Elliptic Curve Cryptography

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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