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Silverman, Joseph Hillel

Author ID: silverman.joseph-hillel Recent zbMATH articles by "Silverman, Joseph Hillel"
Published as: Silverman, Joseph H.; Silverman, J. H.; Silverman, Joseph
Homepage: http://www.math.brown.edu/johsilve/
External Links: MGP · ORCID · Wikidata · Google Scholar · MathOverflow · dblp · GND · IdRef
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Co-Authors

100 single-authored
15 Hoffstein, Jeffrey
9 Kawaguchi, Shu
9 Pipher, Jill Catherine
9 Whyte, William
6 Ingram, Patrick
4 Hindry, Marc
4 Rosen, Michael I.
4 Voloch, José Felipe
3 Call, Gregory S.
3 Cornell, Gary
3 Howgrave-Graham, Nick A.
3 Manes, Michelle
3 Schanck, John M.
3 Shparlinski, Igor E.
3 Stange, Katherine E.
3 Zhang, Zhenfei
2 Doyle, John R.
2 Hsia, Liang-Chung
2 Jacobson, Michael John jun.
2 Jones, Rafe
2 Looper, Nicole R.
2 Morton, Patrick
2 Murty, Maruti Ram
2 Ostafe, Alina
2 Stevens, Glenn
2 Tate, John Torrence jun.
1 Acquista, Karen
1 Ahmadi, Omran
1 Bailey, Daniel V.
1 Baker, Matthew H.
1 Ball, L. Simeon
1 Benedetto, Robert L.
1 Bérczes, Attila
1 Bernstein, Daniel Julius
1 Blache, Régis
1 Blake, Ian F.
1 Blokhuis, Aart
1 Bremner, Andrew
1 Bridy, Andrew
1 Brumer, Armand
1 Buhler, Joe P.
1 Carlet, Claude
1 Castro, Francis Noel
1 Chand Gupta, Kishan
1 Charpin, Pascale
1 Cioabă, Sebastian M.
1 Clausen, Dustin
1 Coates, John Henry
1 Coffin, Daniel
1 Cohen, Stephen D.
1 Colbourn, Charles J.
1 Coulter, Robert S.
1 de Smit, Bart
1 Ding, Jintai
1 Dinitz, Jeffrey H.
1 Doche, Christophe
1 Doröz, Yarkın
1 Dumas, Jean-Guillaume
1 Ebert, Gary Lee
1 Effinger, Gove W.
1 Elbirt, Adam J.
1 Enge, Andreas
1 Evans, Ronald J.
1 Evertse, Jan-Hendrik
1 Fan, Haining
1 Fitzgerald, Robert W.
1 Fried, Michael David
1 Fu, Lei
1 Fuchs, Elena D.
1 Gao, Shuhong
1 Garaev, Moubariz Z.
1 Garcia, Arnaldo
1 Giesbrecht, Mark W.
1 Gong, Guang
1 Goss, David Mark
1 Gow, Roderick
1 Gross, Benedict Hyman
1 Hachenberger, Dirk
1 Hardy, Godfrey Harold
1 Harris, Joseph Daniel
1 Hasan, M. Anwar
1 Heath-Brown, Roger
1 Helleseth, Tor
1 Hindes, Wade
1 Hinkelmann, Franziska
1 Hirschfeld, James William Peter
1 Hou, Xiang-Dong
1 Huffman, W. Cary
1 Jedwab, Jonathan
1 Joyce, Michael
1 Jungnickel, Dieter
1 Juul, Jamie
1 Kaltofen, Erich L.
1 Kholosha, Alexander
1 Koblitz, Neal I.
1 Kyuregyan, Melsik K.
1 Lange, Tanja
1 Laubenbacher, Reinhard C.
1 Lecerf, Grégoire
1 Lee, Chong Gyu
...and 69 more Co-Authors
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Serials

11 Journal of Number Theory
8 Journal für die Reine und Angewandte Mathematik
7 Inventiones Mathematicae
5 Mathematics of Computation
5 Acta Arithmetica
5 Duke Mathematical Journal
5 Graduate Texts in Mathematics
4 Compositio Mathematica
4 Pacific Journal of Mathematics
4 Proceedings of the American Mathematical Society
4 Transactions of the American Mathematical Society
4 Designs, Codes and Cryptography
4 Undergraduate Texts in Mathematics
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Mathematische Annalen
3 Journal de Théorie des Nombres de Bordeaux
3 The New York Journal of Mathematics
3 Mathematical Research Letters
2 American Mathematical Monthly
2 American Journal of Mathematics
2 Journal of the London Mathematical Society. Second Series
2 Manuscripta Mathematica
2 Mathematische Zeitschrift
2 Proceedings of the London Mathematical Society. Third Series
2 Ergodic Theory and Dynamical Systems
2 Journal of the Ramanujan Mathematical Society
2 IMRN. International Mathematics Research Notices
2 Bulletin of the American Mathematical Society. New Series
2 Notices of the American Mathematical Society
2 Experimental Mathematics
2 Journal of Algebraic Geometry
2 Pure and Applied Mathematics Quarterly
1 Discrete Applied Mathematics
1 Rocky Mountain Journal of Mathematics
1 Mathematics Magazine
1 Illinois Journal of Mathematics
1 Journal of Algebra
1 Mathematika
1 Michigan Mathematical Journal
1 Monatshefte für Mathematik
1 Theoretical Computer Science
1 International Journal of Mathematics
1 Nieuw Archief voor Wiskunde. Vierde Serie
1 Boletim da Sociedade Brasileira de Matemática. Nova Série
