J. Silverman

发表

NTRU: A Ring-Based Public Key Cryptosystem

Joseph H. Silverman, Jill Pipher, Jeffrey Hoffstein, 1998, ANTS.

Advanced Topics in the Arithmetic of Elliptic Curves

J. Silverman, 1994 .

Rational Points on Elliptic Curves

J. Silverman, J. Tate, 1992 .

An introduction to mathematical cryptography

J. Hoffstein, J. Pipher, J. Silverman, 2008 .

The Impact of Decryption Failures on the Security of NTRU Encryption

David Pointcheval, William Whyte, Phong Q. Nguyen, 2003, CRYPTO.

Title: Estimated Breaking times for Ntru Lattices

J. Silverman, 1999 .

Invertibility in Truncated Polynomial Rings

J. Silverman, 1998 .

Wieferich's criterion and the abc-conjecture

Joseph H. Silverman, J. Silverman, 1988 .

"Elliptic curve discrete logarithms and index calculus," ASIACRYPT'98

J. Silverman, 1998 .

Ntru: a Public Key Cryptosystem

J. Hoffstein, J. Pipher, J. Silverman, 1999 .

The Arithmetic of Dynamical Systems

J. Silverman, 2007 .

Polynomial Rings and Eecient Public Key Authentication

J. Silverman, 2007 .

Random Small Hamming Weight Products 3 1 Low Hamming Weight Exponents

J. Hoffstein, J. Silverman, 2001 .

NSS : A Lattice-Based Signature Scheme

J. Hoffstein, J. Pipher, J. Silverman, 2001 .

The NTRU Signature Scheme : Theory and Practice

J. Hoffstein, J. Pipher, J. Silverman, 2001 .

NSS : The NTRU Signature Scheme

J. Hoffstein, J. Pipher, J. Silverman, 2000 .

Diophantine Geometry: An Introduction

Joseph H. Silverman, Marc Hindry, J. Silverman, 2000 .

Computing heights on elliptic curves

Joseph H. Silverman, J. Silverman, 1988 .

Current trends and open problems in arithmetic dynamics

J. Silverman, R. Benedetto, T. Tucker, 2018, Bulletin of the American Mathematical Society.

2 6 Ja n 20 04 Common divisors of a n − 1 and b n − 1 over function fields

J. Silverman, 2008 .

Common divisors of an − 1 and bn − 1 over function fields

J. Silverman, 2004 .

Elliptic Curves over Local Fields

J. Silverman, 2009 .

The Formal Group of an Elliptic Curve

J. Silverman, 2009 .

The Geometry of Elliptic Curves

J. Silverman, 2009 .

Elliptic Curves over $$\mathbb{C}$$

J. Silverman, 2009 .

Elliptic Curves over Finite Fields

J. Silverman, 2009 .

Integral Points on Elliptic Curves

J. Silverman, Joseph H. Silverman, 2009 .

Computing the Mordell-Weil Group

J. Silverman, 2009 .

S-INTEGER POINTS ON ELLIPTIC CURVES

J. Silverman, R. Gross, 1995 .

Points of finite order on Elliptic curves

J. Silverman, 1986 .

A quantitative estimate for quasi-integral points in orbits

J. Silverman, Liang-Chung Hsia, 2009, 0910.4498.

NTRUSIGN: Digital Signatures Using the NTRU Lattice

William Whyte, Nick Howgrave-Graham, Joseph H. Silverman, 2003, CT-RSA.

Integrality properties of Böttcher coordinates for one-dimensional superattracting germs

J. Silverman, Adriana Salerno, 2017, Ergodic Theory and Dynamical Systems.

Primitive Divisors, Dynamical Zsigmondy Sets, and Vojta's Conjecture

J. Silverman, 2012, 1209.3491.

Examples of dynamical degree equals arithmetic degree

J. Silverman, Shu Kawaguchi, 2012, 1212.3015.

Rational points on K3 surfaces: A new canonical height

J. Silverman, 1991 .

Uniform bounds for the number of solutions to Yn = f(X)

Jan-Hendrik Evertse, Joseph H. Silverman, J. Silverman, 1986, Mathematical Proceedings of the Cambridge Philosophical Society.

