• Publications
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The arithmetic of elliptic curves
  • J. Silverman
  • Mathematics, Computer Science
  • Graduate texts in mathematics
  • 1986
TLDR
The study of Diophantine equations, that is, the solution of polynomial equations in integers or rational numbers, has a history stretching back to ancient Greece and beyond. Expand
  • 3,357
  • 295
  • PDF
NTRU: A Ring-Based Public Key Cryptosystem
TLDR
We describe NTRU, a new public key cryptosystem that uses a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. Expand
  • 1,384
  • 159
  • PDF
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 rationalExpand
  • 1,598
  • 99
NTRUSIGN: Digital Signatures Using the NTRU Lattice
TLDR
We present a mechanism to encrypt to an arbitrary collection of identities using a variant of the Boneh-Franklin identity based encryption scheme using a logical formulae of conjunctions and disjunctions. Expand
  • 234
  • 35
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 Expand
  • 509
  • 33
  • PDF
Rational Points on Elliptic Curves
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing anExpand
  • 429
  • 28
  • PDF
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 andExpand
  • 421
  • 28
An introduction to mathematical cryptography
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topicsExpand
  • 238
  • 25
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 conditionsExpand
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  • 24
  • PDF
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