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Finite Fields and their Applications
1 Documenta Mathematica
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Journal of the Australian Mathematical Society
1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series
1 CRM Monograph Series
1 Lecture Notes in Computer Science
1 Journal of Mathematical Cryptology
1 Advances in Mathematics of Communications
1 Pure and Applied Undergraduate Texts
1 Discrete Mathematics and its Applications

Publications by Year

Citations contained in zbMATH Open

155 Publications have been cited 5,420 times in 3,637 Documents Cited by Year
The arithmetic of elliptic curves. Zbl 0585.14026
Silverman, Joseph H.
987
1986
The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005
Silverman, Joseph H.
777
2009
Advanced topics in the arithmetic of elliptic curves. Zbl 0911.14015
Silverman, Joseph H.
597
1994
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
448
2008
Diophantine geometry. An introduction. Zbl 0948.11023
Hindry, Marc; Silverman, Joseph H.
290
2000
The arithmetic of dynamical systems. Zbl 1130.37001
Silverman, Joseph H.
280
2007
Handbook of finite fields. Zbl 1319.11001
218
2013
NTRU: A ring-based public key cryptosystem. Zbl 1067.94538
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
199
1998
Rational points on elliptic curves. Zbl 0752.14034
Silverman, Joseph H.; Tate, John
154
1992
Canonical heights on varieties with morphisms. Zbl 0826.14015
Call, Gregory S.; Silverman, Joseph H.
104
1993
Heights and the specialization map for families of abelian varieties. Zbl 0505.14035
Silverman, Joseph H.
77
1983
Wieferich’s criterion and the abc-conjecture. Zbl 0654.10019
Silverman, Joseph H.
70
1988
Rational periodic points of rational functions. Zbl 0819.11045
Morton, Patrick; Silverman, Joseph H.
67
1994
The canonical height and integral points on elliptic curves. Zbl 0657.14018
Hindry, M.; Silverman, J. H.
56
1988
The space of rational maps on \(\mathbf P^1\). Zbl 0966.14031
Silverman, Joseph H.
55
1998
Lower bounds for height functions. Zbl 0579.14035
Silverman, Joseph H.
51
1984
Arithmetic geometry. (Papers presented at the Conference held from July 30 through August 10, 1984 at the University of Connecticut in Storrs). Zbl 0596.00007
51
1986
The difference between the Weil height and the canonical height on elliptic curves. Zbl 0729.14026
Silverman, Joseph H.
48
1990
NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525
Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William
46
2003
Integer points, diophantine approximation, and iteration of rational maps. Zbl 0811.11052
Silverman, Joseph H.
44
1993
Computig heights on elliptic curves. Zbl 0656.14016
Silverman, Joseph H.
43
1988
Periodic points, multiplicities, and dynamical units. Zbl 0813.11059
Morton, Patrick; Silverman, Joseph H.
43
1995
An introduction to mathematical cryptography. Zbl 1160.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
42
2008
Rational points on K3 surfaces: A new canonical height. Zbl 0754.14023
Silverman, Joseph H.
36
1991
Bielliptic curves and symmetric products. Zbl 0727.11023
Harris, Joe; Silverman, Joseph H.
36
1991
Arithmetic distance functions and height functions in diophantine geometry. Zbl 0607.14013
Silverman, Joseph H.
35
1987
Lower bound for the canonical height on elliptic curves. Zbl 0475.14033
Silverman, Joseph H.
31
1981
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115
Kawaguchi, Shu; Silverman, Joseph H.
30
2016
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
30
2009
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
29
2015
The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\). Zbl 0868.11029
Brumer, Armand; Silverman, Joseph H.
29
1996
Moduli spaces and arithmetic dynamics. Zbl 1247.37004
Silverman, Joseph H.
29
2012
Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070
Silverman, Joseph H.
28
2005
Heights and elliptic curves. Zbl 0603.14020
Silverman, Joseph H.
27
1986
Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093
Silverman, Joseph H.
25
2014
Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\). Zbl 1009.11035
Bremner, A.; Silverman, J. H.; Tzanakis, N.
