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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.}

arithmetic, we store a few numbers of signi cant digits (e.g. most signi cant bits, MSBs) and carry out arithmetic operations between them. The resulting value should be rounded again by removing some inaccurate least signi cant bits (LSBs) …

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