Public-Key Cryptosystems with Primitive Power Roots of Unity.

We first consider a variant of the Schmidt-Samoa–Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoring n = p²q. Second, we introduce new cryptographic properties ˵affine″ and ˵pre-image restriction″, which are closely related to homomorphism. Intuitively, ˵affine″ is a tuple of functions which have a special homomorphic property, and ˵pre-image restriction″ is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in ]> . We show that our scheme has the above cryptographic properties. [ABSTRACT FROM AUTHOR]