22
2000
Uniform bounds for the number of solutions to \(Y^ n=f(X)\). Zbl 0611.10009
Evertse, J.-H.; Silverman, J. H.
22
1986
The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377
Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William
22
2003
Current trends and open problems in arithmetic dynamics. Zbl 1468.37001
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J.
22
2019
Divisibility of the specialization map for families of elliptic curves. Zbl 0613.14029
Silverman, Joseph H.
21
1985
Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078
Kawaguchi, Shu; Silverman, Joseph H.
20
2016
An inequality relating the regulator and the discriminant of a number field. Zbl 0552.12003
Silverman, Joseph H.
20
1984
The field of definition for dynamical systems on \(\mathbb{P}^ 1\). Zbl 0849.11090
Silverman, Joseph H.
19
1995
Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084
Kawaguchi, Shu; Silverman, Joseph H.
18
2014
Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091
Silverman, Joseph H.
18
2017
The S-unit equation over function fields. Zbl 0533.10013
Silverman, Joseph H.
17
1984
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500
16
2000
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
16
1998
Choosing parameters for NTRUEncrypt. Zbl 1383.94022
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei
16
2017
The Markoff equation \(X^ 2+Y^ 2+Z^ 2=aXYZ\) over quadratic imaginary fields. Zbl 0702.11012
Silverman, Joseph H.
15
1990
Variation of periods modulo \(p\) in arithmetic dynamics. Zbl 1153.11028
Silverman, Joseph H.
15
2008
Integer points and the rank of Thue elliptic curves. Zbl 0494.14008
Silverman, Joseph H.
15
1982
On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504
Shparlinski, Igor E.; Silverman, Joseph H.
14
2001
On the distribution of integer points on curves of genus zero. Zbl 0979.11037
Silverman, J. H.
14
2000
NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
14
2001
A quantitative version of Siegel’s theorem: integral points on elliptic curves and Catalan curves. Zbl 0608.14021
Silverman, Joseph H.
14
1987
Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035
Kawaguchi, Shu; Silverman, Joseph H.
14
2007
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
13
2012
Geometric and arithmetic properties of the Hénon map. Zbl 0807.58021
Silverman, Joseph H.
13
1994
Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009
Kawaguchi, Shu; Silverman, Joseph H.
13
2009
\(p\)-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024
Silverman, Joseph H.
12
2005
Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015
Silverman, Joseph H.
12
2004
Dimension reduction methods for convolution modular lattices. Zbl 1006.11033
May, Alexander; Silverman, Joseph H.
12
2001
The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049
Silverman, Joseph H.
12
2000
Exceptional units and numbers of small Mahler measure. Zbl 0851.11064
Silverman, Joseph H.
12
1995
Integer points on curves of genus 1. Zbl 0487.10015
Silverman, Joseph H.
12
1983
Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046
Silverman, Joseph H.
11
2013
On the number of rational torsion points on an elliptic curve. (Sur le nombre de points de torsion rationnels sur une courbe elliptique.) Zbl 0993.11028
Hindry, Marc; Silverman, Joseph
11
1999
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004
11
1997
Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079
Silverman, Joseph H.; Stange, Katherine E.
11
2011
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553
Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William
11
2005
Representations of integers by binary forms and the rank of the Mordell- Weil group. Zbl 0525.14012
Silverman, J. H.
11
1983
Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056
Silverman, Joseph H.; Stange, Katherine E.
11
2011
An upper bound for the conductor of an abelian variety. Zbl 0816.14021
Lockhart, Paul; Rosen, Michael; Silverman, Joseph H.
11
1993
Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045
Silverman, Joseph H.
10
1996
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
10
1996
A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041
Baker, Matthew H.; Silverman, Joseph H.
10
2004
A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052
Silverman, Joseph H.
10
2004
Analysis of the Xedni calculus attack. Zbl 0948.11048
Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn
10
2000
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
10
2007
Taxicabs and sums of two cubes. Zbl 0796.11022
Silverman, Joseph H.
9
1993
On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153
Silverman, Joseph H.; Viray, Bianca
9
2013
Common divisors of \(a^n-1\) and \(b^n-1\) over function fields. Zbl 1120.11045
Silverman, Joseph H.
9
2004
The average rank of an algebraic family of elliptic curves. Zbl 0923.11087
Silverman, Joseph H.
9
1998
Random small Hamming weight products with applications to cryptography. Zbl 1028.94023
Hoffstein, Jeffrey; Silverman, Joseph H.
9
2003
On Lehmer’s conjecture for elliptic curves. Zbl 0741.14013
Hindry, Marc; Silverman, Joseph H.
8
1990
Transcript secure signatures based on modular lattices. Zbl 1380.94099
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William
8
2014
Multiplicative dependence among iterated values of rational functions modulo finitely generated groups. Zbl 1490.37115
Bérczes, Attila; Ostafe, Alina; Shparlinski, Igor E.; Silverman, Joseph H.
