MarriageTheoremのこと

_ IACR ePrint 2015/466まで確認済み、ECCC 2003年分まで確認済み

_ 気になった論文：Efficient Fully Homomorphic Encryption with Circularly Secure Key Switching Process, Zhou Tanping*, Yang Xiaoyuan, Zhang Wei and Wu Liqiang, http://eprint.iacr.org/2015/466

Fully homomorphic encryption (FHE) has important applications in cloud computing. However, almost all fully homomorphic encryption schemes share two common flaws that they all use large-scale secret keys and some operations inefficient. In this paper, the “special b” variant of the Learning With Errors problem (bLWE) is presented, and helps us construct the first circularly secure key switching process which can replace the key switching process and similar re-linearization process used by the existing FHE schemes. Then, we present an efficient FHE. Compared with Brakerski’s scheme, our scheme reduces L secret keys to one and is more efficient. Finally, we prove the chosen-plaintext attack (CPA) security of the fully homomorphic scheme and the circular security of key switching process in standard model under the learning with errors problem (LWE) assumption.