Sufficient Conditions for the Computational Intractability of Generic Group Problems

The generic group model is a valuable methodology for analysing the computational hardness some 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 verifiable criteria which guarantee the hardness of a problem in the generic group model. As useful means for formalisation of definitions and proofs we relate the concepts of generic algorithms and straight-line programs that have only been used independently in cryptography so far.