Primeless Factoring-Based Cryptography

–Solving the Complexity Bottleneck of Public-Key Generation–
  • Sonia Bogos
  • Ioana Boureanu
  • Serge Vaudenay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7954)


Factoring-based public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off process, e.g., for forwards secrecy. To this end, we extend the Goldwasser-Micali (GM) cryptosystem to a provably secure system, denoted SIS, where the generation of primes is bypassed. By developing on the correct choice of the parameters of SIS, we align SIS’s security guarantees (i.e., resistance to factoring of moduli, etc.) to those of other well-known factoring-based cryptosystems. Taking into consideration different possibilities to implement the fundamental operations, we explicitly compare and contrast the asymptotic complexity of well-known public-key cryptosystems (e.g., GM and/or RSA) with that of SIS’s. The latter shows that once we are ready to accept an increase in the size of the moduli, SIS offers a generally lower asymptotic complexity than, e.g., GM or even RSA.


Security Parameter Quadratic Residue Homomorphic Encryption Forward Secrecy Asymptotic Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sonia Bogos
    • 1
  • Ioana Boureanu
    • 1
  • Serge Vaudenay
    • 1
  1. 1.École Polytechnique Fédérale de LausanneLausanneSwitzerland

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