Elliptic curve cryptosystems. (English) Zbl 0622.94015

Koblitz, Neal

Math. Comput. 48, 203-209 (1987).

Public key cryptosystems based on the structure of the group of points of an elliptic curve over a large finite field which may be more secure are described. After studying elliptic curve analogs of the Massey-Omura and ElGamal systems, the paper gives concrete examples, deals with primitive points and gives a theorem concerning the probability that the order of a cyclic subgroup generated by a global point is nonsmooth.

Reviewer: Edwin Ederle (München)

MSC:

94A60	Cryptography
14G50	Applications to coding theory and cryptography of arithmetic geometry
11T71	Algebraic coding theory; cryptography (number-theoretic aspects)

Keywords:

Public key cryptosystems; group of points of an elliptic curve over a large finite field