适用于字符串加密的全同态加密方案

Fully Homomorphic Encryption Scheme Applied to String Computer Engineering

摘要:

现有的全同态加密思想主要实现对整数进行加密,在密文的状态下可以实现加、减、乘、除等四则运算,将其密文进行解密得到的结果与对明文做相同运算的结果一致,然而当加密对象为字符串的时候这些运算将变的毫无意义;为了使得全同态加密算法可以应用在字符串中,设计了一个可以适用于字符串加密的全同态加密算法;首先介绍了全同态加密算法在整数上的实现原理,通过对中国剩余定理的证明过程中发现了中国剩余定理具备定位字符的能力,然后将中国剩余定理引入整数上全同态加密的思想中;引入的中国剩余定理便是可以在加密过程中实现字符串的定位,避免出现加密完成后无法按照原有顺序回复出原文；最后通过举例论证的方式,验证了实现字符串全同态加密算法的的正确性；从而丰富了全同态加密算法的使用范围。

Abstract:

Existing full state encryption thought is mainly encrypted integers. Under the secret state,it can conduct add,subtract,multiply,divide and other operations. The results of private texts decryptions are consistent with the results of plain text. However,when the encrypted object becomes the string,these operations will become meaningless. In order to make full state encryption algorithm can be used in the string,the design applies to a whole string of state encryption algorithm. Firstly it introduced full state encryption algorithm theory on integers. During the prove process of Chinese Remainder Theorem,it could be found that Chinese Remainder Theorem has ability to locate character and then introduced Chinese remainder theorem into integer full state encryption thoughts. Introduced Chinese remainder theorem can locate strings in the encryption process and avoid the problem that after the completion of encryption,it could not return to original text based on original order. Finally,by way of example argument,it proved the correctness of string full text encryption algorithm. Thus the application range of full text encryption algorithm could be enriched. 