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Mathematics

Multi-Keyword Searchable Identity-Based Proxy Re-Encryption from Lattices

Er-Shuo Zhuang, Chun‐I Fan

Published Sep 6, 2023• 7 citations
Publisher

Abstract

To protect the privacy of cloud data, encryption before uploading provides a solution. However, searching for target data in ciphertext takes effort. Therefore, searchable encryption has become an important research topic. On the other hand, since the advancement of quantum computers will lead to the crisis of cracking traditional encryption algorithms, it is necessary to design encryption schemes that can resist quantum attacks. Therefore, we propose a multi-keyword searchable identity-based proxy re-encryption scheme from lattices. In addition to resisting quantum attacks, the proposed scheme uses several cryptographic techniques to improve encryption efficiency. First, identity-based encryption is used to reduce the computation and transmission costs caused by certificates. Second, the proposed scheme uses proxy re-encryption to achieve the purpose of outsourced computing, allowing the proxy server to reduce the computation and transmission costs of the users. Third, the proposed multi-keyword searchable encryption can provide AND and OR operators to increase the flexibility of searchability. Moreover, the access structure of the proposed scheme is not based on a linear secret sharing scheme (LSSS), avoiding the errors caused by an LSSS-based structure in decryption or search results. Finally, we also give formal security proof of the proposed scheme under the decisional learning with errors assumption.

