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The ISO/IEC 28033 series specifies several cryptographic mechanisms that allow a function to be computed on encrypted data, while preserving the confidentiality of input, intermediate data, and output of a computation using only FHE. Verification that the function itself is computed correctly is outside of the scope of this document. This document defines the general concepts and principles of FHE including foundational definitions, symbols and formats. This document also describes the security models, hardness assumptions with concrete security, message spaces, plaintext spaces, ciphertext spaces, and key spaces.