8
2021
The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016
Silverman, Joseph H.
8
2004
Rational points on certain families of curves of genus at least 2. Zbl 0642.14006
Silverman, Joseph H.
8
1987
A quantitative estimate for quasiintegral points in orbits. Zbl 1272.37039
Hsia, Liang-Chung; Silverman, Joseph H.
8
2011
The theory of height functions. Zbl 0604.14022
Silverman, Joseph H.
8
1986
Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004
Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H.
8
2017
Height estimates for equidimensional dominant rational maps. Zbl 1311.11057
Silverman, Joseph H.
8
2011
The sign of an elliptic divisibility sequence. Zbl 1148.11013
Silverman, Joseph H.; Stephens, Nelson
8
2006
Computing rational points on rank 1 elliptic curves via \(L\)-series and canonical heights. Zbl 1042.11036
Silverman, Joseph H.
7
1999
Computing canonical heights with little (or no) factorization. Zbl 0898.11021
Silverman, Joseph H.
7
1997
\(S\)-integer points on elliptic curves. Zbl 0824.11038
Gross, Robert; Silverman, Joseph
7
1995
A local-global criterion for dynamics on \({\mathbb P}^1\). Zbl 1243.37066
Silverman, Joseph H.; Voloch, José Felipe
7
2009
Some arithmetic properties of Weierstrass points: Hyperelliptic curves. Zbl 0758.14023
Silverman, Joseph H.
6
1990
Post-critically finite maps on \(\mathbb{P}^n\) for \(n\ge 2\) are sparse. Zbl 1516.37146
Ingram, Patrick; Ramadas, Rohini; Silverman, Joseph H.
1
2023
Multiplicative dependence among iterated values of rational functions modulo finitely generated groups. Zbl 1490.37115
Bérczes, Attila; Ostafe, Alina; Shparlinski, Igor E.; Silverman, Joseph H.
8
2021
The distribution relation and inverse function theorem in arithmetic geometry. Zbl 1472.11200
Matsuzawa, Yohsuke; Silverman, Joseph H.
1
2021
Moduli spaces for dynamical systems with portraits. Zbl 1448.37132
Doyle, John R.; Silverman, Joseph H.
6
2020
GIT stability of Hénon maps. Zbl 1448.37133
Lee, Chong Gyu; Silverman, Joseph H.
4
2020
Erratum to “On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties”. Zbl 1439.37090
Kawaguchi, Shu; Silverman, Joseph H.
2
2020
Integrality properties of Böttcher coordinates for one-dimensional superattracting germs. Zbl 1427.37073
Salerno, Adriana; Silverman, Joseph H.
1
2020
A signature scheme from the finite field isomorphism problem. Zbl 1450.94051
Hoffstein, Jeffrey; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei
1
2020
Current trends and open problems in arithmetic dynamics. Zbl 1468.37001
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J.
22
2019
A uniform field-of-definition/field-of-moduli bound for dynamical systems on \(\mathbb{P}^N\). Zbl 1432.37124
Doyle, John R.; Silverman, Joseph H.
3
2019
A classification of degree \(2\) semi-stable rational maps \(\mathbb{P}^2\rightarrow\mathbb{P}^2\) with large finite dynamical automorphism group. Zbl 1432.37123
Manes, Michelle; Silverman, Joseph H.
1
2019
Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures. Zbl 1396.37097
Silverman, Joseph H.
3
2018
Degeneration of dynamical degrees in families of maps. Zbl 1404.37123
Silverman, Joseph H.; Call, Gregory S.
2
2018
Fully homomorphic encryption from the finite field isomorphism problem. Zbl 1385.94032
Doröz, Yarkın; Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.; Sunar, Berk; Whyte, William; Zhang, Zhenfei
2
2018
Arithmetic and dynamical degrees on abelian varieties. Zbl 1416.11091
Silverman, Joseph H.
18
2017
Choosing parameters for NTRUEncrypt. Zbl 1383.94022
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William; Zhang, Zhenfei
16
2017
Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004
Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H.
8
2017
Rational points on, and the arithmetic of, elliptic curves: a tale of two books (and an article). Zbl 1436.11005
Silverman, Joseph H.
1
2017
On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties. Zbl 1393.37115
Kawaguchi, Shu; Silverman, Joseph H.
30
2016
Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. Zbl 1391.37078
Kawaguchi, Shu; Silverman, Joseph H.
20
2016
Rational points on elliptic curves. 2nd ed. Zbl 1346.11001
Silverman, Joseph H.; Tate, John T.
29
2015
PASS-encrypt: a public key cryptosystem based on partial evaluation of polynomials. Zbl 1356.94061
Hoffstein, Jeffrey; Silverman, Joseph H.
2
2015
Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Zbl 1372.37093
Silverman, Joseph H.
25
2014
Examples of dynamical degree equals arithmetic degree. Zbl 1309.37084
Kawaguchi, Shu; Silverman, Joseph H.
