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.

Chapter Contents:

• 8.1 Introduction
• 8.1.1 Motivation
• 8.1.2 Organization
• 8.2 Preliminaries
• 8.2.1 Basics of identification schemes
• 8.2.2 Multivariate polynomials system
• 8.3 Identification schemes in the post-quantum era
• 8.3.1 Sakumoto et al.' s identification schemes based on MQ polynomials
• 8.3.2 Sakumoto's identification schemes based on MC polynomials
• 8.3.3 Nachef et al.' s identification schemes
• 8.3.4 Monteiro et al.' s identification scheme
• 8.3.5 Soysaldi's identification scheme
• 8.3.6 Akleylek et al.' s identification scheme
• 8.3.7 Comparison of all identification schemes based on multivariate polynomials
• 8.4 Cloud and IoT applications of quantum secure identification scheme
• 8.5 Challenges and future directions
• 8.6 Conclusion
• Acknowledgment
• References

Inspec keywords: Big Data; quantum computing; cryptography; Internet of Things; cloud computing; polynomials

Other keywords: cloud computing; multivariate polynomials; zero knowledge property; finite field; quantum secure identification schemes; Big Data applications; IoT; multivariate quadratic polynomials; post-quantum area

Subjects: Data security; Internet software; Quantum computing techniques; Algebra; Mobile, ubiquitous and pervasive computing