One of the general methods for constructing public key cryptosystems is based on the discrete logarithm problem in finite Abelian groups. The crucial problem in applying this method is to find large classes of groups where the discrete logarithm problem is intractable.

Koblitz studies the class of groups obtained from the Jacobians of hyperelliptic curves as candidates for constructing public key cryptosystems. Special attention is paid to the case where the ground field has characteristic 2. This class seems applicable because one may expect that for groups of “almost prime order” the discrete logarithm problem is intractable.