A Homomorphic Encryption Scheme Based on Affine Transforms

Abstract

As more businesses and consumers move their information storage to the cloud, the need to protect sensitive data is higher than ever. Using encryption, data access can be restricted to only authorized users. However, with standard encryption schemes, modifying an encrypted file in the cloud requires a complete file download, decryption, modification, and upload. This is cumbersome and time-consuming. Recently, the concept of homomorphic computing has been proposed as a solution to this problem. Using homomorphic computation, operations may be performed directly on encrypted files without decryption, hence avoiding exposure of any sensitive user information in the cloud. This also conserves bandwidth and reduces processing time. In this paper, we present a homomorphic computation scheme that utilizes the affine cipher applied to the ASCII representation of data. To the best of the authors» knowledge, this is the first use of affine ciphers in homomorphic computing. Our scheme supports both string operations (encrypted string search and concatenation), as well as arithmetic operations (encrypted integer addition and subtraction). A design goal of our proposed homomorphism is that string data and integer data are treated identically, in order to enhance security.