Black-box constructions for secure computation

Yuval Ishai, Eyal Kushilevitz, Yehuda Lindell, Erez Petrank

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

53 Scopus citations


It is well known that the secure computation of non-trivial functionalities in the setting of no honest majority requires computational assumptions. We study the way such computational assumptions are used. Specifically, we ask whether the secure protocol can use the underlying primitive (e.g., one-way trapdoor permutation) in a black-box way, or must it be nonblack-box (by referring to the code that computes this primitive)? Despite the fact that many general constructions of cryptographic schemes (e.g., CPA-secure encryption) refer to the underlying primitive in a black-box way only, there are some constructions that are inherently nonblack-box. Indeed, all known constructions of protocols for general secure computation that are secure in the presence of a malicious adversary and without an honest majority use the underlying primitive in a nonblack-box way (requiring to prove in zero-knowledge statements that relate to the primitive). In this paper, we study whether such nonblack-box use is essential. We present protocols that use only black-box access to a family of (enhanced) trapdoor permutations or to a homomorphic public-key encryption scheme. The result is a protocol whose communication complexity is independent of the computational complexity of the underlying primitive (e.g., a trapdoor permutation) and whose computational complexity grows only linearly with that of the underlying primitive. This is the first protocol to exhibit these properties.

Original languageEnglish
Title of host publicationSTOC'06
Subtitle of host publicationProceedings of the 38th Annual ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Print)1595931341, 9781595931344
StatePublished - 2006
Event38th Annual ACM Symposium on Theory of Computing, STOC'06 - Seattle, WA, United States
Duration: 21 May 200623 May 2006

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference38th Annual ACM Symposium on Theory of Computing, STOC'06
Country/TerritoryUnited States
CitySeattle, WA


  • Black-box reductions
  • Oblivious transfer
  • Secure computation
  • Theory of cryptography


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