SoK: Learning with Errors, Circular Security, and Fully Homomorphic Encryption

SoK: Learning with Errors, Circular Security, and Fully Homomorphic Encryption

연구 분야: Cryptography

학회: IACR International Conference on Public-Key Cryptography

All known constructions of fully homomorphic encryption (FHE) schemes from the learning with errors (LWE) assumption require the encryption schemes to be circular secure. A long-standing open problem in the study of FHE schemes is to demonstrate evidence for their circular security. In this work, we systematize the flavors of circular security required for a number of FHE constructions, formulate circular security conjectures, show search-to-decision reductions for them, and pose several open problems.