Quantum cryptography is a branch of cryptography that is a mixture of quantum mechanics and classical cryptography. The study of quantum cryptography is to design cryptographic algorithms and protocols that are against quantum computing attacks. In this chapter, the authors focus on analyzing characteristics of the quantum-proof cryptosystem and its applications in the future internet. Lattice-based cryptography provides a much stronger belief of security, in that the average-case of certain problems is equivalent to the worst-case of those problems. With the increase in cryptanalytic attacks conventional cryptographic schemes will soon become obsolete. As the reality of quantum computing approaches, these cryptosystems will need to be replaced with efficient quantum-resistant cryptosystems. We need an alternate security mechanism which is as hard as the existing number theoretic approaches. In this chapter, the authors discuss the security dimension of lattice-based cryptography whose strength lies in the hardness of lattice problems and also study its application areas.
Quantum cryptography is a branch of cryptography that is a mixture of quantum mechanics and classical cryptography. The study of quantum cryptography is to design cryptographic algorithms and protocols that are against quantum computing attacks. In this chapter, the authors focus on analyzing characteristics of the quantum-proof cryptosystem and its applications in the future internet. Lattice-based cryptography provides a much stronger belief of security, in that the average-case of certain problems is equivalent to the worst-case of those problems. With the increase in cryptanalytic attacks conventional cryptographic schemes will soon become obsolete. As the reality of quantum computing approaches, these cryptosystems will need to be replaced with efficient quantum-resistant cryptosystems. We need an alternate security mechanism which is as hard as the existing number theoretic approaches. In this chapter, the authors discuss the security dimension of lattice-based cryptography whose strength lies in the hardness of lattice problems and also study its application areas.
With a recent increase in the advancement of the technology, computer system and it’s sensitive data are getting exhibited to unauthorised users, with steadily corroding the fundamentals of computer security. This, in fact, demanded fundamental innovations that require several cryptographic paradigms and security protocol. Previously it was thought that asymmetric cryptographic key like RSA, Diffie-Hellman, are very hard to decrypt by classical computation, but with the implementation of quantum computation, it is proved that this kind of cryptographic algorithm is very easy to decrypt and hackers can steal important Data [3], [6]. After the release of Ajtai’s research paper " Generating Hard Instances of Lattice Problem" [2], a million reasons arose in the minds of the researchers to develop on methods based on lattice-based cryptography to improve their security needs. Firstly, it provided much stronger security, and the average-case of several problems in lattice-based cryptography seems equivalent to the worst-case problem of these problems [2]. Moreover, lattices have the potential to persuade the cryptanalytic attacks created by any quantum computers i.e Quantum Computational Secure [3]. In this paper, we will discuss lattice-based cryptosystem, it’s security dimensions, a general brief on how it works, future scope, applications and areas of Interest.
Objective: Quantum algorithm are stronger and more secure than the classical computers not because they run on faster harder computers but also, they require fewer steps. With Quantum computers the attackers have high computing power and with quantum algorithm can easily break the cryptographic system. Lattice is regularly spaced grid of points stretching to infinity. Quantum safe security algorithms are resistant to both attacks caused by classical computers and the attack caused by quantum computers. Lattice based cryptography are the post quantum cryptographic standards which are resistant to the attacks from quantum computers hence has advantage of strong security and high efficiency. The main objective of the paper is to study lattice, lattice properties, lattice – based cryptographic algorithm to design new lattice based cryptographic algorithm which are quantum resistant in future. Methods: In this paper the lattice-based cryptography is discussed right from its seminal work to its efficient cryptographic schemes. Paper discusses what is lattice, lattice properties, lattice problem and algorithmic solution to lattice problem and lattice-based cryptography. Findings: After studying post quantum cryptographic algorithms using lattice it was found that lattice-based post quantum cryptographic algorithms are resistant to quantum computer attacks. Novelty: Paper discusses lattice, properties of lattice in a simple way. Widely used cryptographic algorithms like RSA, Diffie-Hellman Key exchange, Elliptic Curve Cryptography are not resistant to quantum computers attacks. Paper discusses the importance of post quantum algorithm using lattice that are resistant to quantum computer attacks.
