Lattice-based cryptography (LBC) has been the subject of numerous studies conducted by researchers during the past few years. LBC is a part of post-quantum cryptography, and it has undergone rapid development in recent years and is very attractive due to the low asymptotic complexity and potential resistance to quantum computing attacks. LBC is considered a quantum-safe alternative for the replacement of currently used schemes based on RSA and discrete logarithms on prime fields, elliptic curves, etc. This paper is intended to be a survey about LBC, its applications, and its future scope.
Lattice-based cryptography (LBC) has been the subject of numerous studies conducted by researchers during the past few years. LBC is a part of post-quantum cryptography, and it has undergone rapid development in recent years and is very attractive due to the low asymptotic complexity and potential resistance to quantum computing attacks. LBC is considered a quantum-safe alternative for the replacement of currently used schemes based on RSA and discrete logarithms on prime fields, elliptic curves, etc. This paper is intended to be a survey about LBC, its applications, and its future scope.
Due to recent advancements in technology, our computer systems, the data stored on computer systems, and our daily communications through mobile devices and other electronic devices are not entirely safe.The emergence of quantum computers has attracted the attention of researchers and computer scientists.Because, the security of our data and daily communications depends on cryptographic primitives based on discrete logarithmic problems and integer factorization problems, which are not safe in the current quantum computing era.So, there is a need for cryptographic systems that are safe in a quantum computing environment.Researchers have found that cryptographic algorithms based on lattices are secure against quantum computing attacks.Lattice-Based Cryptography (LBC) is considered an alternative to classical cryptosystems based on discrete logarithmic problems and integer factorization problems in a quantum computing environment.This paper aims to provide an overview of LBC, its significance, and its fields of interest.
Alongside the growth of technology is the increasing demand for security of data and communication channels. As attacking power grows, devices become smaller and data expands, the security needs to be stronger yet less resource-consuming than ever before. Public key cryptography (PKC) is used in the majority of today's communications systems. The security of public-key cryptographic schemes, such as RSA and elliptic curve cryptography (ECC), is based on underlying mathematical problems such as factoring large integers or solving the discrete log problem. However, the discovery of Shor's Algorithm in 1994 insinuates that these schemes will be insecure when a full-scale quantum computer is developed, as these problems will be solvable in polynomial time. Therefore attention has moved towards post-quantum, or quantum-safe, cryptography (QSC). In 2016, the National Institute of Standards and Technology (NIST) announced the beginning of their efforts to migrate to QSC, a standardisation process which has involved the cryptographic community worldwide. There are five main types of QSC being considered for standardisation; lattice-based, code-based, multivariate-based, hash-based and isogeny-based. Lattice-based cryptography (LBC) offers a promising alternative to today's classical approaches. Hard problems based on lattices are believed to be unsolvable, even by a quantum-computer, in a feasible amount of time. In 1995, Ajtai showed that the average case complexity of these problems is at least as hard as solving the problems in the worst case. Furthermore, lattice-based schemes are the only remaining contender in the NIST process to provide the important primitives of encryption, key encapsulation and digital signature schemes (DSSs). A well-recognised open problem surrounding quantum-safe cryptography is its increase in bandwidth and computational complexity in comparison to existing cryptography. However, in comparison to other quantum-safe schemes, LBC has been shown to be relatively efficient. In this thesis, novel software designs of lattice-based schemes are presented and shown to be competitive with existing PKC. Additionally, physical attacks are considered and countermeasures are incorporated into the designs. DSSs are required for authentication, integrity and non-repudiation of data. This thesis provides an evaluation of three leading signature schemes, BLISS-B, Dilithium and \textsc{Falcon}, which vary in terms of their key features, such as the sampling processes used, and the structure of the lattices. Physical attacks on the three schemes are considered and the effect on performance of appropriate attack countermeasures is evaluated. A novel fault attack on the NIST candidate \textsc{Falcon} is also proposed. A further advantage of LBC is the ability to support cryptographic primitives with extended capabilities to facilitate certificate management and compute on encrypted data. The complexity of today's technology advances mean applications require more sophisticated primitives, which contrastingly are required to run on even smaller platforms. This thesis presents novel quantum-safe advanced cryptographic schemes, specifically lattice-based identity-based encryption (IBE) and hierarchical identity-based encryption (HIBE). IBE removes the need for certificate management, as a user's public key depends on their public identity. IBE is currently used in vital applications such as emergency services communication and so the development of a high-performance quantum-safe alternative is imperative. This thesis also introduces the first scalable HIBE scheme based on lattices. The first HIBE scheme based on structured lattices, Latte, was proposed by the National Centre for Cyber Security (NCSC) in 2017. However, the public key and ciphertext sizes increased with each delegation and hence it was not feasible to scale the algorithm. Skinny Latte, proposed in this thesis, remedies this issue by fixing the dimension of the lattice, thereby making public key and ciphertext sizes constant. This research also shows that it is practical for real-world deployment. Overall, this thesis demonstrates that lattice-based cryptography is practical for real-world applications. It considers both theoretical and physical attacks, and presents novel designs of advanced quantum-safe cryptographic primitives, which have only yet been realised by lattices.
The latest quantum computers have the ability to solve incredibly complex classical cryptography equations particularly to decode the secret encrypted keys and making the network vulnerable to hacking. They can solve complex mathematical problems almost instantaneously compared to the billions of years of computation needed by traditional computing machines. Researchers advocate the development of novel strategies to include data encryption in the post-quantum era. Lattices have been widely used in cryptography, somewhat peculiarly, and these algorithms have been used in both; (a) cryptoanalysis by using lattice approximation to break cryptosystems; and (b) cryptography by using computationally hard lattice problems (non-deterministic polynomial time hardness) to construct stable cryptographic functions. Most of the dominant features of lattice-based cryptography (LBC), which holds it ahead in the post-quantum league, include resistance to quantum attack vectors, high concurrent performance, parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. While these methods offer possible security for classical cryptosytems in theory and experimentation, their implementation in energy-restricted Internet-of-Things (IoT) devices requires careful study of regular lattice-based implantation and its simplification in lightweight lattice-based cryptography (LW-LBC). This streamlined post-quantum algorithm is ideal for levelled IoT device security. The key aim of this survey was to provide the scientific community with comprehensive information on elementary mathematical facts, as well as to address real-time implementation, hardware architecture, open problems, attack vectors, and the significance for the IoT networks.
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 rapid growth of quantum computing poses a critical threat to classical cryptographic systems. That is due in large part to the fact that they represent efficient solutions for some of the most challenging mathematical problems such as integer factoring or finding discrete logarithms. Schemes currently in wide use including RSA, Diffie–Hellman, and elliptic curve cryptography are particularly susceptible to being attacked by quantum computers, using algorithms like Shor's Algorithm and Grover's Algorithm. The advent of post-quantum cryptography (PQC) provides a promising potential answer to providing longterm security from adversaries using quantum computing capabilities. This paper presents a comprehensive state-of-the-art review of various PQC techniques currently being researched, including lattice-based methods, code-based methods, multivariate methods, hash-based methods, and isogeny-based methods. key challenges that will need to be addressed include computational overhead, large key sizes and implementation complexity. Furthermore the study reviews the current standardization efforts by the National Institute of Standards and Technology related to PQC and discusses some of the very specific practical considerations that need to be considered before widely deploying these techniques. The paper concludes by a complete list of existing research challenges and proposed future work that will assist in the development of efficient and scalable systems that will resist attacks from quantum computers.
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.