How to build a faster private information retrieval protocol?

A CPA secure multi-bit somewhat homomorphic encryption scheme based on Learning With Errors over Rings assumption is presented. We use canonical embedding to transform ring elements into vectors over Zq, and thus decrease encryption and decryption cost. Comparing with GHV scheme appeared in 2010, to encrypt n bits, this scheme can reduce encryption cost from O(n3/2) into O(nlog n). Finally, an efficient private information retrieval protocol that employs this scheme is presented.

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