Small interval interpolation fitting bootstrapping method based on residue number system

Aiming at the problem that the bootstrapping time of approximate homomorphic encryption scheme is too long, a small interval interpolation fitting method based on residue system is proposed. In this paper, the sinusoidal function by using interpolating and fitting method between the multiple cells to avoid the increase in bootstrapping time or decrease in calculation accuracy caused by the high degree of fitting polynomial is calculated. And the efficiency of modular multiplication and modular inversion in the calculation process is improved by combining the residual system. Lagrange interpolation polynomial is used to interpolate and fit the sine function among different intervals. The comparison function is implemented by the compound implementation of low-degree polynomials, and an interval judgment algorithm is proposed to identify the interval of the ciphertext. Finally, under the precision of 24 bits, the modular operation time in the bootstrapping process decreased to 8% of the HEAAN. When the number of slots is 65 536, the average module operation time per slot is 0.028 ms.