18
2014
Transcript secure signatures based on modular lattices. Zbl 1380.94099
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William
8
2014
Practical signatures from the partial Fourier recovery problem. Zbl 1356.94060
Hoffstein, Jeff; Pipher, Jill; Schanck, John M.; Silverman, Joseph H.; Whyte, William
6
2014
An introduction to mathematical cryptography. 2nd ed. Zbl 1297.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
6
2014
Handbook of finite fields. Zbl 1319.11001
218
2013
Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture. Zbl 1297.37046
Silverman, Joseph H.
11
2013
On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture. Zbl 1347.37153
Silverman, Joseph H.; Viray, Bianca
9
2013
What is …the \(p\)-adic Mandelbrot set? Zbl 1322.28001
Silverman, Joseph H.
1
2013
Moduli spaces and arithmetic dynamics. Zbl 1247.37004
Silverman, Joseph H.
29
2012
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
13
2012
Elliptic Carmichael numbers and elliptic Korselt criteria. Zbl 1304.11047
Silverman, Joseph H.
6
2012
Algebraic divisibility sequences over function fields. Zbl 1251.11008
Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco
6
2012
An algebraic approach to certain cases of Thurston rigidity. Zbl 1291.37072
Silverman, Joseph H.
2
2012
Terms in elliptic divisibility sequences divisible by their indices. Zbl 1225.11079
Silverman, Joseph H.; Stange, Katherine E.
11
2011
Amicable pairs and aliquot cycles for elliptic curves. Zbl 1269.11056
Silverman, Joseph H.; Stange, Katherine E.
11
2011
A quantitative estimate for quasiintegral points in orbits. Zbl 1272.37039
Hsia, Liang-Chung; Silverman, Joseph H.
8
2011
Height estimates for equidimensional dominant rational maps. Zbl 1311.11057
Silverman, Joseph H.
8
2011
Lang’s height conjecture and Szpiro’s conjecture. Zbl 1304.11046
Silverman, Joseph H.
1
2010
The arithmetic of elliptic curves. 2nd ed. Zbl 1194.11005
Silverman, Joseph H.
777
2009
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
30
2009
Nonarchimedean Green functions and dynamics on projective space. Zbl 1161.32009
Kawaguchi, Shu; Silverman, Joseph H.
13
2009
A local-global criterion for dynamics on \({\mathbb P}^1\). Zbl 1243.37066
Silverman, Joseph H.; Voloch, José Felipe
7
2009
On a dynamical Brauer-Manin obstruction. Zbl 1196.37131
Hsia, Liang-Chung; Silverman, Joseph
4
2009
Canonical heights and the arithmetic complexity of morphisms on projective space. Zbl 1221.11152
Kawaguchi, Shu; Silverman, Joseph H.
4
2009
Lifting and elliptic curve discrete logarithms. Zbl 1256.94065
Silverman, Joseph H.
2
2009
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
448
2008
An introduction to mathematical cryptography. Zbl 1160.94001
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
42
2008
Variation of periods modulo \(p\) in arithmetic dynamics. Zbl 1153.11028
Silverman, Joseph H.
15
2008
The arithmetic of dynamical systems. Zbl 1130.37001
Silverman, Joseph H.
280
2007
Dynamics of projective morphisms having identical canonical heights. Zbl 1130.11035
Kawaguchi, Shu; Silverman, Joseph H.
14
2007
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
10
2007
Divisibility sequences and powers of algebraic integers. Zbl 1135.11058
Silverman, Joseph H.
1
2007
The sign of an elliptic divisibility sequence. Zbl 1148.11013
Silverman, Joseph H.; Stephens, Nelson
8
2006
Timing attacks on NTRUEncrypt via variation in the number of hash calls. Zbl 1177.94174
Silverman, Joseph H.; Whyte, William
4
2006
Height bounds and preperiodic points for families of jointly regular affine maps. Zbl 1154.11328
Silverman, Joseph H.
3
2006
Generalized greatest common divisors, divisibility sequences, and Vojta’s conjecture for blowups. Zbl 1197.11070
Silverman, Joseph H.
28
2005
\(p\)-adic properties of division polynomials and elliptic divisibility sequences. Zbl 1066.11024
Silverman, Joseph H.
12
2005
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. Zbl 1079.94553
Howgrave-Graham, Nick; Silverman, Joseph H.; Whyte, William
11
2005
An algebraic approach to NTRU (\(q = 2^{n}\)) via Witt vectors and overdetermined systems of nonlinear equations. Zbl 1116.94333
Silverman, J. H.; Smart, N. P.; Vercauteren, F.
1
2005
Common divisors of elliptic divisibility sequences over function fields. Zbl 1128.11015
Silverman, Joseph H.
12
2004
A lower bound for the canonical height on abelian varieties over abelian extensions. Zbl 1060.11041
Baker, Matthew H.; Silverman, Joseph H.
