Cryptosystems with a multi prime composite modulus

Shay Gueron, Nir Drucker

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


Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.

Original languageEnglish
Title of host publicationCCNC 2018 - 2018 15th IEEE Annual Consumer Communications and Networking Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages7
ISBN (Electronic)9781538647905
StatePublished - 16 Mar 2018
Event15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018 - Las Vegas, United States
Duration: 12 Jan 201815 Jan 2018


Conference15th IEEE Annual Consumer Communications and Networking Conference, CCNC 2018
Country/TerritoryUnited States
CityLas Vegas

Bibliographical note

Funding Information:
This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1018/16), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office.

Publisher Copyright:
© 2018 IEEE.

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Signal Processing
  • Media Technology


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