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Homomorphic Indistinguishability Obfuscation and Its Applications

Authors Kaartik Bhushan, Venkata Koppula, Manoj Prabhakaran

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Author Details

Kaartik Bhushan
  • IIT Bombay, India
Venkata Koppula
  • IIT Delhi, India
Manoj Prabhakaran
  • IIT Bombay, India

Funding

  • Bhushan, Kaartik: Funded by Prime Minister Research Fellowship, Government of India.

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Kaartik Bhushan, Venkata Koppula, and Manoj Prabhakaran. Homomorphic Indistinguishability Obfuscation and Its Applications. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.14

Abstract

In this work, we propose the notion of homomorphic indistinguishability obfuscation (HiO) and present a construction based on subexponentially-secure iO and one-way functions. An HiO scheme allows us to convert an obfuscation of circuit C to an obfuscation of C'∘C, and this can be performed obliviously (that is, without knowing the circuit C). A naïve solution would be to obfuscate C'∘iO(C). However, if we do this for k hops, then the size of the final obfuscation is exponential in k. HiO ensures that the size of the final obfuscation remains polynomial after repeated compositions. As an application, we show how to build function-hiding hierarchical multi-input functional encryption and homomorphic witness encryption using HiO.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Program Obfuscation
  • Homomorphisms

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