A vector compression coding algorithm based on SIMD(VCABSIMD)

Abstract

In the vector operation system, each data operation will only increase or decrease the same number for each component of the vector, that is to say, the vector is regarded as a data object on the whole, and each operation is carried out on the whole. For example, translation, scaling and other operations in computer graphics. Such computing systems are currently widely used in graphics, machine learning, mathematical modeling and other fields. When the data in the vector computing system is homomorphic encrypted and uploaded to the cloud server, the problem of low vector coding efficiency and polynomial coefficient expansion caused by a large number of polynomial operations is generated. The existing SIMD coding algorithm encodes an n-dimensional vector integer into a polynomial. The number of calculations increases exponentially with the increase of n, and the coding efficiency of the vector is very low. For typical FHE schemes such as BGV, BFV and CKKS, the main performance bottleneck comes from a large number of polynomial algorithms. Specifically, encrypted data is typically composed of a pair of polynomials with coefficients of hundreds or thousands of bits, requiring expensive multiword arithmetic. In addition, large polynomial lengths increase the computational complexity. Therefore, in this paper, a vector compression coding algorithm based on SIMD(VCABSIMD) is proposed to solve the performance problem when the data in the vector computing system is homomorphically encrypted and uploaded to the cloud server for calculation. The vector coding efficiency and polynomial calculation are deeply optimized.