Multi-bit homomorphic encryption based on learning with errors over rings

Basing on Learning with errors over rings (RLWE) assumption, we provide a new multi-bit somewhat homomorphic encryption scheme. We introduce canonical embedding to transform a ring element into a vector, such that polynomial multiplication can be performed in  ~ (nlog n) scalar operations, and ciphertext size is reduced at the same time. The CPA security of this scheme can be reduced into RLWE assumption. Keywords-fully homomorphic encryption; somewhat homomorphic encryption; lattice hard problems; RLWE assumption; canonical embedding

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