On the Analysis of Cryptographic Assumptions in the Generic Ring Model

  • Tibor Jager
  • Jörg Schwenk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5912)

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tibor Jager
    • 1
  • Jörg Schwenk
    • 1
  1. 1.Horst Görtz Institute for IT SecurityRuhr-University BochumGermany

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