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Elliptic curve cryptosystems
TLDR
The question of primitive points on an elliptic curve modulo p is discussed, and a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point is given.
p-adic Numbers, p-adic Analysis, and Zeta-Functions
P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).
Introduction to Elliptic Curves and Modular Forms
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book
CM-Curves with Good Cryptographic Properties
  • N. Koblitz
  • Mathematics, Computer Science
    CRYPTO
  • 11 August 1991
Our purpose is to describe elliptic curves with complex multiplication which in characteristic 2 have the following useful properties for constructing Diffie-Hellman type cryptosystems: (1) they are
Hyperelliptic cryptosystems
  • N. Koblitz
  • Mathematics, Computer Science
    Journal of Cryptology
  • 3 January 1989
TLDR
A source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups are the jacobians of hyperelliptic curves defined over finite fields.
The State of Elliptic Curve Cryptography
TLDR
This paper surveys the development of elliptic curve cryptosystems from their inception in 1985 by Koblitz and Miller to present day implementations.
Algebraic aspects of cryptography
  • N. Koblitz
  • Mathematics, Computer Science
    Algorithms and computation in mathematics
  • 1998
TLDR
1. Cryptography.- 1. Early History.; 2. The Idea of Public Key Cryptography.; 3. The RSA Cryptosystem.; 4. Diffie-Hellman and the Digital Signature Algorithm; 5. Secret Sharing, Coin Flipping, and Time Spent on Homework.; 6. Passwords, Signatures, and Ciphers; 7. Randomized Algorithms and Complexity Classes.
Radical Equations : Math Literacy and Civil Rights
The book is divided into two parts. Part I gives a vivid picture of the civil rights movement in Mississippi in the years 1961–1964. Moses not only conveys the drama of impoverished black
Pairing-Based Cryptography at High Security Levels
TLDR
This paper examines the implications of heightened security needs for pairing-based cryptosystems and describes three different reasons why high-security users might have concerns about the long-term viability of these systems.
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