Homomorphic Encryption for Arithmetic of Approximate …

Homomorphic Encryptionfor Arithmetic of Approximate NumbersJung Hee Cheon1, Andrey Kim1, Miran Kim2, and Yongsoo Song11 Seoul National University, Republic of Korea{jhcheon, kimandrik, of California, San suggest a method to construct a Homomorphic Encryption scheme for approxi-mate Arithmetic . It supports an Approximate addition and multiplication of encrypted messages,together with a newrescalingprocedure for managing the magnitude of plaintext. This proce-dure truncates a ciphertext into a smaller modulus, which leads to rounding of plaintext. Themain idea is to add a noise following significant figures which contain a main message. This noiseis originally added to the plaintext for security, but considered to be a part of error occurringduring Approximate computations that is reduced along with plaintext by rescaling. As a re-sult, our decryption structure outputs an Approximate value of plaintext with a also propose a new batching technique for a RLWE-based construction.}

Keywords. Homomorphic encryption, approximate arithmetic 1 Introduction Homomorphic encryption (HE) is a cryptographic scheme that enables homomorphic oper-ations on encrypted data without decryption. Many of HE schemes (e.g. [18, 6, 7, 4, 5, 25, 33, 2, 26, 13, 12, 21, 19]) have been suggested following Gentry’s blueprint [23]. HE can be

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  Schemes, Encryption, Homomorphic, Homomorphic encryption

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