Arithmetic operations on encrypted data

Abstract

In a conventional cryptosystem, decryption must be conducted when we need to do some arithmetic operations on two encrypted data. That is, one has to convert the encrypted data to their plaintext form before doing arithmetic operations. This will cause the explosure of secret data. In this paper, we propose a method based on the theory of quadratic residue Theory to process data in their encrypted forms directly. From the method, the security of processed data can be greatly enchanced.

Keywords:

• Cryptosystem
• theory of Quadratic Residue
• Legendre symbol
• Chinese Remainder Theorem