10
2004
A lower bound for the canonical height on elliptic curves over abelian extensions. Zbl 1053.11052
Silverman, Joseph H.
10
2004
Common divisors of \(a^n-1\) and \(b^n-1\) over function fields. Zbl 1120.11045
Silverman, Joseph H.
9
2004
The rank of elliptic surfaces in unramified abelian towers. Zbl 1105.11016
Silverman, Joseph H.
8
2004
NTRUSign: Digital signatures using the NTRU lattice. Zbl 1039.94525
Hoffstein, Jeffrey; Howgrave-Graham, Nick; Pipher, Jill; Silverman, Joseph H.; Whyte, William
46
2003
The impact of decryption failures on the security of NTRU encryption. Zbl 1122.94377
Howgrave-Graham, Nick; Nguyen, Phong Q.; Pointcheval, David; Proos, John; Silverman, Joseph H.; Singer, Ari; Whyte, William
22
2003
Random small Hamming weight products with applications to cryptography. Zbl 1028.94023
Hoffstein, Jeffrey; Silverman, Joseph H.
9
2003
On the linear complexity of the Naor-Reingold pseudo-random function from elliptic curves. Zbl 1077.11504
Shparlinski, Igor E.; Silverman, Joseph H.
14
2001
NSS: an NTRU lattice-based signature scheme. Zbl 0981.94039
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
14
2001
Dimension reduction methods for convolution modular lattices. Zbl 1006.11033
May, Alexander; Silverman, Joseph H.
12
2001
Optimizations for NTRU. Zbl 0987.94027
Hoffstein, Jeffrey; Silverman, Joseph
6
2001
Cryptography and lattices. 1st international conference, CaLC 2001, Providence, RI, USA, March 29–30, 2001. Revised papers. Zbl 0971.00060
2
2001
NTRU in constrained devices. Zbl 1012.94548
Bailey, Daniel V.; Coffin, Daniel; Elbirt, Adam; Silverman, Joseph H.; Woodbury, Adam D.
1
2001
Polynomial rings and efficient public key authentication. II. Zbl 1002.94535
Hoffstein, Jeffrey; Silverman, Joseph H.
1
2001
Diophantine geometry. An introduction. Zbl 0948.11023
Hindry, Marc; Silverman, Joseph H.
290
2000
Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\). Zbl 1009.11035
Bremner, A.; Silverman, J. H.; Tzanakis, N.
22
2000
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Paperback ed. Zbl 1051.11500
16
2000
On the distribution of integer points on curves of genus zero. Zbl 0979.11037
Silverman, J. H.
14
2000
The Xedni calculus and the elliptic curve discrete logarithm problem. Zbl 0948.11049
Silverman, Joseph H.
12
2000
Analysis of the Xedni calculus attack. Zbl 0948.11048
Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn
10
2000
A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension. Zbl 0951.14023
Silverman, Joseph H.
6
2000
On the number of rational torsion points on an elliptic curve. (Sur le nombre de points de torsion rationnels sur une courbe elliptique.) Zbl 0993.11028
Hindry, Marc; Silverman, Joseph
11
1999
Computing rational points on rank 1 elliptic curves via \(L\)-series and canonical heights. Zbl 1042.11036
Silverman, Joseph H.
7
1999
Fast multiplication in finite fields GF\((2^N)\). Zbl 0993.11065
Silverman, Joseph H.
5
1999
Divisibility of the specialization map for twists of abelian varieties. Zbl 0938.11030
Silverman, Joseph H.
1
1999
NTRU: A ring-based public key cryptosystem. Zbl 1067.94538
Hoffstein, Jeffrey; Pipher, Jill; Silverman, Joseph H.
199
1998
The space of rational maps on \(\mathbf P^1\). Zbl 0966.14031
Silverman, Joseph H.
55
1998
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
16
1998
The average rank of an algebraic family of elliptic curves. Zbl 0923.11087
Silverman, Joseph H.
9
1998
Elliptic curve discrete logarithms and the index calculus. Zbl 0944.11043
Silverman, Joseph H.; Suzuki, Joe
6
1998
Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. Zbl 0878.11004
11
1997
Computing canonical heights with little (or no) factorization. Zbl 0898.11021
Silverman, Joseph H.
7
1997
A friendly introduction to number theory. Zbl 0973.11003
Silverman, Joseph H.
1
1997
The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\). Zbl 0868.11029
Brumer, Armand; Silverman, Joseph H.
29
1996
Small Salem numbers, exceptional units, and Lehmer’s conjecture. Zbl 0883.11045
Silverman, Joseph H.
10
1996
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
10
1996
Rational functions with a polynomial iterate. Zbl 0848.11049
Silverman, Joseph H.
