Reference Work Entry

Encyclopedia of Cryptography and Security

pp 397-397

Elliptic Curve Cryptography

  • Darrel HankersonAffiliated withDepartment of Mathematics, Auburn University
  • , Alfred MenezesAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo

Synonyms

ECC

Related Concepts

Public Key Cryptography

Definition

Elliptic curve cryptography (ECC) encompasses the design and analysis of public-key cryptographic schemes that can be implemented using elliptic curves.

Background

Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz [5] and Victor Miller [6]. They are the elliptic curve analogues of schemes based on the discrete logarithm problem, where the underlying group is the group of points on an elliptic curve defined over a finite field [13]. See [4] for a historical account of the development and commercial acceptance of ECC.

Theory

The security of all elliptic curve signature schemes, elliptic curve key agreement schemes and elliptic curve public-key encryption schemes is based on the apparent intractability of the elliptic curve discrete logarithm problem (ECDLP). Unlike the case of the ordinary discrete logarithm problem in the multiplicative grou ...

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