FFHEField Feeding in a Hot Environment
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In this section, we follow Gentry's approach to transform RSHE into a fully homomorphic encryption scheme (FFHE), and we identify the scheme supporting operations over floating-point numbers.
Formally, according to RSHE in Section 5.1, we define FFHE as follows.
To securely store a floating-point number, we use FFHE to encrypt it as ([[s']], [[s]], [[e]]), where s' [member of] {0,1} is the sign bit of x, s is a k-bits number.
The input of our FFHE scheme is binary bit; therefore, the ciphertext is
The FFHE scheme completely simulates a floating-point operation in plaintext in the form of a circuit so that the relative error of operation result in ciphertext is not increased compared with the result in plaintext.
In Sections 5 and 6, we proposed our revised somewhat homomorphic encryption scheme (RSHE) and our floating-point fully homomorphic encryption scheme (FFHE).
Using Taylor series, our FFHE can homomorphically evaluate analytic functions f(%) taking floating-point numbers as input.
The precision of floating-point numbers in our FFHE is k.
FFHE scheme is a fully homomorphic encryption scheme that supports analytic function operations based on floating-point numbers.
We constructed a revised floating-point fully homomorphic encryption scheme (FFHE).