This paper consists of three parts. First, various types of Diffie-Hellman oracles for a cyclic group G and subgroups of G are defined and their equivalence is proved. In particular, the security of using a subgroup of G instead of G in the Diffie-Hellman protocol is investigated. Second, we derive several new conditions for the polynomial-time equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms in G which extend former results by den Boer and Maurer. Finally, efficient constructions of Diffie-Hellman groups with provable equivalence are described.
CITATION STYLE
Maurer, U. M., & Wolf, S. (1996). Diffie-Hellman Oracles. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1109, pp. 268–282). Springer Verlag. https://doi.org/10.1007/3-540-68697-5_21
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