A New Public-Key Cryptosystem via Mersenne Numbers

  • Divesh AggarwalEmail author
  • Antoine Joux
  • Anupam Prakash
  • Miklos Santha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10993)


In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number \(p = 2^n - 1\), where n is a prime, a positive integer h, and two n-bit integers TR, decide whether their exist n-bit integers FG each of Hamming weight less than h such that \(T = F\cdot R + G\) modulo p.



This research was partially funded by the Singapore Ministry of Education and the National Research Foundation, also through the Tier 3 Grant “Random numbers from quantum processes”, MOE2012-T3-1-009. This work has been supported in part by the European Union’s H2020 Programme under grant agreement number ERC-669891 and the French ANR Blanc program under contract ANR-12-BS02-005 (RDAM project). The second author is grateful to CQT where the work has started during his visit.


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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Divesh Aggarwal
    • 1
    Email author
  • Antoine Joux
    • 2
  • Anupam Prakash
    • 3
    • 4
  • Miklos Santha
    • 4
    • 5
  1. 1.School of Computing and Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  2. 2.Chaire de Cryptologie de la Fondation SU, Sorbonne Université, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Inria, CNRS, Univ Paris DiderotParisFrance
  3. 3.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  4. 4.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  5. 5.IRIF, Université Paris Diderot, CNRSParisFrance

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