Sufficient Conditions for Intractability over Black-Box Groups: Generic Lower Bounds for Generalized DL and DH Problems

Authors:
Andy Rupp;Gregor Leander;Endre Bangerter;Alexander W. Dent;Ahmad-Reza Sadeghi
Affiliations:
Horst Görtz Institute for IT-Security, (Germany);Horst Görtz Institute for IT-Security, (Germany);Bern University of Applied Sciences, (Switzerland);Royal Holloway, University of London, (United Kingdom);Horst Görtz Institute for IT-Security, (Germany)
Venue:
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Year:
2008

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Abstract

The generic group model is a valuable methodology for analyzing the computational hardness of number-theoretic problems used in cryptography. Although generic hardness proofs exhibit many similarities, still the computational intractability of every newly introduced problem needs to be proven from scratch, a task that can easily become complicated and cumbersome when done rigorously. In this paper we make the first steps towards overcoming this problem by identifying criteria which guarantee the hardness of a problem in an extended generic model where algorithms are allowed to perform any operation representable by a polynomial function.