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DGHV方案是第一个基于整数的全同态加密方案,但该方案中同态操作导致密文尺寸成倍增长,必须通过同态解密算法,才能够将密文尺寸控制在一个多项式界珟O(λ7)以内,而且同态解密算法的内部运算过程中,密文数据的尺寸仍在不断增加。这里给出一个紧致优化技术,控制同态乘和同态加操作中的密文,使得该方案的密文尺寸始终保持在珟O(λ5)以内,消除了同态操作对密文尺寸的影响,并进一步分析了优化方案的同态运算能力。
The DGHV scheme is the first integer-based homomorphic encryption scheme, but the homomorphic operation in this scheme leads to double the size of the ciphertext, and the homomorphic decryption algorithm must be used to control the size of the ciphertext in a polynomial boundary (λ7), and the size of ciphertext data is still increasing in the internal computing process of homomorphic decryption algorithm. Here a compact optimization technique is proposed to control the ciphertext in the homomultiplier and homomorphism operations so that the ciphertext size of the scheme stays within 珟 O (λ5), eliminating the effect of homomorphism on ciphertext size Influence, and further analysis of the optimization program of the homomorphic computing power.