Category: homomophic encryption

Paper by Wang, et.al.

Dealing with noise is what slows down homomorphic encryption because the encryption has continuously to be refreshed.

Abstract

Achieving both simplicity and efficiency in fully homomorphic encryption (FHE) schemes is important for practical applications. In the simple FHE scheme proposed by Ducas and Micciancio (DM), ciphertexts are refreshed after each homomorphic operation. And ciphertext refreshing has become a major bottleneck for the overall efficiency of the scheme. In this paper, we propose a more efficient FHE scheme with fewer ciphertext refreshings. Based on the DM scheme and another simple FHE scheme proposed by Gentry, Sahai, and Waters (GSW), ciphertext matrix operations and ciphertext vector additions are both applied in our scheme. Compared with the DM scheme, one more homomorphic NOT AND (NAND) operation can be performed on ciphertexts before ciphertext refreshing. Results show that, under the same security parameters, the computational cost of our scheme is obviously lower than that of GSW and DM schemes for a depth-2 binary circuit with NAND gates. And the error rate of our scheme is kept at a sufficiently low level.

https://www.hindawi.com/journals/scn/2018/8706940/

Paper by Alexandru et. al.

Abstract

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party’s inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs.

https://arxiv.org/abs/1809.02267v1

Paper by Chaoju Hu and Jianwei Zhao

ABSTRACT

The public key of the integer homomorphic encryption scheme which was proposed by Van Dijk et al. is long, so the scheme is almost impossible to use in practice. By studying the scheme and Coron’s public key compression technique, a scheme which is able to encrypt n bits plaintext once was obtained. The scheme improved the efficiency of the decrypting party and increased the number of encrypting parties, so it meets the needs of cloud computing better. The security of the scheme is based on the approximate GCD problem and the sparse-subset sum problem.

https://www.scirp.org/journal/PaperInformation.aspx?PaperID=87252