Homomorphic public-key cryptosystems and encrypting boolean circuits

International audienceGiven 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