On the Analysis of Cryptographic Assumptions in the Generic Ring Model
- Tibor JagerAffiliated withHorst Görtz Institute for IT Security, Ruhr-University Bochum
- , Jörg SchwenkAffiliated withHorst Görtz Institute for IT Security, Ruhr-University Bochum
At Eurocrypt 2009 Aggarwal and Maurer proved that breaking RSA is equivalent to factoring in the generic ring model. This model captures algorithms that may exploit the full algebraic structure of the ring of integers modulo n, but no properties of the given representation of ring elements. This interesting result raises the question how to interpret proofs in the generic ring model. For instance, one may be tempted to deduce that a proof in the generic model gives some evidence that solving the considered problem is also hard in a general model of computation. But is this reasonable?
We prove that computing the Jacobi symbol is equivalent to factoring in the generic ring model. Since there are simple and efficient non-generic algorithms computing the Jacobi symbol, we show that the generic model cannot give any evidence towards the hardness of a computational problem. Despite this negative result, we also argue why proofs in the generic ring model are still interesting, and show that solving the quadratic residuosity and subgroup decision problems is generically equivalent to factoring.
- On the Analysis of Cryptographic Assumptions in the Generic Ring Model
- Book Title
- Advances in Cryptology – ASIACRYPT 2009
- Book Subtitle
- 15th International Conference on the Theory and Application of Cryptology and Information Security, Tokyo, Japan, December 6-10, 2009. Proceedings
- pp 399-416
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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