## Cryptology ePrint Archive: Report 2016/402

Fully Homomorphic Encryption for Point Numbers

Seiko Arita and Shota Nakasato

Abstract: In this paper, based on the FV scheme, we construct a first fully homomorphic encryption scheme FHE4FX that can homomorphically compute addition and/or multiplication of encrypted fixed point numbers without knowing the secret key. Then, we show that in the FHE4FX scheme one can efficiently and homomorphically compare magnitude of two encrypted numbers. That is, one can compute an encryption of the greater-than bit that represents whether or not $x > x'$ given two ciphertexts $c$ and $c'$ (of $x$ and $x'$, respectively) without knowing the secret key. Finally we show that these properties of the FHE4FX scheme enables us to construct a fully homomorphic encryption scheme FHE4FL that can homomorphically compute addition and/or multiplication of encrypted floating point numbers.

Category / Keywords: public-key cryptography / Fully homomorphic encryption, FV scheme, Fixed point number, Floating point number, Greater-than bit.

Date: received 22 Apr 2016, last revised 22 Apr 2016

Contact author: arita at iisec ac jp

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2016/402

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