• Publications
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The arithmetic of elliptic curves
  • J. Silverman
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1986
It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
NTRU: A Ring-Based Public Key Cryptosystem
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.
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
NTRUSIGN: Digital Signatures Using the NTRU Lattice
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.
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
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
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
An introduction to mathematical cryptography
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.