Regularity of Lossy RSA on Subdomains and Its Applications

  • Mark Lewko
  • Adam O’Neill
  • Adam Smith
Conference paper

DOI: 10.1007/978-3-642-38348-9_4

Volume 7881 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Lewko M., O’Neill A., Smith A. (2013) Regularity of Lossy RSA on Subdomains and Its Applications. In: Johansson T., Nguyen P.Q. (eds) Advances in Cryptology – EUROCRYPT 2013. EUROCRYPT 2013. Lecture Notes in Computer Science, vol 7881. Springer, Berlin, Heidelberg


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 \(\mathbb{Z}_\emph{N}\) and the security of RSA-based constructions.


RSA encryption PKCS #1 v1.5 Lossy trapdoor functions φ-Hiding Assumption Gauss sums 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Mark Lewko
    • 1
  • Adam O’Neill
    • 2
  • Adam Smith
    • 3
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.Boston UniversityUSA
  3. 3.Pennsylvania State UniversityUSA