The Catalan equation over function fields

J. Silverman, 1982 .

Integer Points on Curves of Genus 1

J. Silverman, 1983 .

Variation of periods modulo p in arithmetic dynamics

J. Silverman, 2007, 0707.1505.

IEEE P1363.1 Draft 10: Draft Standard for Public Key Cryptographic Techniques Based on Hard Problems over Lattices.

Nick Howgrave-Graham, Joseph H. Silverman, Philip S. Hirschhorn, 2008 .

Heights and the specialization map for families of abelian varieties.

Joseph H. Silverman, J. Silverman, 1983 .

Elliptic Curves over Local Fields

J. Silverman, 2009 .

Elliptic Curves over Finite Fields

J. Silverman, 2009 .

DIVISIBILITY OF THE SPECIALIZATION MAP FOR TWISTS OF ABELIAN VARIETIES

J. Silverman, 1999 .

Variation of the canonical height on elliptic surfaces I: Three examples.

J. Silverman, 1992 .

Elliptic curves

Joseph H. Silverman, J. Silverman, 2013, Handbook of Finite Fields.

On the distribution of integer points on curves of genus zero

Joseph H. Silverman, J. Silverman, 2000, Theor. Comput. Sci..

Integer Factorization and RSA

J. Hoffstein, J. Pipher, J. Silverman, 2014 .

A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.

Joseph H. Silverman, J. Silverman, 1987 .

The Distribution Relation and Inverse Function Theorem in Arithmetic Geometry

J. Silverman, Yohsuke Matsuzawa, 2020, 2008.08149.

The average elliptic curve has few integral

Katherine E. Stange, Henry Cohn, J. Silverman, 2014 .

Lower bounds for height functions

J. Silverman, 1984 .

The Néron fiber of abelian varieties with potential good reduction

J. Silverman, 1983 .

Elliptic curves

J. Silverman, 2013, Handbook of Finite Fields.

Elliptic Curves and Cryptography

J. Hoffstein, J. Pipher, J. Silverman, 2014 .

On the independence of Heegner points associated to distinct quadratic imaginary fields

J. Silverman, M. Rosen, 2005, math/0508259.

p-adic properties of division polynomials and elliptic divisibility sequences

J. Silverman, 2004, math/0404412.

A lower bound for the canonical height on abelian varieties over abelian extensions

J. Silverman, M. Baker, 2003, math/0312393.

A lower bound for the canonical height on elliptic curves over abelian extensions

J. Silverman, 2003, math/0305041.

Orbits on K3 Surfaces of Markoff Type

J. Silverman, E. Fuchs, M. Litman, 2022, 2201.12588.

Counting integer and rational points on varieties

J. Silverman, 2019 .

Lower bound for the canonical height on elliptic curves

Joseph H. Silverman, J. Silverman, 1981 .

Integral Points in Arithmetic Progression on y2=x(x2−n2)

J. Silverman, N. Tzanakis, A. Bremner, 2000 .

Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

J. Silverman, I. Shparlinski, Alina Ostafe, 2018, International Mathematics Research Notices.

Bielliptic curves and symmetric products

Joe W. Harris, J. Silverman, J. Harris, 1991 .

O ct 2 01 9 POST-CRITICALLY FINITE MAPS ON P n FOR n ≥ 2 ARE SPARSE

J. Silverman, Patrick Ingram, Rohini Ramadas, 2019 .

An Alternative Approach using Quotient Varieties 18

J. Silverman, 2018 .

A classification of degree $2$ semi-stable rational maps $\mathbb{P}^2\to\mathbb{P}^2$ with large finite dynamical automorphism group

J. Silverman, M. Manes, 2016, 1607.05772.

What is... the p-adic Mandelbrot set?

