Plaintext recovery attacks and their mitigation in an application-specific SHE scheme

In addition to storage and computing power, cloud providers ensure confidentiality of user data through the use of various encryption technologies. The need to decrypt the data before it can be operated upon exposes a possible security hole which could be exploited by untrustworthy system administrators. Homomorphic encryption allows operations on encrypted data without the need to first decrypt it making it attractive for cloud computing. However, it incurs significant overhead of storage and computation and is therefore infeasible in practice. Somewhat homomorphic schemes have been proposed to handle specific applications - one such scheme, the Zhou Wornell Scheme, operates on vectors of integers. We demonstrate that this scheme is vulnerable to plaintext recovery attacks for a range of vector sizes. We explore the trade-offs between plaintext vector length, public key size and security. Increasing vector length increases security but at the cost of greatly increased public key size. We suggest a way of reducing the size of the public key by up to 90%. Finally, we propose a variant of this scheme which is secure against plaintext recovery attacks.