Universite Blaise Pascal - Clermont-Ferrand
The authors propose a generic approach to design homomorphic encryption schemes, which extends Gjosteen's framework. From this generic method, they deduce a new homomorphic encryption scheme in a composite-order subgroup of points of an elliptic curve which admits a pairing e : GxG->Gt. This scheme has some interesting theoretical and practical properties: it allows an arbitrary number of multiplications in the groups G and Gt, as well as a pairing evaluation on the underlying plaintexts. They prove the semantic security under chosen plaintext attack of their scheme under a generalized subgroup membership assumption, and they also prove that it cannot achieve ind-cca1 security.