CCA1 secure FHE from PIO, revisited

Abstract

Abstract Fully data using only public information. So far, most FHE schemes are CPA secure. In PKC 2017, Canetti et al. extended the generic transformation of Boneh, Canetti, Halevi and Katz to turn any multi-key identity-based FHE scheme into a CCA1-secure FHE scheme. Their main construction of multi-key identity-based FHE is from probabilistic indistinguishability obfuscation (PIO) and statistical trapdoor encryption. We show that the above multi-key identity-based FHE is not secure by giving an attack. Then we give a solution to avoid the attack and redesign a more succinct and efficient multi-key identity-based FHE scheme. Compared with the scheme of Canetti et al., ours has smaller secret key of one identity and more efficient homomorphic operations. Thus we obtain a more efficient CCA1 secure FHE scheme.

Keywords

• Fully homomorphic encryption
• CCA1
• Probabilistic indistinguishability obfuscation