6
1996
...and 55 more Documents
all top 5

Cited by 3,542 Authors

63 Silverman, Joseph Hillel
43 Shparlinski, Igor E.
28 Ghioca, Dragos
27 Zannier, Umberto M.
21 Ingram, Patrick
21 Tucker, Thomas John
20 Hindes, Wade
19 Ostafe, Alina
18 Doyle, John R.
16 Murty, Maruti Ram
15 Clark, Peter Louis
15 Galbraith, Steven D.
15 Kraus, Alain
15 Levin, Aaron
15 Lozano-Robledo, Álvaro
15 Siksek, Samir
14 Koo, Jakyung
14 Morton, Patrick
14 Petit, Christophe
14 Poulakis, Dimitrios
14 Sha, Min
14 Stoll, Michael
13 Corvaja, Pietro
13 Dujella, Andrej
13 Lauter, Kristin Estella
13 Masser, David William
13 Poonen, Bjorn
13 Shamsi Zargar, Arman
13 Sutherland, Andrew V.
13 Top, Jaap
12 Benedetto, Robert L.
12 Choudhry, Ajai
12 Daniels, Harris B.
12 Fisher, Tom A.
12 Flynn, Eugene Victor
12 González-Jiménez, Enrique
12 Hutz, Benjamin
12 Mukhamedov, Farruh Maksutovich
12 Zhang, Yong
11 Bleher, Frauke M.
11 De Feo, Luca
11 DeMarco, Laura Grace
11 Everest, Graham Robert
11 Freitas, Nuno
11 Okuyama, Yûsuke
11 Pazuki, Fabien
11 Sadek, Mohammad
11 Silverberg, Alice
10 Akbary, Amir
10 Bars Cortina, Francesc
10 Byeon, Dongho
10 Habegger, Philipp
10 Hsia, Liang-Chung
10 Jeong, Sangtae
10 Kihara, Shoichi
10 Manes, Michelle
10 Najman, Filip
10 Ono, Ken
10 Pasten, Hector V.
10 Shin, Dong Hwa
10 Ulas, Maciej
10 Wang, Julie Tzu-Yueh
9 Bell, Jason P.
9 Bridy, Andrew
9 Castryck, Wouter
9 Cremona, John E.
9 Dokchitser, Vladimir
9 Fan, Shilei
9 Jones, Rafe
9 Kundu, Debanjana
9 Liao, Lingmin
9 Miller, Steven J.
9 Moody, Dustin
9 Nguyen, Khoa Dang
9 Petsche, Clayton
9 Ray, Anwesh
9 Rouse, Jeremy A.
9 Rubin, Karl Cooper
9 Schoen, Chad
9 Takagi, Tsuyoshi
9 Vercauteren, Frederik
9 Voloch, José Felipe
9 Wong, Siman
8 Baragar, Arthur
8 Canci, Jung Kyu
8 Dąbrowski, Andrzej Bogdan
8 Gauthier, Thomas
8 Grant, David R.
8 Im, Bo-Hae
8 Kawaguchi, Shu
8 Kutas, Péter
8 Matsuzawa, Yohsuke
8 Mazur, Barry
8 Mello, Jorge
8 Miret, Josep M.
8 Müller, Jan Steffen
8 Ozman, Ekin
8 Paladino, Laura
8 Peral Alonso, Juan Carlos
8 Perucca, Antonella
...and 3,442 more Authors
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Cited in 369 Serials

385 Journal of Number Theory
120 Mathematics of Computation
107 Transactions of the American Mathematical Society
103 International Journal of Number Theory
96 Journal de Théorie des Nombres de Bordeaux
90 Proceedings of the American Mathematical Society
75 Mathematische Annalen
65 Acta Arithmetica
60 Journal of Algebra
58 Compositio Mathematica
57 Research in Number Theory
54 Finite Fields and their Applications
51 Rocky Mountain Journal of Mathematics
48 Duke Mathematical Journal
47 Mathematische Zeitschrift
46 Proceedings of the Japan Academy. Series A
41 Inventiones Mathematicae
36 Designs, Codes and Cryptography
36 The Ramanujan Journal
35 Advances in Mathematics
35 Experimental Mathematics
34 Annales de l’Institut Fourier
32 Manuscripta Mathematica
30 Journal of Pure and Applied Algebra
29 Mathematical Proceedings of the Cambridge Philosophical Society
29 Monatshefte für Mathematik
29 Algebra & Number Theory
28 Functiones et Approximatio. Commentarii Mathematici
28 Journal of Mathematical Cryptology
27 Bulletin of the Australian Mathematical Society
25 Journal für die Reine und Angewandte Mathematik
25 LMS Journal of Computation and Mathematics
24 European Journal of Mathematics
23 Bulletin of the American Mathematical Society. New Series
23 Comptes Rendus. Mathématique. Académie des Sciences, Paris
22 Bulletin of the London Mathematical Society
21 Archiv der Mathematik
20 Communications in Algebra
19 Journal of Cryptology
19 Journal of Discrete Mathematical Sciences & Cryptography
18 Israel Journal of Mathematics
18 Journal of the London Mathematical Society. Second Series
18 Journal of High Energy Physics
17 Journal of Symbolic Computation
15 Pacific Journal of Mathematics
15 Ergodic Theory and Dynamical Systems
15 Journal of the American Mathematical Society
14 Periodica Mathematica Hungarica
14 Annals of Mathematics. Second Series
13 Theoretical Computer Science
13 Journal of the European Mathematical Society (JEMS)
13 Integers
13 Research in the Mathematical Sciences
12 Communications in Mathematical Physics
12 Journal of Mathematical Analysis and Applications
