On generic constructions of circularly-secure, leakage-resilient public-key encryption schemes

Mohammad Hajiabadi, Bruce M. Kapron, Venkatesh Srinivasan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We propose generic constructions of public-key encryption schemes, satisfying key-dependent message (KDM) security for projections and different forms of key-leakage resilience, from CPA-secure private-key encryption schemes with two main abstract properties: (1) a form of (additive) homomorphism with respect to both plaintexts and randomness, and (2) reproducibility, providing a means for reusing encryption randomness across independent secret keys. More precisely, our construction transforms a private-key scheme with the stated properties (and one more mild condition) into a public-key one, providing:–KDM-projection security, an extension of circular security, where the adversary may also ask for encryptions of negated secret key bits;–a (1− o(1)) resilience rate in the bounded-memory leakage model of Akavia et al. (TCC 2009); and–Auxiliary-input security against subexponentially-hard functions. We introduce homomorphic weak pseudorandom functions, a homomorphic version of the weak PRFs proposed by Naor and Reingold (FOCS’95) and use them to realize our base encryption scheme. We in turn obtain homomorphic weak PRFs from homomorphic hash-proof systems (HHPS). We also show how the base encryption scheme may be realized using subgroup indistinguishability (implied, in particular, by quadratic residuosity (QR) and decisional composite residuosity (DCR)). As corollaries of our results, we obtain (1) the first multiple-key projection-secure bit-encryption scheme (as well as the first scheme with a (1 − o(1)) resilience rate) based solely on the HHPS assumption, and (2) a unifying approach explaining the results of Boneh et al. (CRYPTO’08) and Brakerski and Goldwasser (CRYPTO’10). Finally, by observing that Applebaum’s KDM amplification method (EUROCRYPT’11) preserves both types of leakage resilience, we obtain schemes providing at the same time high leakage resilience and KDM security against any fixed polynomial-sized circuit family.

Original languageEnglish (US)
Title of host publicationPublic-Key Cryptography – PKC 2016 - 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, Proceedings
EditorsChen-Mou Cheng, Kai-Min Chung, Bo-Yin Yang, Giuseppe Persiano
PublisherSpringer Verlag
Pages129-158
Number of pages30
ISBN (Print)9783662493861
DOIs
StatePublished - 2016
Event19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016 - Taipei, Taiwan, Province of China
Duration: Mar 6 2016Mar 9 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9615
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016
Country/TerritoryTaiwan, Province of China
CityTaipei
Period3/6/163/9/16

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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