With the rapid development and popularization of cloud computing, the security multiparty computation becomes a hot issue for the current research. This paper combs and analyzes the research of general security multiparty computation in cloud computing environment, and introduces the solution encryption schemes, including multi-key fully homomorphic encryption scheme based on Learning with errors and multi-key fully homomorphic attribute-based encryption scheme. This paper discusses the directions for future works in the end.
With the rapid development and popularization of cloud computing, the security multiparty computation becomes a hot issue for the current research. This paper combs and analyzes the research of general security multiparty computation in cloud computing environment, and introduces the solution encryption schemes, including multi-key fully homomorphic encryption scheme based on Learning with errors and multi-key fully homomorphic attribute-based encryption scheme. This paper discusses the directions for future works in the end.
We construct protocols for secure multiparty computation with the help of a computationally powerful party, namely the “cloud”. Our protocols are simultaneously ecient in a number of metrics: • Rounds: our protocols run in 4 rounds in the semi-honest setting, and 5 rounds in the malicious setting. • Communication: the number of bits exchanged in an execution of the protocol is independent of the complexity of function f being computed, and depends only on the length of the inputs and outputs. • Computation: the computational complexity of all parties is independent of the complexity of the function f, whereas that of the cloud is linear in the size of the circuit computing f. In the semi-honest case, our protocol relies on the “ring learning with errors” (RLWE) assumption, whereas in the malicious case, security is shown under the Ring LWE assumption as well as the existence of simulation-extractable NIZK proof systems and succinct non-interactive arguments. In the malicious setting, we also relax the communication and computation requirements above, and only require that they be “small” ‐ polylogarithmic in the computation size and linear in the size of the joint size of the inputs. Our constructions leverage the key homomorphic property of the recent fully homomorphic encryption scheme of Brakerski and Vaikuntanathan (CRYPTO 2011, FOCS 2011). Namely, these schemes allow combining encryptions of messages under dierent keys to produce an encryption (of the sum of the messages) under the sum of the keys. We also design an ecient, non-interactive threshold decryption protocol for these fully homomorphic encryption schemes.
Abstract. Fully homomorphic encryption (FHE) enables secure computation over the encrypted data of a single party. We explore how to extend this to multiple parties, using threshold fully homomorphic encryption (TFHE). In such scheme, the parties jointly generate a common FHE public key along with a secret key that is shared among them; they can later cooperatively decrypt ciphertexts without learning anything but the plaintext. We show how to instantiate this approach efficiently, by extending the recent FHE schemes of Brakerski, Gentry and Vaikuntanathan (CRYPTO ’11, FOCS ’11, ITCS ’12) based on the (ring) learning with errors assumption. Our main tool is to exploit the property that such schemes are additively homomorphic over their keys. Using TFHE, we construct simple multiparty computation protocols secure against fully malicious attackers, tolerating any number of corruptions, and providing security in the universal composability framework. Our protocols have the following properties: Low interaction: 3 rounds of interaction given a common random string, or 2 rounds with a public-key infrastructure. Low communication: independent of the function being computed (proportional to just input and output sizes). Cloud-assisted computation: the bulk of the computation can be efficiently outsourced to an external entity (e.g. a cloud service) so that the computation of all other parties is independent of the complexity of the evaluated function. 1
Fully homomorphic encryption (FHE) allows arbitrary computations to be performed directly on encrypted data and is a core technology for privacy computing and secure cloud computing. The Number Theory Research Unit (NTRU) has become a research topic in this field by virtue of its lattice-based anti-quantum security, efficient polynomial operation characteristics and natural multi-key homomorphism capability. In this paper, we systematically review the key advances of NTRU-based FHE, covering the directions of the design of FHE, the optimization of bootstrapping techniques, and the application to FHE for multi-key approaches. Furthermore, the innovativeness and practical application challenges of the schemes are analyzed, and the future research trends are envisioned.
Aiming at the problems of large ciphertext size and low efficiency in the current secure multi-party computation (SMC) protocol based on fully homomorphic encryption (FHE), the paper proves that the fully homomorphic encryption scheme that supports multi-bit encryption proposed by Chen Li et al. satisfies the key homomorphism. Based on this scheme and threshold decryption, a three-round, interactive, leveled, secure multi-party computation protocol under the Common Random String (CRS) model is designed. The protocol is proved to be safe under the semi-honest model and the semi-malicious model. From the non-interactive zero-knowledge proof, it can be concluded that the protocol is also safe under the malicious model. Its security can be attributed to the Decisional Learning With Errors (DLWE) and a variant of this problem (some-are-errorless LWE). Compared with the existing secure multi-party computation protocol based on fully homomorphic encryption under the CRS model, the ciphertext size of this protocol is smaller, the efficiency is higher, the storage overhead is smaller, and the overall performance is better than the existing protocol.
Abstract Data can be stored and processed in an encrypted format using fully homomorphic encryption, which makes cloud computing provider can process data well without even knowing data information. However, most existing homomorphic encryption schemes based on ring learning with errors, focus on the special classes of rings, such as power-of-two cyclotomic rings, which significantly limits its application efficiency in cloud computing. Therefore, in this letter, to solve this problem above, an efficient fully homomorphic encryption scheme is proposed based on ring learning with errors in arbitrary cyclotomic rings. Particularly, a “somewhat homomorphic encryption” scheme is firstly proposed based on ring learning with errors. A novel fully homomorphic encryption scheme is further presented using key-switching. With theoretical and experimental verification, the proposed scheme has advantage of high efficiency of encryption and decryption. The security of our scheme strictly reduces to hardness of decision ring learning with errors problem in the random oracle model.
With the popularization of cloud computing model, the outsourcing of data storage and computing services has become an indispensable trend, which lead to the related data security and privacy protection issues that have attracted extensive attention in the industry. Fully homomorphic encryption, as an encryption technology that can process ciphertext information without exposing plaintext information, has natural user data security and privacy protection characteristics. Meanwhile, the excellent quantum-resistant performance and homomorphic properties of lattice ciphers have made lattice-based homomorphic encryption schemes a much-attend research hotspot in the field of cryptography in recent years. In this paper we mainly introduce the status of all-pass encryption and several typical references for the research of lattice-based all-homomorphic cryptography.