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Hyperelliptic cryptosystems. (English) Zbl 0674.94010
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
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