical systems on $\mathbb {P}^1$ (1995) (11)
Version 2 Title : Enhanced Encoding and Verification Methods for the NTRU Signature Scheme (2001) (11)
Some arithmetic properties of Weierstrass points: Hyperelliptic curves (1990) (11)
"Elliptic curve discrete logarithms and index calculus," ASIACRYPT'98 (1998) (11)
Rational Functions with a Polynomial Iterate (1996) (11)
Hecke points on modular curves (1990) (11)
Cryptography and Lattices: International Conference, CaLC 2001, Providence, RI, USA, March 29-30, 2001. Revised Papers (2001) (11)
Common divisors of elliptic divisibility sequences over function fields (2004) (11)
A quantitative estimate for quasi-integral points in orbits (2009) (10)
Rational Points on Symmetric Products of a Curve (1991) (9)
The Néron fiber of abelian varieties with potential good reduction (1983) (9)
An Algebraic Approach to NTRU (q = 2n) via Witt Vectors and Overdetermined Systems of Nonlinear Equations (2004) (9)
On a Dynamical Brauer-Manin Obstruction (2008) (9)
Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps (2006) (8)
Moduli spaces for dynamical systems with portraits (2018) (8)
The field of definition of dynamical systems on P (1995) (8)
An algebraic approach to certain cases of Thurston rigidity (2010) (8)
Integral points on Abelian varieties (1985) (8)
Rings of Low Multiplicative Complexity (2000) (8)
Dynamical Canonical Heights for Jordan Blocks and Arithmetic Degrees of Orbits (2013) (7)
Choosing Parameter Sets forwithand (2005) (7)
A Survey of Local and Global Pairings on Elliptic Curves and Abelian Varieties (2010) (7)
Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures (2017) (6)
The NTRU Signature Scheme : Theory and Practice (2001) (6)
Elliptic Curves and Cryptography (2014) (6)
Addendum to “p-adic properties of division polynomials and elliptic divisibility sequences” (2005) (6)
Divisibility Sequences and Powers of Algebraic Integers (2006) (6)
MiniPASS: Authentication and Digital Signatures in a Constrained Environment (2000) (6)
A Survey of the Arithmetic Theory of Elliptic Curves (1997) (5)
Canonical heights and the arithmetic complexity of morphisms on projective space (2007) (5)
Geometry and Arithmetic (2015) (5)
Integral points on abelian surfaces are widely spaced (1987) (4)
Multiple Weierstrass points (1991) (4)
The Geometry of Elliptic Curves (2009) (4)
Erratum to On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties (J. reine angew. Math. 713 (2016), 21–48) (2019) (4)
The aritmetic of elliptic curves (1986) (4)
A signature scheme from the finite field isomorphism problem (2020) (3)
PASS-Encrypt: a public key cryptosystem based on partial evaluation of polynomials (2015) (3)
A uniform quantitative Manin-Mumford theorem for curves over function fields (2021) (3)
Title: Plaintext Awareness and the Ntru Pkcs (1998) (3)
Elliptic curves of bounded degree and height (1989) (3)
Orbits on K3 Surfaces of Markoff Type (2022) (3)
The Distribution Relation and Inverse Function Theorem in Arithmetic Geometry (2020) (3)
The Space of Rational Maps on P (1996) (3)
The Group of Rational Points (1992) (3)
Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves (2012) (2)
A classification of degree $2$ semi-stable rational maps $\mathbb{P}^2\to\mathbb{P}^2$ with large finite dynamical automorphism group (2016) (2)
Common divisors of and over function fields. (2004) (2)
Post-Critically Finite Maps on $\mathbb{P}^n$ for $n\ge2$ are Sparse (2019) (2)
A Zeta Function over a Recurrent Sequence: 10486 (1999) (2)
Integrality properties of Böttcher coordinates for one-dimensional superattracting germs (2017) (2)
An Introduction to Cryptography (2014) (2)
GIT stability of Hénon maps (2019) (2)
Degeneration of Dynamical Degrees in Families of Maps (2016) (2)
Families of Dynamical Systems (2007) (2)
Lang's height conjecture and Szpiro's conjecture (2009) (2)
A uniform field-of-definition/field-of-moduli bound for dynamical systems on PN (2018) (2)
Counting integer and rational points on varieties (2019) (2)
Counting integer and rational points on varieties (2019) (2)
Further Results and Open Problems (2000) (1)
Lattices, cryptography, and the NTRU public key cryptosystem (2000) (1)
The Impa t of De ryption Failureson the Se urity of NTRU En ryptionNi (2007) (1)
Modified Parameter Attacks: Practical Attacks against CCA2 Secure Cryptosystems and Countermeasures (2004) (1)
Rational Points on Elliptic Surfaces (1998) (1)
Rational Points on Elliptic Surfaces (1998) (1)
Discrete Logarithms and Diffie Hellman (2014) (1)
The Néron Model (1994) (1)
Elliptic Curves over Finite Fields (2009) (1)
Field of moduli and field of definition (2012) (1)
Integral Points on Elliptic Curves (2009) (1)
Divisor Divisibility Sequences on Tori (2015) (1)
Lattices and Cryptography (2014) (1)
classification of degree 2 semi-stable rational maps P 2 → P 2 with large finite dynamical automorphism group (2019) (1)
A classification of degree $2$ semi-stable rational maps $\protect \mathbb{P}^2\rightarrow \protect \mathbb{P}^2$ with large finite dynamical automorphism group (2019) (1)
Algorithmic Aspects of Elliptic Curves (2009) (1)
