Efficient identity-based leveled fully homomorphic encryption from RLWE

Based on the learning with errors over rings (RLWE) assumption, a leveled fully homomorphic encryption (FHE) by the approximate eigenvector method under the same public key is proposed, which security can be reduced to the shortest vector problem on ideal lattices in the worst case. And the leveled FHE under different public keys is realized by the secret key switching without dimension reduction. Combine the public key of leveled FHE with the identity, we bring forward an efficient identity-based leveled FHE scheme from the RLWE assumption. The security analysis shows that our identity-based leveled FHE scheme is selective-ID secure against chosen-plaintext attacks in the random oracle model. And the efficiency analysis and simulation results show that the proposed identity-based leveled FHE scheme is much more efficient than Gentry's and Wang's identity-based cryptosystems based on the learning with errors assumption. Copyright (c) 2016 John Wiley & Sons, Ltd.