The arithmetic of elliptic curves. - Joseph H. Silverman (Springer, 1986)

Exceptional Units and Numbers of Small Mahler Measure. - Joseph H. Silverman (Exp. Math., 1995)

Computing the canonical height on K3 surfaces. - Gregory S. Call; Joseph H. Silverman (Math. Comput., 1996)

Computing canonical heights with little (or no) factorization. - Joseph H. Silverman (Math. Comput., 1997)

NTRU: A Ring-Based Public Key Cryptosystem. - Jeffrey Hoffstein; Jill Pipher; Joseph H. Silverman (ANTS, 1998)

Elliptic Curve Discrete Logarithms and the Index Calculus. - Joseph H. Silverman; Joe Suzuki (ASIACRYPT, 1998)

Fast Multiplication in Finite Fields GF(2N). - Joseph H. Silverman (CHES, 1999)

Computing rational points on rank 1 elliptic curves via L-series and canonical heights. - Joseph H. Silverman (Math. Comput., 1999)

MiniPASS: Authentication and Digital Signatures in a Constrained Environment. - Jeffrey Hoffstein; Joseph H. Silverman (CHES, 2000)

Lattices, cryptography, and the NTRU public key cryptosystem. - Joseph H. Silverman (Unusual Applications of Number Theory, 2000)

Analysis of the Xedni Calculus Attack. - Michael J. Jacobson Jr.; Neal Koblitz; Joseph H. Silverman; Andreas Stein; Edlyn Teske (Des. Codes Cryptogr., 2000)

The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem. - Joseph H. Silverman (Des. Codes Cryptogr., 2000)

On the distribution of integer points on curves of genus zero. - Joseph H. Silverman (Theor. Comput. Sci., 2000)

Dimension Reduction Methods for Convolution Modular Lattices. - Alexander May 001; Joseph H. Silverman (CaLC, 2001)

NTRU in Constrained Devices. - Daniel V. Bailey; Daniel Coffin; Adam J. Elbirt; Joseph H. Silverman; Adam D. Woodbury (CHES, 2001)

NSS: An NTRU Lattice-Based Signature Scheme. - Jeffrey Hoffstein; Jill Pipher; Joseph H. Silverman (EUROCRYPT, 2001)

On the Linear Complexity of the Naor-Reingold Pseudo-random Function from Elliptic Curves. - Igor E. Shparlinski; Joseph H. Silverman (Des. Codes Cryptogr., 2001)

The Impact of Decryption Failures on the Security of NTRU Encryption. - Nick Howgrave-Graham; Phong Q. Nguyen; David Pointcheval; John Proos; Joseph H. Silverman; Ari Singer; William Whyte (CRYPTO, 2003)

NTRUSIGN: Digital Signatures Using the NTRU Lattice. - Jeffrey Hoffstein; Nick Howgrave-Graham; Jill Pipher; Joseph H. Silverman; William Whyte (CT-RSA, 2003)

Random small Hamming weight products with applications to cryptography. - Jeffrey Hoffstein; Joseph H. Silverman (Discret. Appl. Math., 2003)

NAEP: Provable Security in the Presence of Decryption Failures. - Nick Howgrave-Graham; Joseph H. Silverman; Ari Singer; William Whyte (IACR Cryptol. ePrint Arch., 2003)

An Algebraic Approach to NTRU (q = 2n) via Witt Vectors and Overdetermined Systems of Nonlinear Equations. - Joseph H. Silverman; Nigel P. Smart; Frederik Vercauteren (SCN, 2004)

Modified Parameter Attacks: Practical Attacks against CCA2 Secure Cryptosystems and Countermeasures. - Nick Howgrave-Graham; Joseph H. Silverman; Ari Singer; William Whyte (IACR Cryptol. ePrint Arch., 2004)

Choosing Parameter Sets forwithand. - Nick Howgrave-Graham; Joseph H. Silverman; William Whyte (CT-RSA, 2005)

Performance Improvements and a Baseline Parameter Generation Algorithm for NTRUSign. - Jeffrey Hoffstein; Nick Howgrave-Graham; Jill Pipher; Joseph H. Silverman; William Whyte (IACR Cryptol. ePrint Arch., 2005)

Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3. - Nick Howgrave-Graham; Joseph H. Silverman; William Whyte (IACR Cryptol. ePrint Arch., 2005)

Timing Attacks on NTRUEncrypt Via Variation in the Number of Hash Calls. - Joseph H. Silverman; William Whyte (CT-RSA, 2007)

Lifting and Elliptic Curve Discrete Logarithms. - Joseph H. Silverman (Selected Areas in Cryptography, 2008)

A Survey of Local and Global Pairings on Elliptic Curves and Abelian Varieties. - Joseph H. Silverman (Pairing, 2010)

Local-global aspects of (hyper)elliptic curves over (in)finite fields. - Joseph H. Silverman (Adv. Math. Commun., 2010)

Amicable Pairs and Aliquot Cycles for Elliptic Curves. - Joseph H. Silverman; Katherine E. Stange (Exp. Math., 2011)

Elliptic curves. - Joseph H. Silverman (Handbook of Finite Fields, 2013)

Practical Signatures from the Partial Fourier Recovery Problem. - Jeffrey Hoffstein; Jill Pipher; John M. Schanck; Joseph H. Silverman; William Whyte (IACR Cryptol. ePrint Arch., 2013)

Transcript Secure Signatures Based on Modular Lattices. - Jeffrey Hoffstein; Jill Pipher; John M. Schanck; Joseph H. Silverman; William Whyte (IACR Cryptol. ePrint Arch., 2014)

PASS-Encrypt: a public key cryptosystem based on partial evaluation of polynomials. - Jeffrey Hoffstein; Joseph H. Silverman (Des. Codes Cryptogr., 2015)

Choosing Parameters for NTRUEncrypt. - Jeffrey Hoffstein; Jill Pipher; John M. Schanck; Joseph H. Silverman; William Whyte; Zhenfei Zhang (IACR Cryptol. ePrint Arch., 2015)

DA-Encrypt: Homomorphic Encryption via Non-Archimedean Diophantine Approximation - Preliminary Report. - Jeffrey Hoffstein; Jill Pipher; John M. Schanck; Joseph H. Silverman; William Whyte; Zhenfei Zhang (IACR Cryptol. ePrint Arch., 2015)

Fully Homomorphic Encryption from the Finite Field Isomorphism Problem. - Yarkin Doröz; Jeffrey Hoffstein; Jill Pipher; Joseph H. Silverman; Berk Sunar; William Whyte; Zhenfei Zhang (IACR Cryptol. ePrint Arch., 2017)

MMSAT: A Scheme for Multimessage Multiuser Signature Aggregation. - Yarkin Doröz; Jeffrey Hoffstein; Joseph H. Silverman; Berk Sunar (IACR Cryptol. ePrint Arch., 2020)

A signature scheme from the finite field isomorphism problem. - Jeffrey Hoffstein; Joseph H. Silverman; William Whyte; Zhenfei Zhang (J. Math. Cryptol., 2020)

A Heuristic Subexponential Algorithm to Find Paths in Markoff Graphs Over Finite Fields. - Joseph H. Silverman (CoRR, 2022)

Orbits on K3 Surfaces of Markoff Type. - Elena Fuchs; Matthew Litman; Joseph H. Silverman; Austin Tran (Exp. Math., 2024)