Structure vs. Hardness through the obfuscation lens

Nir Bitansky, Akshay Degwekar, Vinod Vaikuntanathan

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


Much of modern cryptography, starting from public-key encryption and going beyond, is based on the hardness of structured (mostly algebraic) problems like factoring, discrete log or finding short lattice vectors. While structure is perhaps what enables advanced applications, it also puts the hardness of these problems in question. In particular, this structure often puts them in low complexity classes such as NP ∩ coNP or statistical zero-knowledge (SZK). Is this structure really necessary? For some cryptographic primitives, such as one-way permutations and homomorphic encryption, we know that the answer is yes—they imply hard problems in NP ∩ coNP and SZK, respectively. In contrast, one-way functions do not imply such hard problems, at least not by fully black-box reductions. Yet, for many basic primitives such as public-key encryption, oblivious transfer, and functional encryption, we do not have any answer. We show that the above primitives, and many others, do not imply hard problems in NP ∩ coNP or SZK via fully black-box reductions. In fact, we first show that even the very powerful notion of Indistinguishability Obfuscation (IO) does not imply such hard problems, and then deduce the same for a large class of primitives that can be constructed from IO.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings
EditorsHovav Shacham, Jonathan Katz
Number of pages28
StatePublished - 2017
Externally publishedYes
Event37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States
Duration: 20 Aug 201724 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10401 LNCS


Conference37th Annual International Cryptology Conference, CRYPTO 2017
Country/TerritoryUnited States
CitySanta Barbara


  • Collision-resistant hashing
  • Indistinguishability obfuscation
  • NP ∩ coNP
  • Statistical zero-knowledge
  • Structured hardness

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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