J. Silverman, 2013 .

LANDEN TRANSFORMS AS FAMILIES OF (COMMUTING) RATIONAL SELF-MAPS OF PROJECTIVE SPACE

J. Silverman, Shu Kawaguchi, Michael Joyce, 2013, 1308.5355.

An algebraic approach to certain cases of Thurston rigidity

J. Silverman, 2010, 1010.4562.

Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta’s Conjecture for Blowups

J. Silverman, 2004, math/0407415.

Elliptic curves of bounded degree and height

J. Silverman, 1989 .

History and Overview of Peer Review of The NTRUEncrypt Public Key Cryptosystem

J. Pipher, J. Silverman, 2001 .

Liang-Chung HSIA et Joseph SILVERMAN On a dynamical Brauer–Manin obstruction

J. Silverman, 2009 .

An inequality relating the regulator and the discriminant of a number field

J. Silverman, 1984 .

classification of degree 2 semi-stable rational maps P 2 → P 2 with large finite dynamical automorphism group

J. Silverman, M. Manes, 2019 .

Moduli Spaces and Arithmetic Dynamics

J. Silverman, 2012 .

Canonical heights and the arithmetic complexity of morphisms on projective space

J. Silverman, Shu Kawaguchi, 2007, 0706.2166.

The space of rational maps on P^1

J. Silverman, 1996, math/9609212.

Sur le nombre de points de torsion rationnels sur une courbe elliptique

Joseph H. Silverman, Marc Hindry, J. Silverman, 1999 .

Good reduction of dynamical systems with preperiodic level structure and a Shafarevich-type conjecture

J. Silverman, 2017 .

Common divisors of elliptic divisibility sequences over function fields

J. Silverman, 2004, math/0402016.

Integer Points on Cubic Curves

J. Silverman, J. Tate, 2015 .

Random small Hamming weight products with applications to cryptography

J. Hoffstein, J. Silverman, 2003, Discret. Appl. Math..

The sign of an elliptic divisibility sequence

J. Silverman, N. Stephens, 2004, math/0402415.

Powers of Algebraic Integers

J. Silverman, 2006 .

Rational Points on Elliptic Curves

J. Silverman, J. Tate, 1992 .

THE AVERAGE RANK OF AN ALGEBRAIC FAMILY OF ELLIPTIC CURVES

J. Silverman, 1998 .

Cryptography and Lattices

Joseph H. Silverman, J. Silverman, 2001, Lecture Notes in Computer Science.

Choosing Parameters for NTRUEncrypt

William Whyte, Joseph H. Silverman, Zhenfei Zhang, 2017, CT-RSA.

NTRUSIGN: Digital Signatures Using the NTRU Lattice

Nick Howgrave-Graham, J. Hoffstein, J. Pipher, 2003, CT-RSA.

A Heuristic Subexponential Algorithm to Find Paths in Markoff Graphs Over Finite Fields

J. Silverman, 2022, ArXiv.

MMSAT: A Scheme for Multimessage Multiuser Signature Aggregation

Berk Sunar, Joseph H. Silverman, Jeffrey Hoffstein, 2020, IACR Cryptol. ePrint Arch..

ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS

Katherine E. Stange, J. Silverman, Marco Streng, 2011, Journal of the Australian Mathematical Society.

Integer points, Diophantine approximation, and iteration of rational maps

Joseph H. Silverman, J. Silverman, 1993 .

Bibliography for Arithmetic Dynamical Systems

J. Silverman, 2007 .

The Neron-Tate height on elliptic curves

Joseph H. Silverman, J. Silverman, 1982 .

Computing rational points on rank 1 elliptic curves via L-series and canonical heights

Joseph H. Silverman, J. Silverman, 1999, Math. Comput..

Rational Points on Elliptic Surfaces

J. Silverman, 1998 .

The arithmetic of elliptic curves

Joseph H. Silverman, J. Silverman, 1986, Graduate texts in mathematics.

Weierstrass equations and the minimal discriminant of an elliptic curve

Joseph H. Silverman, J. Silverman, 1984 .

