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Elliptic curve cryptosystems
We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure,Expand
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A Course in Number Theory and Cryptography
1: Some Topics in Elementary Number Theory. 2: Finite Fields and Quadratic Residues. 3: Cryptography. 4: Public Key. 5: Primality and Factoring. 6: Elliptic Curves.
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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).
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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 bookExpand
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CM-Curves with Good Cryptographic Properties
  • N. Koblitz
  • Mathematics, Computer Science
  • CRYPTO
  • 11 August 1991
TLDR
We describe elliptic curves with complex multiplication which in characteristic 2 have the following useful properties for constructing Diffie-Hellman type cryptosystems: (1) they are nonsupersingular (so that one cannot use the Menezes-Okamoto-Vanstone reduction of discrete log to finite fields). Expand
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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. Expand
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Hyperelliptic cryptosystems
  • N. Koblitz
  • Mathematics, Computer Science
  • Journal of Cryptology
  • 3 January 1989
TLDR
We discuss a source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups. Expand
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Algebraic aspects of cryptography
  • N. Koblitz
  • Mathematics, Computer Science
  • Algorithms and computation in mathematics
  • 1998
TLDR
1. Algebra.- 1. Basic Definitions and Properties.- 2. Length of Numbers.- Exercises.- 3. Zeros and Poles.- 4. Divisors.- 5. Representing Semi-Reduced Divissors.- 6. Hyperelliptic Curve Cryptosystems . Expand
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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 blackExpand
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Pairing-Based Cryptography at High Security Levels
TLDR
In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. Expand
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