The security of classical public-key cryptosystems, which operate based on the computational intractability of integer factorization and discrete logarithm problems, is profoundly threatened by the rapid development of quantum computing. Post-Quantum Cryptography (PQC) has been proposed to improve security against quantum attacks. Lattice-based cryptography is widely regarded as one of the most promising PQC method because of its proven security, efficient implementation, and functional versatility, and it has achieved significant progress in both algorithmic design and engineering implementation in recent years. This paper presents a systematic survey of the status of research on lattice-based cryptographic algorithms. First, the fundamental theory of lattices and their core hard problems are discussed. Next, the technical characteristics and performance of encryption and key encapsulation mechanisms, digital signature schemes, and key exchange protocols constructed based on lattice hard problems are reviewed and compared. Subsequently, the principles and optimization paths of two key technologies for lattice cryptography implementation, namely polynomial multiplication using the fast Number Theoretic Transform (NTT) and pre-image sampling algorithms, are discussed. Finally, considering the PQC standardization process of the National Institute of Standards and Technology (NIST), an outlook on future research directions for lattice-based cryptography is presented. The research directions include the development of more "succinct" fundamental hard problems, strengthening security proofs, improving algorithm efficiency, and countering novel attacks. This review serves as a reference for promoting the practical deployment and further research of lattice-based cryptography.
The landscape of modern cryptography, traditionally anchored in the computational hardness of number-theoretic problems such as integer factorization and the discrete logarithm problem, faces an existential threat from the advent of quantum computing. Shor's algorithm, discovered in 1994, demonstrates the theoretical capability of a sufficiently powerful quantum computer to efficiently solve these problems, rendering widely used cryptographic schemes like RSA and Elliptic Curve Cryptography (ECC) insecure. This imminent threat necessitates a paradigm shift towards post-quantum cryptography (PQC), which aims to develop cryptographic algorithms resistant to both classical and quantum attacks. Among the various candidates for PQC, lattice-based cryptography has emerged as a particularly promising area. This paper provides a comprehensive overview of the transition from classical number theory-based cryptography to lattice-based schemes. We explore the fundamental mathematical principles underlying lattices, introduce key lattice problems such as the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Small Integer Solution (SIS), and Learning With Errors (LWE), and discuss their application in constructing quantum-resistant cryptographic primitives. Furthermore, we analyze the security, efficiency, and practical considerations of prominent lattice-based cryptosystems, highlighting their role in the ongoing NIST post-quantum cryptography standardization process. The paper concludes by discussing the challenges and future directions in the deployment and research of lattice-based cryptographic solutions.
The advent of quantum computing has profound implications for digital security. Traditional cryptographic methods, which currently protect online banking, secure communications, and digital asset transfers, stand at risk of obsolescence once large-scale quantum computers become a reality. This chapter offers a conceptual and theoretical exploration of quantum-resistant cryptography within the broader context of post-quantum security. It examines key theoretical frameworks underpinning cryptographic protocols, highlights the historical and contemporary debates on transitioning to post-quantum algorithms, and synthesizes existing scholarly research to identify enduring gaps. The chapter proposes new conceptual models to guide practitioners, policymakers, and researchers as they navigate the complex shift from classical cryptography to quantum-resistant techniques. By analyzing essential constructs such as lattice-based cryptography, code-based approaches, and multivariate polynomial cryptosystems, the discussion illuminates both challenges and opportunities.
The need and emergence of quantum computing under National Quantum Mission threatens the cyber-security of existing cryptographic protocols, especially public-key schemes built on integer factorization and discrete logarithms. Lattice-based cryptography has gained prominence as a robust candidate for post-quantum cryptography—offering security against quantum attacks while enabling efficient operations, parallelization, and novel functionalities. This paper analyzes the mathematical foundations of lattices, explores hardness assumptions underlying widely studied lattice problems, highlights prominent cryptographic constructions, analyzes performance trade-offs, and reviews standardization efforts. This paper concludes by identifying ongoing issues and future directions for lattice-based cryptographic systems in a quantum-secure digital world. The algorithm has been implemented in Python.