The rank of elliptic surfaces in unramified abelian towers

J. Silverman, 2003, math/0305028.

A Bound For The Mordell-Weil Rank Of An Elliptic Surface After A Cyclic Base Extension

J. Silverman, 1998 .

A uniform field-of-definition/field-of-moduli bound for dynamical systems on PN

J. Doyle, J. Silverman, 2018, Journal of Number Theory.

Moduli spaces for dynamical systems with portraits

J. Doyle, J. Silverman, 2018, 1812.09936.

Elliptic Curve Discrete Logarithms and the Index Calculus

Joe Suzuki, Joseph H. Silverman, J. Suzuki, 1998, ASIACRYPT.

NAEP: Provable Security in the Presence of Decryption Failures

William Whyte, Nick Howgrave-Graham, Joseph H. Silverman, 2003, IACR Cryptol. ePrint Arch..

NSS: An NTRU Lattice-Based Signature Scheme

Joseph H. Silverman, Jill Pipher, Jeffrey Hoffstein, 2001, EUROCRYPT.

Performance Improvements and a Baseline Parameter Generation Algorithm for NTRUSign

William Whyte, Nick Howgrave-Graham, Joseph H. Silverman, 2005, IACR Cryptol. ePrint Arch..

Fast Multiplication in Finite Fields GF(2N)

Joseph H. Silverman, J. Silverman, 1999, CHES.

Lifting and Elliptic Curve Discrete Logarithms

Joseph H. Silverman, J. Silverman, 2009, Selected Areas in Cryptography.

Cubic Curves over Finite Fields

J. Silverman, J. Tate, 2015 .

Variation of the Canonical Height On Elliptic-Surfaces II:: Local Analyticity Properties

J. Silverman, 1994 .

Variation of the Canonical Height On Elliptic Surfaces III: Global Boundedness Properties

J. Silverman, 1994 .

The average elliptic curve has few integral points

Katherine E. Stange, Henry Cohn, J. Silverman, 2014 .

A Uniform Bound for Rational Points on Twists of a Given Curve

J. Silverman, 1993 .

A uniform quantitative Manin-Mumford theorem for curves over function fields

Robert Wilms, Joseph Silverman, Nicole R. Looper, 2021, 2101.11593.

Propagation of Zariski Dense Orbits

J. Silverman, H. Pasten, 2023, 2307.12097.

FINITE RAMIFICATION FOR PREIMAGE FIELDS OF POSTCRITICALLY FINITE MORPHISMS

Alon Y. Levy, J. Silverman, M. Manes, 2015, 1511.00194.

Arithmetic and Dynamical Degrees on Abelian Varieties

J. Silverman, 2015, 1501.04205.

On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties

J. Silverman, Shu Kawaguchi, 2012, 1208.0815.

Amicable Pairs and Aliquot Cycles for Elliptic Curves

Joseph H. Silverman, Katherine E. Stange, J. Silverman, 2009, Exp. Math..

Height Estimates for Equidimensional Dominant Rational Maps

J. Silverman, 2009, 0908.3835.

Dynamics of projective morphisms having identical canonical heights

J. Silverman, Shu Kawaguchi, 2007 .

Rational Functions with a Polynomial Iterate

J. Silverman, 1996 .

Rational Points on Certain Families of Curves of Genus at Least 2

J. Silverman, 1987 .

Arithmetic distance functions and height functions in diophantine geometry

Joseph H. Silverman, J. Silverman, 1987 .

Addendum to “Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties"

J. Silverman, Shu Kawaguchi, 2013, Transactions of the American Mathematical Society.

Dynamical Canonical Heights for Jordan Blocks and Arithmetic Degrees of Orbits

J. Silverman, Shu Kawaguchi, 2013 .

Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space

J. Silverman, 2011, Ergodic Theory and Dynamical Systems.

Canonical heights on varieties with morphisms

Gregory S. Call, J. Silverman, 1993 .

The space of rational maps on $\mathbb{P}^1$

Joseph H. Silverman, J. Silverman, 1998 .

Integral points on curves and surfaces

J. Silverman, 1989 .

Geometric and arithmetic properties of the Hénon map

J. Silverman, 1994 .

Rational periodic points of rational functions

Joseph H. Silverman, Patrick Morton, J. Silverman, 1994 .

