N. Koblitz

Publications146
h-index37
Citations14,143
Highly Influential Citations939
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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
  • 4,878
  • 375
  • PDF
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.
  • 1,114
  • 64
  • PDF
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).
  • 949
  • 53
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… Expand
  • 761
  • 53
  • PDF
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
  • 428
  • 41
  • PDF
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
  • 560
  • 38
  • PDF
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
  • 342
  • 37
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
  • 463
  • 34
  • PDF
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… Expand
  • 376
  • 30
  • PDF
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
  • 320
  • 25
  • PDF