In this chapter, we survey the identification schemes based on multivariate polynomials over a finite field. We provide some basic definitions needed to construct the structure of identification schemes based on multivariate polynomials over a finite field. Then, we provide a brief survey of identification schemes based on multivariate polynomials by considering applications in different platforms. We analyze them in view of the zero knowledge property and the number of passes such as 3-pass and 5-pass. By considering open problems in the literature, we propose a novel identification scheme based on multivariate quadratic polynomials. Then, we compare them in terms of efficiency. We also provide a discussion for cloud, IoT, and big data applications of quantum secure identification schemes.
In this chapter, we survey the identification schemes based on multivariate polynomials over a finite field. We provide some basic definitions needed to construct the structure of identification schemes based on multivariate polynomials over a finite field. Then, we provide a brief survey of identification schemes based on multivariate polynomials by considering applications in different platforms. We analyze them in view of the zero knowledge property and the number of passes such as 3-pass and 5-pass. By considering open problems in the literature, we propose a novel identification scheme based on multivariate quadratic polynomials. Then, we compare them in terms of efficiency. We also provide a discussion for cloud, IoT, and big data applications of quantum secure identification schemes.
Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure 3-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability compared to the work of Sakumoto et al. We also propose a new signature scheme constructed from the proposed identification scheme. In addition, we compare the signature scheme with the previous schemes in view of signature and key sizes. We improve the signature size compared to that given in previous work by Chen et al.
It is very important that the communicating parties are able to verify their identity in order to communicate with each other properly. Identification schemes are used for this purpose. The identification schemes, widely used in applications, are based on the hardness of the discrete logarithm or integer factorization problem. Shor proposed an algorithm that solve discrete logarithm and factorization problems by using quantum computers in polynomial-time. Therefore, there is a huge need for identification schemes which can be used post-quantum. In this paper, the identification schemes based on hardness of different lattice problems are surveyed. In addition, a new zero-knowledge lattice-based identification scheme is proposed.
The rapid proliferation of Internet of Things (IoT) devices has heightened concerns regarding their security and privacy. Conventional cryptographic methods underpinning IoT security are increasingly threatened by the emergence of quantum computing, which promises to break widely used encryption algorithms such as RSA and ECC. This paper explores post-quantum cryptographic (PQC) algorithms tailored to the resource-constrained nature of IoT environments. It analyzes lattice-based, hash-based, code-based, and multivariate polynomial cryptographic schemes as promising candidates for securing IoT communications against quantum attacks. The paper further discusses implementation challenges, performance considerations, and potential pathways for integrating PQC within existing IoT architectures. Empirical data on computational efficiency and security strength are also presented to guide future deployment.
With the progress of technology and widespread use of internet, the data has become digital. It is getting easier day by day to copy, modify and transform digital data / applications into another form. The term of digital rights management (DRM) has been suggested to limit the use of data in digital media and to protect copyrights. Different architectures / technologies are used to provide DRM. In existing architectures, the user is unaware whether the license, which was purchased, is used by an unauthorized party. In this paper, a structure is given to resolve this problem and fairness property is added for DRM architectures. Moreover, a post-quantum reliable identification protocol based on multivariate quadratic systems, which can be used for access control in DRM architecture, is proposed.
Quantum computing is rapidly advancing and threatens the cryptographic systems that secure digital communications. Classical cryptosystems, such as RSA and ECC, rely on mathematical problems that are difficult for classical computers but can be solved easily by quantum algorithms, such as Shor’s. This challenge underscores the pressing need for Post-Quantum Cryptography (PQC) to safeguard data against both classical and quantum threats. This study provides a comprehensive review of PQC Approaches in securing data against quantum threats by analyzing reviewed journals, conference proceedings, book chapters, and websites. Several researchers reviewed relevant literature published between 2019 and 2026 using the ACM Digital Library, Wiley Online Library, Taylor & Francis, Springer, ScienceDirect, MDPI, IEEE Xplore Digital Library, and Google Scholar. The review evaluates lattice-based, code-based, Hash-based, multivariate, and isogeny-based schemes across security strength, performance, interoperability, and deployment feasibility in heterogeneous environments, including cloud platforms and Internet of Things devices. The findings indicate that lattice-based schemes, particularly CRYSTALS-Kyber and CRYSTALS-Dilithium, currently offer the most balanced trade-off between efficiency and quantum resistance, while Hash-based schemes such as SPHINCS+ prioritize conservative security at notable performance cost. Code-based approaches, including McEliece, demonstrate strong long-term security but remain constrained by large key sizes. The review highlights implementation, energy, migration, and governance barriers that must be addressed before adoption. The review concludes by emphasizing that transitioning to PQC requires a collaborative effort from academia, industry, and government. Future research should focus on integrating lightweight PQC in IoT, 5G/6G, and cloud environments, as well as developing hybrid models that combine classical and quantum-safe systems. Addressing these issues is crucial for establishing secure data protection in the quantum era.
Basic security requirements such as confidentiality, user authentication and data integrity, are assured by using public-key cryptography (PKC). In particular, public-key signature schemes provide non-repudiation, integrity of transmitted messages and authentication. The presence of a large scale quantum computer would be a real threat to break the most widely used public-key cryptographic algorithms in practice, RSA, DSA, ECDSA signature schemes and Diffie-Hellman key exchange. Thus, all security protocols and applications where these public-key cryptographic algorithms are used are vulnerable to quantum-computer attacks. There are five directions of cryptographic primitives secure against a quantum computer: multivariate quadratic equation-based, hash-based, lattice-based, code-based and supersingular isogeny-based cryptography. These primitives could serve as replacements for current public-key cryptographic algorithms to prepare for post-quantum era. It is important to prioritize the fields to be replaced by post-quantum cryptography (PQC) since it is hard to replace the currently deployed PKC with PQC at the same time. The fields directly connected to human life such as vehicular communications should be the primary targets of PQC applications. This survey is dedicated to providing guidelines for adapting the most suitable post-quantum candidates to the requirements of various devices and suggesting efficient and physically secure implementations that can be built into existing embedded applications as easily as traditional PKC. It focuses on the five types of post-quantum signature schemes and investigates their theoretical backgrounds, structures, state-of-the-art constructions and implementation aspects on various platforms raging from resource constrained IoT devices to powerful servers connected to the devices for secure communications in post-quantum era. It offers appropriate solutions to find tradeoffs between key sizes, signature lengths, performance, and security for practical applications.