More constructions of lossy and correlation-secure trapdoor functions

David Mandell Freeman, Oded Goldreich, Eike Kiltz, Alon Rosen, Gil Segev

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

83 Scopus citations

Abstract

We propose new and improved instantiations of lossy trapdoor functions (Peikert and Waters, STOC '08), and correlation-secure trapdoor functions (Rosen and Segev, TCC '09). Our constructions widen the set of number-theoretic assumptions upon which these primitives can be based, and are summarized as follows: Lossy trapdoor functions based on the quadratic residuosity assumption. Our construction relies on modular squaring, and whereas previous such constructions were based on seemingly stronger assumptions, we present the first construction that is based solely on the quadratic residuosity assumption. Lossy trapdoor functions based on the composite residuosity assumption. Our construction guarantees essentially any required amount of lossiness, where at the same time the functions are more efficient than the matrix-based approach of Peikert and Waters. Lossy trapdoor functions based on the d-Linear assumption. Our construction both simplifies the DDH-based construction of Peikert and Waters, and admits a generalization to the whole family of d-Linear assumptions without any loss of efficiency. Correlation-secure trapdoor functions related to the hardness of syndrome decoding.

Original languageAmerican English
Title of host publicationPublic Key Cryptography, PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
Pages279-295
Number of pages17
DOIs
StatePublished - 2010
Externally publishedYes
Event13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010 - Paris, France
Duration: 26 May 201028 May 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6056 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010
Country/TerritoryFrance
CityParis
Period26/05/1028/05/10

Keywords

  • Public-key encryption
  • correlation-secure trapdoor functions
  • lossy trapdoor functions

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