Computing discrete logarithms in real quadratic congruence function fieldsof large genus

The discrete logarithm problem in various finite abelian groups is the basi s for some well known public key cryptosystems. Recently, real quadratic co ngruence function fields were used to construct a public key distribution s ystem. The security of this public key system is based on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of suffic iently large genus. This algorithm is a generalization of similar algorithm s for real quadratic number fields.