Applicable Algebra in Engineering, Communication and Computing

, Volume 17, Issue 3, pp 239–255

Homomorphic Public-Key Cryptosystems and Encrypting Boolean Circuits

Original article

DOI: 10.1007/s00200-006-0005-x

Cite this article as:
Grigoriev, D. & Ponomarenko, I. AAECC (2006) 17: 239. doi:10.1007/s00200-006-0005-x


Given an arbitrary finite nontrivial group, we describe a probabilistic public-key cryptosystem in which the decryption function is chosen to be a suitable epimorphism from the free product of finite Abelian groups onto this finite group. It extends the quadratic residue cryptosystem (based on a homomorphism onto the group of two elements) due to Rabin – Goldwasser – Micali. The security of the cryptosystem relies on the intractability of factoring integers. As an immediate corollary of the main construction, we obtain a more direct proof (based on the Barrington technique) of Sander-Young-Yung result on an encrypted simulation of a boolean circuit of the logarithmic depth.


Homomorphic cryptosystemFree product of groupsEncrypting boolean circuits

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.IRMARUniversité de RennesRennesFrance
  2. 2.Steklov Institute of MathematicsSt. PetersburgRussia