Corrigendum to Integral points on Abelian varieties (1986) (1)
DIVISIBILITY OF THE SPECIALIZATION MAP FOR TWISTS OF ABELIAN VARIETIES (1999) (1)
Revised Papers from the International Conference on Cryptography and Lattices (2001) (1)
Good reduction of dynamical systems with preperiodic level structure and a Shafarevich-type conjecture (2017) (1)
What is... the p-adic Mandelbrot set? (2013) (1)
Rational Points on Abelian Varieties (2000) (1)
Rational points on, and the arithmetic of, elliptic curves: A tale of two books (and an article) (2017) (1)
The Geometry of Curves and Abelian Varieties (2000) (1)
The Rice University CCD Imager for Gamma-Ray Burst Studies (2006) (0)
Course Outline and Project Descriptions for a Course on Arithmetic Dynamics Arizona Winter (2009) (0)
Course Outline and Project Descriptions for a Course on Arithmetic Dynamics Arizona Winter (2009) (0)
An Introduction to Classical Dynamics (2007) (0)
LANDEN TRANSFORMS AS FAMILIES OF (COMMUTING) RATIONAL SELF-MAPS OF PROJECTIVE SPACE (2013) (0)
Powers of Algebraic Integers (2006) (0)
Additional Topics in Cryptography (2014) (0)
The average elliptic curve has few integral points (2014) (0)
Note for Technical Report #007 Version 2. the Material on Oaep in This Report Has Been Superceded by Ntru Technical Report #016, " Protecting Ntru against Chosen Ciphertext and Reaction Attacks, " Available At (1998) (0)
Dynamical moduli spaces–Further topics (2012) (0)
2 6 Ja n 20 04 Common divisors of a n − 1 and b n − 1 over function fields (2008) (0)
History and Overview of Peer Review of The NTRUEncrypt Public Key Cryptosystem (2001) (0)
Dynamics in Dimension Greater Than One (2007) (0)
Moduli spaces associated to dynamical systems (2012) (0)
A Century of Elliptic Curves (2015) (0)
Diophantine Approximation and Integral Points on Curves (2000) (0)
Elliptic Curves over $$\mathbb{C}$$ (2009) (0)
1998 Steele Prizes (1998) (0)
Integer Factorization and RSA (2014) (0)
An Alternative Approach using Quotient Varieties 18 (2018) (0)
Random Small Hamming Weight Products 3 1 Low Hamming Weight Exponents (2001) (0)
DA-Encrypt: Homomorphic Encryption via Non-Archimedean Diophantine Approximation - Preliminary Report (2015) (0)
Book Review: Some problems of unlikely intersections in arithmetic and geometry (2012) (0)
Rational points on elliptic curves : with 34 illustrations (2010) (0)
Points of Finite Order (2015) (0)
A Lehmer-type height lower bound for abelian surfaces over function fields (2021) (0)
Elliptic Curves over Local Fields (2009) (0)
The Formal Group of an Elliptic Curve (2009) (0)
To Write or Not to Write...A Book, and When? (2019) (0)
Review of the Book " an Introduction to Mathematical Cryptography " 3 Main Review (0)
Mean and Variance for Covering Sets of Congruences (1978) (0)
Combinatorics, Probability, and Information Theory (2014) (0)
Dynamics over Local Fields: Bad Reduction (2007) (0)
PASS-Encrypt: a public key cryptosystem based on partial evaluation of polynomials (2015) (0)
Elliptic Curves over ℂ (1986) (0)
A Heuristic Subexponential Algorithm to Find Paths in Markoff Graphs Over Finite Fields (2022) (0)
Local Height Functions (1994) (0)
Elliptic and Modular Functions (1994) (0)
NSS : A Lattice-Based Signature Scheme (2001) (0)
Elliptic curves (2013) (0)
Bibliography for Arithmetic Dynamical Systems (2007) (0)
NTRUSign : Digital Signatures Using the NTRULatti eJe (2002) (0)
Rational Points on Curves of Genus at Least 2 (2000) (0)
The average elliptic curve has few integral (2014) (0)
Dynamics over Global Fields (2007) (0)
Liang-Chung HSIA et Joseph SILVERMAN On a dynamical Brauer–Manin obstruction (2009) (0)
Book Review: Arithmetic of algebraic curves (1996) (0)
Dynamics of projective morphisms having identical canonical heights (2008) (0)
Elliptic Curves over Complete Fields (1994) (0)
N T ] 2 F eb 2 00 4 Common Divisors of Elliptic Divisibility Sequences over Function Fields (2004) (0)
An Accompaniment to Higher Mathematics.@@@Journey into Mathematics: An Introduction to Proofs.@@@Mathematical Thinking: Problem Solving and Proofs. (1999) (0)
Integer Points on Cubic Curves (2015) (0)
Local-global aspects of (hyper)elliptic curves over (in)finite fields (2010) (0)
Points of finite order on Elliptic curves (1986) (0)
An Accompaniment to Higher Mathematics. By George R. Exner, Journey into Mathematics: An Introduction to Proofs. By Joseph Rotman, Mathematical Thinking: Problem Solving and Proofs. By John P. D'Angelo and Douglas B. West (1999) (0)
The size of semigroup orbits modulo primes (2023) (0)
Dynamics Associated to Algebraic Groups (2007) (0)
Dynatomic polynomials and dynamical modular curves (2012) (0)
The geometry of dynamical moduli spaces (2012) (0)
DYNAMICS AND RATIONAL MAPS A NEW SECTION FOR CHAPTER 7 OF THE ARITHMETIC OF DYNAMICAL SYSTEMS (2014) (0)
Review: Serge Lang, Introduction to Arakelov theory (1989) (0)
On Lehmer's Conjecture for Polynomials and for Elliptic Curves (2010) (0)
Computing the Mordell-Weil Group (2009) (0)
Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization (2017) (0)
Cubic Curves over Finite Fields (2015) (0)

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