On the regularity of lossy RSA: Improved bounds and applications to padding-based encryption

Adam Smith, Ye Zhang

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

4 Scopus citations

Abstract

We provide new bounds on how close to regular the map x ↦ xe is on arithmetic progressions in ℤN, assuming e|Φ(N) and N is composite. We use these bounds to analyze the security of natural cryptographic problems related to RSA, based on the well-studied Φ-Hiding assumption. For example, under this assumption, we show that RSA PKCS #1 v1.5 is secure against chosen-plaintext attacks for messages of length roughly bits, whereas the previous analysis, due to [19], applies only to messages of length less than. In addition to providing new bounds, we also show that a key lemma of [19] is incorrect. We prove a weaker version of the claim which is nonetheless sufficient for most, though not all, of their applications. Our technical results can be viewed as showing that exponentiation in ℤN is a deterministic extractor for every source that is uniform on an arithmetic progression. Previous work showed this type of statement only on average over a large class of sources, or for much longer progressions (that is, sources with much more entropy).

Original languageEnglish (US)
Title of host publicationTheory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings
EditorsYevgeniy Dodis, Jesper Buus Nielsen
PublisherSpringer Verlag
Pages609-628
Number of pages20
ISBN (Electronic)9783662464939
StatePublished - Jan 1 2015
Event12th Theory of Cryptography Conference, TCC 2015 - Warsaw, Poland
Duration: Mar 23 2015Mar 25 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9014
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th Theory of Cryptography Conference, TCC 2015
CountryPoland
CityWarsaw
Period3/23/153/25/15

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Smith, A., & Zhang, Y. (2015). On the regularity of lossy RSA: Improved bounds and applications to padding-based encryption. In Y. Dodis, & J. B. Nielsen (Eds.), Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings (pp. 609-628). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9014). Springer Verlag.