Boolean Cipher Circuits Using Fully Homomorphic Encryption and OpenFHE

DM (FHEW) [1] uses a LWE (Learning With Error) method that provides fully homomorphic encryption (FHE). It is able to evaluate cipher data applied onto Boolean circuits and uses bootstrapping after each gate evaluation. This allows the evaluation to be conducted in less than 0.1 seconds. The gates implemented are AND, OR, NAND, NOR, and NOT. In homomorphic encryption, the noise in the computation increases as we perform operations. This is typically when we perform a large number of additions. and multiplications will often reduce the amount of noise. A bootstrapping process allows for us to reset the noise and will introduce a delay in the computation. In this case, we will use the Gama-Izabachene-Nguyen-Xie (GINX) [2] bootstrapping method.

In this case, we will use the Boolean circuit:

This gives us a Truth Table of:

b1  b2  (b1.b2)  (b1.NOT(b2)  Z
--------------------------------
0   0   0         0           0
0   1   0         0           0
1   0   0         1           1
1   1   1         0           1