Lattice-based Public Key Encryption with Multi-Ciphertexts Equality Test in Cloud Computing

Nowadays, together with stormy technology advancement, billions of interconnected devices are constantly collecting data around us. In that fashion, privacy protection has become a major concern. The data must be in encrypted form before being stored on the cloud servers. As a result, the cloud servers are unable to perform calculations on en- crypted data, such as searching and matching keywords. In the PKE- MET setting, a cloud server can perform an equality test on a number of ciphertexts which encrypted with the same designated number. In this paper, we propose, for the first time, an efficient construction of a quantum-safe PKE-MET system based on the hardness of the Learning with Errors (LWE) problem in the lattice setting. Furthermore, we also discuss the first lattice-base public key encryption with flexible multi- ciphertext equality test (PKE-FMET) constructions, which allow per- forming equality test on multiple ciphertexts whose designated numbers are less than a threshold number. Our proposed schemes are proven to be secure in the standard model

Public Key Encryption with Equality Test in the Standard Model

Public key encryption with equality test (PKEET) is a cryptosystem that allows a tester who has trapdoors issued by one or more users $U_i$ to perform equality tests on ciphertexts encrypted using public key(s) of $U_i$. Since this feature has a lot of practical applications including search on encrypted data, several PKEET schemes have been proposed so far. However, to the best of our knowledge, all the existing proposals are proven secure only under the hardness of number-theoretic problems and the random oracle heuristics. In this paper, we show that this primitive can be achieved not only generically from well-established other primitives but also even without relying on the random oracle heuristics. More precisely, our generic construction for PKEET employs a two-level hierarchical identity-based encryption scheme, which is selectively secure against chosen plaintext attacks, a strongly unforgeable one-time signature scheme and a cryptographic hash function. Our generic approach toward PKEET has several advantages over all the previous works; it directly leads the first standard model construction and also directly implies the first lattice-based construction. Finally, we show how to extend our approach to the identity-based setting

Learning with Errors is easy with quantum samples

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with Errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the Learning with Errors problem where the error distribution is the one used in cryptography. While our quantum learning algorithm does not break the LWE-based encryption schemes proposed in the cryptography literature, it does have some interesting implications for cryptography: first, when building an LWE-based scheme, one needs to be careful about the access to the public-key generation algorithm that is given to the adversary; second, our algorithm shows a possible way for attacking LWE-based encryption by using classical samples to approximate the quantum sample state, since then using our quantum learning algorithm would solve LWE

Lattice-Based proof of a shuffle

In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft

Puncturable Encryption: A Generic Construction from Delegatable Fully Key-Homomorphic Encryption

Puncturable encryption (PE), proposed by Green and Miers at IEEE S&P 2015, is a kind of public key encryption that allows recipients to revoke individual messages by repeatedly updating decryption keys without communicating with senders. PE is an essential tool for constructing many interesting applications, such as asynchronous messaging systems, forward-secret zero round-trip time protocols, public-key watermarking schemes and forward-secret proxy re-encryptions. This paper revisits PEs from the observation that the puncturing property can be implemented as efficiently computable functions. From this view, we propose a generic PE construction from the fully key-homomorphic encryption, augmented with a key delegation mechanism (DFKHE) from Boneh et al. at Eurocrypt 2014. We show that our PE construction enjoys the selective security under chosen plaintext attacks (that can be converted into the adaptive security with some efficiency loss) from that of DFKHE in the standard model. Basing on the framework, we obtain the first post-quantum secure PE instantiation that is based on the learning with errors problem, selective secure under chosen plaintext attacks (CPA) in the standard model. We also discuss about the ability of modification our framework to support the unbounded number of ciphertext tags inspired from the work of Brakerski and Vaikuntanathan at CRYPTO 2016