Abstract Multi-key fully homomorphic encryption (MFHE) supports arbitrary meaningful computations on encrypted data under different public keys even without access to the secret key, which is well tailored for the secure multiparty computation scenarios. Based on the Gentry–Sahai–Waters scheme (a single-key FHE in Crypto 2013) with the underlying learning with errors problem, MW16 scheme (Eurocrypt 2016) utilizes the method of ‘linear combination procedure’ (LCP) as a subroutine to construct the auxiliary information for the expanded ciphertexts of MFHE scheme. However, every party shares a common random string (CRS) to be distributed by a trusted setup, which is unpractical. Meanwhile, the noise in the auxiliary information is too much compared with the one in fresh ciphertexts. In this paper, we propose a modified MFHE scheme in the plain model, i.e. without CRS, to enhance the practicability of MFHE. Specifically, every involved party generates his own public key independent on a CRS. Then a potential improvement on the LCP is developed to provide auxiliary information, which largely reduces the noise and leads to a smaller modulus for our MFHE. Furthermore, the feasibility of our proposal is also proved by theoretical performance comparisons.

Abstract Authenticated key exchange protocol is widely applied in the Internet services. Lattice‐based key exchange protocols turn out to be quantum‐resistant and hence have attracted tremendous attention. A lattice‐based explicit authenticated key exchange protocol is constructed by combining an IND‐CPA key encapsulation mechanism with a strong EUF‐CMA digital signature under the message‐recovery mode. Concrete parameter specifications are suggested under the 102 and 218 bits post‐quantum security, respectively. Compared with the implicit authenticated key exchange derived directly from the key encapsulation mechanism, our proposals reduce the communication costs by 21.7% and 25.7%, respectively, under the same post‐quantum security level. Rough analysis shows that the proposals also obtain some advantages over previous constructions in term of computational efficiency. Moreover, our scheme achieves perfect forward secrecy while the original scheme only satisfies weak forward secrecy.

Private information retrieval (PIR) protocol is a powerful cryptographic tool and has received considerable attention in recent years as it can not only help users to retrieve the needed data from database servers but also protect them from being known by the servers. Although many PIR protocols have been proposed, it remains an open problem to design an efficient PIR protocol whose communication overhead is irrelevant to the database size N . In this paper, to answer this open problem, we present a new communication-efficient PIR protocol based on our proposed single-ciphertext fully homomorphic encryption (FHE) scheme, which supports unlimited computations with single variable over a single ciphertext even without access to the secret key. Specifically, our proposed PIR protocol is characterized by combining our single-ciphertext FHE with Lagrange interpolating polynomial technique to achieve better communication efficiency. Security analyses show that the proposed PIR protocol can efficiently protect the privacy of the user and the data in the database. In addition, both theoretical analyses and experimental evaluations are conducted, and the results indicate that our proposed PIR protocol is also more efficient and practical than previously reported ones. To the best of our knowledge, our proposed protocol is the first PIR protocol achieving O1 communication efficiency on the user side, irrelevant to the database size N .

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.