紧致优化DGHV全同态加密方案

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~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~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。

Compactly- Optimized DGHV Fully- Homomorphic Encryption Scheme

DGHV scheme is the first fully-homomorphic encryption scheme based on the integers, but ho- momorphic operation in this scheme would result in double increase of the ciphertext size. The ciphertext size must be controlled to a magnitude of less than polynomial bound ~O（λ7）by homorphical decrypting al- gorithm, while the ciphertext size would become increasingly large in the internal operation of the homo- morphic decryption algorithm. Thus a compact-optimization technique for controlling the ciphertext in ho- momorphic addition and homomorphic multiplication is proposed, so that the ciphertext size in this scheme would remain within ~O（λ5）, thus eliminating the influence of homomorphic operation on the eiphertext size, and meanwhile the homomorphic evaluation capability of the optimized scheme is further analyzed .