Regularity of lossy RSA on subdomains and its applications

Mark Lewko, Adam O'Neill, Adam Smith

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

8 Scopus citations

Abstract

We build on an approach of Kiltz et al. (CRYPTO '10) and bring new techniques to bear on the study of how "lossiness" of the RSA trapdoor permutation under the φ-Hiding Assumption (φA) can be used to understand the security of classical RSA-based cryptographic systems. In particular, we show that, under φA, several questions or conjectures about the security of such systems can be reduced to bounds on the regularity (the distribution of the primitive e-th roots of unity mod N) of the "lossy" RSA map (where e divides φ(N)). Specifically, this is the case for: (i) showing that large consecutive runs of the RSA input bits are simultaneously hardcore, (ii) showing the widely-deployed PKCS #1 v1.5 encryption is semantically secure, (iii) improving the security bounds of Kiltz et al. for RSA-OAEP. We prove several results on the regularity of the lossy RSA map using both classical techniques and recent estimates on Gauss sums over finite subgroups, thereby obtaining new results in the above applications. Our results deepen the connection between "combinatorial" properties of exponentiation in ℤN and the security of RSA-based constructions.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Pages55-75
Number of pages21
DOIs
StatePublished - 2013
Event32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013 - Athens, Greece
Duration: May 26 2013May 30 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7881 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013
CountryGreece
CityAthens
Period5/26/135/30/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Regularity of lossy RSA on subdomains and its applications'. Together they form a unique fingerprint.

Cite this