Polynomial approximation method for homomorphic function modulo

By proposing a polynomial approximation method for modulo-finding homomorphic functions in total homomorphic encryption technology, the problem of low efficiency of bootstrap algorithm is solved, and the function of running polynomial functions at the same time in homomorphic modulo-finding is realized, which significantly improves the computational efficiency.

CN119691343APending Publication Date: 2025-03-25ENG UNIV OF THE CHINESE PEOPLES ARMED POLICE FORCE
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Patent Information

Application Number
CN202411744169.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-30
Publication Date
2025-03-25

AI Technical Summary

Technical Problem

In the existing all-homomorphic encryption technology, the bootloader algorithm is inefficient, especially the homomorphic mode-finding algorithm is low, resulting in low computational efficiency.

Method used

A polynomial approximation method for modulus calculation of homomorphic functions is proposed. By designing modulus calculation and calculating the whole function, the given polynomial function is simultaneously run in homomorphic modulus calculation, thereby improving the efficiency of the algorithm. This method uses trigonometric functions as intermediate variables, uses low-order polynomial functions to approximate expressing advanced functions to calculate modulus functions, and adjusts the algorithm accuracy by adjusting the number of polynomials and the number of trigonometric functions.

Benefits of technology

By integrating modulus calculation and function calculation, the bootstrap algorithm and homomorphic calculation efficiency are improved, and the given objective function can be calculated while implementing bootstrap, which significantly improves the calculation efficiency.

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Abstract

The invention discloses a polynomial approximation method for modulus calculation of homomorphic functions, which comprises the following steps that: operation in all steps is homomorphic operation performed on a ciphertext: (1) polynomial representation of basic trigonometric functions sin x and cos x: using a polynomial to represent the trigonometric functions, wherein x is a variable; (2) calculation of multiple angle trigonometric functions sin kx and cos kx: the basic trigonometric function is used to calculate the multiple angle trigonometric functions sin kx and cos kx, and k is an integer; and (3) combination of the trigonometric functions to obtain function modulo operation: giving a function f to be calculated, a modulus q and a function modulo F (x) = f (x mod q), and calculating by using the combination of the trigonometric functions to obtain an approximate result # imgabs0 # of the function modulo. The modulo operation and the calculation function are integrally designed, so that a given objective function can be operated while the bootstrap algorithm is calculated, and the calculation efficiency is improved. And the algorithm efficiency is improved.
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