11 Proceedings of the London Mathematical Society. Third Series
11 Expositiones Mathematicae
11 Journal of Algebraic Geometry
11 The New York Journal of Mathematics
11 Forum of Mathematics, Sigma
10 Discrete Applied Mathematics
10 Bulletin de la Société Mathématique de France
10 Glasgow Mathematical Journal
10 Mathematische Nachrichten
10 Revista Matemática Iberoamericana
10 Journal of the Institute of Mathematics of Jussieu
10 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
9 American Mathematical Monthly
9 Journal of Geometry and Physics
9 Canadian Journal of Mathematics
9 Canadian Mathematical Bulletin
9 Mathematika
9 Michigan Mathematical Journal
9 Tôhoku Mathematical Journal. Second Series
9 Discrete & Computational Geometry
9 Indagationes Mathematicae. New Series
9 Selecta Mathematica. New Series
9 JP Journal of Algebra, Number Theory and Applications
9 Cryptography and Communications
8 Discrete Mathematics
8 Information Processing Letters
8 Czechoslovak Mathematical Journal
8 Nagoya Mathematical Journal
8 Proceedings of the Edinburgh Mathematical Society. Series II
8 Forum Mathematicum
8 Journal of the Ramanujan Mathematical Society
8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
8 Advances in Mathematics of Communications
7 Applied Mathematics and Computation
7 Journal of the Mathematical Society of Japan
7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
7 Linear Algebra and its Applications
7 Applicable Algebra in Engineering, Communication and Computing
7 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
7 Documenta Mathematica
7 Acta Mathematica Sinica. English Series
7 Journal of the Australian Mathematical Society
7 Kyoto Journal of Mathematics
7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
6 Nuclear Physics. B
...and 269 more Serials
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Cited in 58 Fields

2,591 Number theory (11-XX)
1,594 Algebraic geometry (14-XX)
489 Information and communication theory, circuits (94-XX)
469 Dynamical systems and ergodic theory (37-XX)
141 Quantum theory (81-XX)
131 Computer science (68-XX)
116 Field theory and polynomials (12-XX)
87 Group theory and generalizations (20-XX)
72 Several complex variables and analytic spaces (32-XX)
63 Commutative algebra (13-XX)
55 Combinatorics (05-XX)
50 Functions of a complex variable (30-XX)
49 Associative rings and algebras (16-XX)
43 Special functions (33-XX)
42 Mathematical logic and foundations (03-XX)
32 Algebraic topology (55-XX)
30 Geometry (51-XX)
26 Convex and discrete geometry (52-XX)
23 \(K\)-theory (19-XX)
23 Numerical analysis (65-XX)
21 Difference and functional equations (39-XX)
18 Linear and multilinear algebra; matrix theory (15-XX)
17 Manifolds and cell complexes (57-XX)
16 Functional analysis (46-XX)
15 Topological groups, Lie groups (22-XX)
15 Global analysis, analysis on manifolds (58-XX)
15 Probability theory and stochastic processes (60-XX)
14 Differential geometry (53-XX)
14 Relativity and gravitational theory (83-XX)
12 Nonassociative rings and algebras (17-XX)
12 Ordinary differential equations (34-XX)
12 Statistical mechanics, structure of matter (82-XX)
10 General and overarching topics; collections (00-XX)
9 History and biography (01-XX)
8 Partial differential equations (35-XX)
7 General algebraic systems (08-XX)
6 Category theory; homological algebra (18-XX)
5 Real functions (26-XX)
5 Operator theory (47-XX)
5 Operations research, mathematical programming (90-XX)
4 Mechanics of particles and systems (70-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Measure and integration (28-XX)
3 Potential theory (31-XX)
3 Approximations and expansions (41-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
2 Sequences, series, summability (40-XX)
2 Statistics (62-XX)
2 Fluid mechanics (76-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Systems theory; control (93-XX)
2 Mathematics education (97-XX)
1 Abstract harmonic analysis (43-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 General topology (54-XX)
1 Mechanics of deformable solids (74-XX)
1 Optics, electromagnetic theory (78-XX)
1 Geophysics (86-XX)

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