Hyperelliptic cryptosystems. (English) Zbl 0674.94010

Koblitz, Neal

J. Cryptology 1, No. 3, 139-150 (1989).

Summary: In this paper we discuss a source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups. They are the jacobians of hyperelliptic curves defined over finite fields. Special attention is given to curves defined over the field of two elements. Explicit formulas and examples are given, and the problem of finding groups of almost prime order is discussed.

MSC:

94A60	Cryptography
14H40	Jacobians, Prym varieties
14G15	Finite ground fields in algebraic geometry

Keywords:

public key; discrete logarithm; finite abelian groups; cryptosystems; jacobians of hyperelliptic curves; finite fields; groups of almost prime order

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