The random oracle hypothesis is false

Richard Chang, Benny Chor, Oded Goldreich, Juris Hartmanis, Johan Håstad, Desh Ranjan, Pankaj Rohatgi

Research output: Contribution to journalArticlepeer-review


The Random Oracle Hypothesis, attributed to Bennett and Gill, essentially states that the relationships between complexity classes which hold for almost all relativized worlds must also hold in the unrelativized case. Although this paper is not the first to provide a counterexample to the Random Oracle Hypothesis, it does provide a most compelling counterexample by showing that for almost all oracles A, IPA ≠ PSPACEA. If the Random Oracle Hypothesis were true, it would contradict Shamir’s result that IP = PSPACE. In fact, it is shown that for almost all oracles A, co-NPA ⊈ IPA. These results extend to the multiprover proof systems of Ben-Or, Goldwasser, Killian, and Wigderson. In addition, this paper shows that the Random Oracle Hypothesis is sensitive to small changes in the definition. A class IPP, similar to IP, is defined. Surprisingly, the IPP = PSPACE result holds for all oracle worlds.

Original languageEnglish
Pages (from-to)24-39
Number of pages16
JournalJournal of Computer and System Sciences
Issue number1
StatePublished - Aug 1994
Externally publishedYes


FundersFunder number
National Science FoundationCCR-88-23053
International Business Machines Corporation88-00282
Marketing Science Institute
United States-Israel Binational Science Foundation88-00301
African Institute for Mathematical Sciences


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