J. Silverman

Publications269
h-index46
Citations14,614
Highly Influential Citations1,320
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The arithmetic of elliptic curves
  • J. Silverman
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1986
TLDR
It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
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NTRU: A Ring-Based Public Key Cryptosystem
TLDR
NTRU encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory to create a new public key cryptosystem.
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Advanced Topics in the Arithmetic of Elliptic Curves
In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational…
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NTRUSIGN: Digital Signatures Using the NTRU Lattice
TLDR
A mechanism to encrypt to an arbitrary collection of identities using a variant of the Boneh-Franklin identity based encryption scheme that enables a simple mechanism to drive access control to broadcast encrypted data using user identities as the public keys.
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The Arithmetic of Dynamical Systems
* Provides an entry for graduate students into an active field of research * Each chapter includes exercises, examples, and figures * Will become a standard reference for researchers in the field …
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Diophantine Geometry: An Introduction
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and…
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The canonical height and integral points on elliptic curves
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Canonical heights on varieties with morphisms
© Foundation Compositio Mathematica, 1993, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…
Heights and the specialization map for families of abelian varieties.
Let C be a non-singular projective curve, and let A — > C be a (flat) family of abelian varieties, all defmed over a global field K. There are three natural height functions associated to such a…
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An introduction to mathematical cryptography
TLDR
The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling.
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