Divisibility of the Specialization Map for Families of Elliptic Curves

Joseph H. Silverman, J. Silverman, 1985 .

Divisibility Sequences and Powers of Algebraic Integers

Joseph H. Silverman, J. Silverman, 2006 .

N T ] 2 F eb 2 00 4 Common Divisors of Elliptic Divisibility Sequences over Function Fields

J. Silverman, 2004 .

On the Linear Complexity of the Naor–Reingold Pseudo-random Function from Elliptic Curves

Igor E. Shparlinski, Joseph H. Silverman, J. Silverman, 2001, Des. Codes Cryptogr..

ON THE RANK OF ELLIPTIC CURVES

J. Silverman, 1999 .

Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps

J. Silverman, 2006 .

GIT stability of Hénon maps

J. Silverman, C. Lee, 2019, Proceedings of the American Mathematical Society.

Periodic points, multiplicities, and dynamical units.

Joseph H. Silverman, Patrick Morton, J. Silverman, 1995 .

Integral points on Abelian varieties

J. Silverman, 1985 .

Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3

William Whyte, Nick Howgrave-Graham, Joseph H. Silverman, 2005, IACR Cryptol. ePrint Arch..

Timing Attacks on NTRUEncrypt Via Variation in the Number of Hash Calls

William Whyte, Joseph H. Silverman, J. Silverman, 2007, CT-RSA.

Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures

J. Silverman, 2017, 1703.00823.

Divisor Divisibility Sequences on Tori

J. Silverman, 2015, 1511.09038.

Algorithmic Aspects of Elliptic Curves

Joseph H. Silverman, J. Silverman, 2009 .

Nonarchimedean Green functions and dynamics on projective space

J. Silverman, Shu Kawaguchi, 2007, 0706.2169.

An Introduction to Lattices, Lattice Reduction, and Lattice-Based Cryptography

J. Silverman, 2022 .

Lattices and Cryptography

J. Hoffstein, J. Pipher, J. Silverman, 2014 .

Some arithmetic properties of Weierstrass points: Hyperelliptic curves

J. Silverman, 1990 .

Addendum to “p-adic properties of division polynomials and elliptic divisibility sequences”

J. Silverman, 2005 .

On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture

J. Silverman, B. Viray, 2011, 1109.0207.

A Friendly Introduction to Number Theory

Joseph H. Silverman, J. Silverman, 1996 .

Computing rational points on rank 1 elliptic curves via L-series and canonical heights

J. Silverman, 1999, Mathematics of Computation.

Computing heights on elliptic curves

J. Silverman, 1988 .

Analysis of the Xedni Calculus Attack

Andreas Stein, Michael J. Jacobson, Joseph H. Silverman, 2000, Des. Codes Cryptogr..

The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem

Joseph H. Silverman, J. Silverman, 2000, Des. Codes Cryptogr..

The number of elliptic curves over ℚ with conductorNwith conductorN

J. Silverman, A. Brumer, 1996 .

Taxicabs and sums of two cubes

J. Silverman, 1993 .

The canonical height and integral points on elliptic curves

Joseph H. Silverman, J. Silverman, M. Hindry, 1988 .

Representations of integers by binary forms and the rank of the Mordell-Weil group

J. Silverman, 1983 .

Computing canonical heights with little (or no) factorization

Joseph H. Silverman, J. Silverman, 1997, Math. Comput..

The difference between the Weil height and the canonical height on elliptic curves

Joseph H. Silverman, J. Silverman, 1990 .

Computing the canonical height on K3 surfaces

Joseph H. Silverman, Gregory S. Call, J. Silverman, 1996, Math. Comput..

A Lehmer-type height lower bound for abelian surfaces over function fields

Joseph H. Silverman, Nicole R. Looper, J. Silverman, 2021, 2108.09577.

The size of semigroup orbits modulo primes

J. Silverman, W. Hindes, 2023, Pacific Journal of Mathematics.