An efficient CCA-secure cryptosystem over ideal lattices from identity-based encryption

We first construct an efficient IND-sID-CPA secure IBE cryptosystem from ideal lattices, and proceed with its security proof under the standard model in detail. Then with an asymptotically efficient strongly unforgeable one-time signature, we propose a new CCA secure public key encryption (PKE) scheme over ideal lattices by universal paradigm of IBE transformation. Performance of the resulting PKE system is very close to the underlying IBE scheme and its security can be tightly reduced to decisional R-LWE hardness assumption. Compared with known CCA secure PKE schemes from standard lattices, our new scheme is simpler and more efficient.