Improved Cryptanalysis of a Fully Homomorphic Symmetric Encryption Scheme

Baocang Wang,Quanbo Qu,Zhili Zhang,Yuan Ping

doi:10.1155/2019/8319508

Baocang Wang, Quanbo Qu + Show 2 more

Open Access

https://doi.org/10.1155/2019/8319508

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Abstract

Homomorphic encryption is widely used in the scenarios of big data and cloud computing for supporting calculations on ciphertexts without leaking plaintexts. Recently, Li et al. designed a symmetric homomorphic encryption scheme for outsourced databases. Wang et al. proposed a successful key-recovery attack on the homomorphic encryption scheme but required the adversary to know some plaintext/ciphertext pairs. In this paper, we propose a new ciphertext-only attack on the symmetric fully homomorphic encryption scheme. Our attack improves the previous Wang et al.’s attack by eliminating the assumption of known plaintext/ciphertext pairs. We show that the secret key of the user can be recovered by running lattice reduction algorithms twice. Experiments show that the attack successfully and efficiently recovers the secret key of the randomly generated instances with an overwhelming probability.

Highlights

With the rapid development of big data, the significance of privacy and security issues was highly regarded
A series of cryptoghraphic applications, such as fair electronic transaction [1], outsourcing data classification [2], lightweight security system of Internet of Things [3], mobile Ecommerce [4], and data mining based on homomorphic encryption, have been proposed
Thereafter, significant efforts had been performed to improve the efficiency of homomorphic encryption schemes [8,9,10]

Summary

Introduction

With the rapid development of big data, the significance of privacy and security issues was highly regarded. Li et al [16] designed a symmetric homomorphic encryption scheme for outsourced databases that allow multiple data owners to efficiently share their data securely without compromising the privacy of the data. Wang et al [17] observed that if some plaintext/ciphertext pairs were succesfully overdropped, one can efficiently recover the corresponding secret key of the scheme from the obtained plaintext/ciphertext pairs. In practical scenarios, it may be difficult for the adversary to capture plaintext/ciphertext pairs. We propose a new efficient cryptanalytic attack on Li et al.’s homomorphic encryption scheme.

Preliminaries

The Proposed Attack

Conclusion