ABSTRACT Public auditing is a method used to verify the integrity of data stored in the cloud without requiring access to the actual data. However, the advancement of quantum computers poses significant security threats to existing public auditing schemes, as these schemes are based on conventional cryptography hard problems, which are vulnerable to quantum attacks. To address this, NIST has launched the development of post‐quantum cryptographic primitives and protocols. Among the various approaches, lattice‐based cryptography (LBC) is considered one of the most promising candidates due to its strong security guarantees and inherent resistance to quantum attacks. Leveraging LBC, several researchers have proposed lattice‐based public auditing (LBPA) schemes for cloud storage security based on lattice hardness assumptions. This paper provides a comprehensive survey of existing LBPA schemes for cloud storage, presenting a detailed taxonomy and analyzing their similarities, differences, and performance. Additionally, it highlights key challenges and outlines future research directions for designing efficient and secure public auditing schemes in the post‐quantum era.

Public Key Authenticated Encryption with Keyword Search (PAEKS) allows keyword searches over encrypted data in the cloud without revealing actual data and the receiver can verify the sender’s authenticity or detect tampering. However, the existing PAEKS schemes are based on classical hard problems that are vulnerable to quantum attacks. To overcome these issues, lattice-based PAEKS schemes have been proposed, which provide post quantum security but incur high computational overhead and suffer from inherent issues such as the Certificate Management Problem (CMP) or Key Escrow Problem (KEP). To address the above problems, in this paper, we introduce a Module Lattice-based Certificateless Signcryption with Keyword Search (ML-CLSCKS), which relies on Module Learning with Errors (MLWE) and Module Short Integer Solution (MSIS). The security analysis proves that ML-CLSCKS achieves both confidentiality and unforgeability against Type I and Type II adversaries in the Random Oracle Model (ROM). The performance analysis shows that ML-CLSCKS outperforms than existing lattice-based PAEKS schemes and makes the practical quantum-resistant scheme suitable for searchable encryption in cloud environments.

Ciphertext Policy Attribute-Based Encryption (CP-ABE) is one of the most prevalent cryptographic primitives for realizing privacy and fine-grained access control in cloud computing. However, most of the existing CP-ABE schemes constructed using Paring-Based Cryptography (PBC) from Discrete Logarithm Problem (DLP) or Diffie Hellman Problem (DHP) assumptions are susceptible to quantum attacks, whereas CP-ABE schemes constructed using lattice-based cryptography based on Learning with Errors (LWE) and Ring-LWE (R-LWE) assumptions are quantum-safe and ensure fine-grained access control. This paper comprehensively surveys the existing Lattice-based CP-ABE (LCP-ABE) schemes based on LWE and R-LWE assumptions. Further, this paper analyzes and compares the security and performance features of existing LCP-ABE schemes. Finally, this paper identifies the open issues and future directions that need further investigation on LCP-ABE schemes.

Ciphertext-Policy Attribute-Based Encryption (CPABE) is the most promising scheme to achieve fine-grained access control and data privacy in a cloud environment by offering oneto-many encryption. However, most existing CP-ABE schemes are fragile to quantum attacks because they are constructed using bilinear pairing assumptions. This paper proposes a Secure Lattice-Based CP-ABE scheme (SL-CP-ABE) from the Module Learning With Errors (M-LWE) to defend against quantum attacks and to realize fine-grained access control and data privacy in the cloud storage. The security of SL-CP-ABE proved against the Indistinguishable Selective Chosen Plaintext Attack (INDsCPA) under the hardness of the M-LWE. The performance analysis demonstrates that the SL-CP-ABE scheme is efficient and practical.

Attribute-based keyword search (ABKS) achieves privacy-preserving keyword search and fine-grained access control over encrypted data in the cloud. However, existing ABKS schemes cannot be directly applied for resource-constrained (such as Internet of Things) devices due to heavy computation overhead. In addition, identifying the malicious user who misuses the secret key is difficult if more than one user is having the same set of attributes. Furthermore, user revocation and attribute revocation are two important challenges in real-world applications. To address these challenges, this article proposes a FELT-ABKS: fog-enabled lightweight traceable ABKS over encrypted data by using ciphertext-policy ABKS to realize keyword search and fine-grained access control. FELT-ABKS achieves minimal computation cost at end users by transferring maximum computation to fog nodes. Furthermore, FELT-ABKS traces the malicious users who misuse their secret key. Besides, it supports user revocation and attribute revocation. The security analysis proves that FELT-ABKS is secure against the chosen keyword attack, chosen-plaintext attack, and modify secret key attack. Finally, experiments demonstrate that FELT-ABKS is lightweight and feasible.

Attribute-based searchable encryption (ABSE) schemes provide searchability and fine-grained access control over encrypted data in the cloud. Although prior ABSE schemes are designed to provide data protection and retrieval efficiency, they are suffering from the following issues. 1) A key-escrow problem, which may lead to the misuse of the user's secret key. 2) A single keyword search, which may produce irrelevant search results and also vulnerable in real-world applications. 3) A static policy update mechanism, which incurs high computation and communication overheads. In this paper, we propose a novel ABSE scheme called a key-escrow free attribute-based multi-keyword search with dynamic policy updates in cloud computing (KAMS-PU) to addresses all the above-stated issues. The security analysis proves that KAMS-PU is secure against malicious authority attacks and chosen keyword attack (CKA) in the random oracle model. Furthermore, performance analysis proves that KAMS-PU is efficient and practical in real-world applications.