DOI
10.3390/math11183830

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To protect the privacy of cloud data, encryption before uploading provides a solution. However, searching for target data in ciphertext takes effort. Therefore, searchable encryption has become an important research topic. On the other hand, since the advancement of quantum computers will lead to the crisis of cracking traditional encryption algorithms, it is necessary to design encryption schemes that can resist quantum attacks. Therefore, we propose a multi-keyword searchable identity-based proxy re-encryption scheme from lattices. In addition to resisting quantum attacks, the proposed scheme uses several cryptographic techniques to improve encryption efficiency. First, identity-based encryption is used to reduce the computation and transmission costs caused by certificates. Second, the proposed scheme uses proxy re-encryption to achieve the purpose of outsourced computing, allowing the proxy server to reduce the computation and transmission costs of the users. Third, the proposed multi-keyword searchable encryption can provide AND and OR operators to increase the flexibility of searchability. Moreover, the access structure of the proposed scheme is not based on a linear secret sharing scheme (LSSS), avoiding the errors caused by an LSSS-based structure in decryption or search results. Finally, we also give formal security proof of the proposed scheme under the decisional learning with errors assumption.
With the growing need for secure cloud storage and the threat of quantum attacks, we propose a post-quantum secure lattice-based multi-authority attribute-based multi-keyword searchable encryption scheme with dynamic membership. Based on the decisional learning with errors assumption, the proposed scheme resists quantum adversaries while supporting flexible multi-keyword search, decentralized authority to avoid key escrow, and dynamic attribute updates without affecting other users. It enables users to independently generate search tokens, allowing offline authorities and reducing communication overhead. Despite higher encryption costs, experimental results demonstrate that search and decryption remain efficient compared to existing post-quantum lattice-based solutions. The proposed scheme achieves strong data confidentiality and keyword privacy in the post-quantum setting.
Summary With the advent of cloud computing, more and more consumers prefer to use the cloud services with the pay‐as‐you‐consume mode. The cloud storage brings about great convenience to users, who store data in cloud and access to it using the smart devices anytime and anywhere. Consumers' information should be encrypted to guarantee the data privacy. Flexible searching on ciphertext is a critical challenge to be solved for effective data utilization. In this paper, we propose a novel semantic keyword searchable proxy re‐encryption scheme for secure cloud storage. A highlight of this work is that the scheme is quantum attack resistant, while most of the available searchable encryption schemes are not. It supports not only exact keyword search but also synonym keyword search. Moreover, the data owner is capable to delegate his search right to another user using the proxy re‐encryption mechanism. In the generation process of re‐encryption key, the delegator and delegatee do not need to be interactive with each other. The scheme is also collusion resistant. Under the learning with errors hardness problem, this scheme is proved secure in standard model.
To ensure the privacy and security of the stored data, the data can be encrypted first and then stored on the cloud. However, it faces the problem that users cannot search keywords in a large amount of data, which limits the flexibility of file sharing in the cloud environment. Searchable encryption can effectively support users to retrieve encrypted data in the cloud. Public key searchable encryption (PEKS) is used to retrieve the target encrypted data by searching specific keywords. However, the development of quantum computers has led to attacks on conventional encryption algorithms, and it is necessary to design searchable encryption schemes that can resist quantum attacks. Therefore, we propose a lattice puncturable PEKS scheme. Besides resisting quantum attacks, the proposed scheme attains efficient and flexible user revocation. Firstly, identity-based encryption is employed to minimize the complexity of key management. Secondly, the puncturable encryption technology is integrated into the proposed encryption to revoke the decryption capability for selected messages, enabling authorized recipients to repeatedly update their decryption keys to retrieve the currently encrypted messages. Finally, we prove the security of our scheme under the indistinguishability against chosen keyword attack (IND-PUN-sID-CKA), and conduct a comparison with other schemes to emphasize its advantages. Although the scheme does not have an edge in size, it holds an advantage in key update after adding the puncture function and also realizes higher security.
Proxy re-encryption plays an important role for data security in cloud computing and big data, but the traditional re-encryption scheme based on the classical number theory problem cannot resist quantum attack, and the lattice-based cryptosystem has been proved to have the ability to resist quantum attack, so the lattice-based re-encryption scheme has always been a research hotspot. In view of the problem that collusion-resistance and multi-hop cannot be satisfied at the same time in existing schemes, this paper proposes a new identity-based proxy re-encryption scheme on lattice. Firstly, the scheme uses trapdoors as private keys to achieve one-way anti-collusion. In addition, we construct a variant of Learning with Errors (LWE), which uses a convert algorithm to transform the user matrix and replace the vector with a uniform matrix, so that the scheme can meet the requirements of multi-hop and encrypt multiple bits of messages at one time. Theoretical analysis and experimental simulation prove that the security of the new scheme can be reduced to a decision LWE problem, which can reach the IND-sID-CPA security in the standard model and can improve the encryption efficiency while ensuring the security.
Abstract. When data is outsourced to a remote storage server, search-able encryption plays an important role to protect data privacy while allowing users to retrieve data in the massive ciphertext. As far as we know, most of the existing searchable encryption schemes work based on the bilinear map. These schemes may not be secure in the quantum age. Both discrete logarithms and factorization can be solved by quantum computer in a polynomial time. There is very few searchable encryption scheme that can be proved secure in post quantum age. In this paper, in order to construct a post-quantum secure scheme for future cloud stor-age, we suggest a public key encryption with semantic keyword search using the lattice based mechanism. The suggested scheme is proved se-cure against indistinguishable chosen-keyword attacks (IND-CKA) based on learning with errors (LWE) problem. This scheme is believed to be secure in quantum-era due to the quantum intractability of the LWE problem.
Multi-Writer Searchable Encryption, also known as public-key encryption with keyword search(PEKS), serves a wide spectrum of data sharing applications. It allows users to search over encrypted data encrypted via different keys. However, most of the existing PEKS schemes are built on classic security assumptions, which are proven to be untenable to overcome the threats of quantum computers. To address the above problem, in this paper, we propose a lattice-based searchable encryption scheme from the learning with errors (LWE) hardness assumption. Specifically, we observe that the keys of each user in a basic scheme are composed of large-sized matrices and basis of the lattice. To reduce the complexity of key management, our scheme is designed to enable users to directly use their identity for data encryption. We present several optimization techniques for implementation to make our design nearly practical. For completeness, we conduct rigorous security, complexity, and parameter analysis on our scheme, and perform comprehensive evaluations at a commodity machine. With a scenario of 100 users, the cost of key generation for each user is 125s, and the cost of searching a document with 1000 keywords is 13.4ms.