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Designs, Codes and Cryptography

, Volume 77, Issue 2–3, pp 587–610 | Cite as

The random oracle model: a twenty-year retrospective

  • Neal Koblitz
  • Alfred J. Menezes
Article

Abstract

It has been roughly two decades since the random oracle model for reductionist security arguments was introduced and one decade since we first discussed the controversy that had arisen concerning its use. In this retrospective we argue that there is no evidence that the need for the random oracle assumption in a proof indicates the presence of a real-world security weakness in the corresponding protocol. We give several examples of attempts to avoid random oracles that have led to protocols that have security weaknesses that were not present in the original ones whose proofs required random oracles. We also argue that the willingness to use random oracles gives one the flexibility to modify certain protocols so as to reduce dependence on potentially vulnerable pseudorandom bit generators. Finally, we discuss a modified version of ECDSA, which we call ECDSA\({}^+\), that may have better real-world security than standard ECDSA, and compare it with a modified Schnorr signature. If one is willing to use the random oracle model (and the analogous generic group model), then various security arguments are known for these two schemes. If one shuns these models, then no provable security result is known for them.

Keywords

Cryptography Public key Random oracle 

Mathematics Subject Classification

94A60 

Notes

Acknowledgments

We would like to thank Dan Brown for valuable discussions of security reductions for ECDSA, Kenwrick Mayo for useful discussions of obfuscation constructions, Sanjit Chatterjee for thoughtful comments on an earlier draft, and Ann Hibner Koblitz for helpful editorial suggestions. We would also like to thank Dan Bernstein for informing us of the work [11] and Francisco Rodríguez-Henríquez for bringing the paper [54] to our attention. Finally, we thank the referees for their helpful comments.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

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