This article addresses the challenges in improving the efficiency of solving the lattice-based cryptographic, Shortest Vector Problem (SVP), which is a crucial element to improve the security against the potential quantum attacks. We present a novel algorithm that integrates the concept of subsets generation with the SVP to enhance the efficiency of the lattice-based cryptographic schemes. This research delivers advancement by providing a more efficient method of solving the SVP. The method in this paper contributes towards the development of the security and privacy in cryptographic systems in the post-quantum era, surfacing the way for a vigorous encryption protocol.
This article addresses the challenges in improving the efficiency of solving the lattice-based cryptographic, Shortest Vector Problem (SVP), which is a crucial element to improve the security against the potential quantum attacks. We present a novel algorithm that integrates the concept of subsets generation with the SVP to enhance the efficiency of the lattice-based cryptographic schemes. This research delivers advancement by providing a more efficient method of solving the SVP. The method in this paper contributes towards the development of the security and privacy in cryptographic systems in the post-quantum era, surfacing the way for a vigorous encryption protocol.
This paper delves into lattice-based cryptography as a cornerstone of post-quantum cryptography (PQC), exploring its evolution, key principles, and applications. It examines how lattice-based schemes leverage the inherent hardness of problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE) to provide quantum-resistant encryption, digital signatures, and homomorphic encryption. The paper also outlines the historical development of lattice-based cryptography, emphasizing its resilience to quantum attacks in contrast to traditional schemes like RSA and ECC, which are vulnerable to Shor's algorithm. Core concepts, including lattice trapdoors, parameter optimization, and real-world applications in blockchain, cryptocurrencies, and secure communication protocols, are explored in detail. Furthermore, the paper highlights ongoing standardization efforts led by NIST, ethical considerations, practical challenges, and future research directions aimed at improving efficiency, ensuring interoperability, and expanding lattice cryptography’s use in advanced security frameworks. Through comprehensive analysis, this research underscores the importance of lattice-based cryptography as a critical pillar for securing the digital ecosystem against the emerging threat of quantum computing.
The rapid advancements in quantum computing pose a significant threat to traditional cryptographic systems. Latticebased cryptography has emerged as a cornerstone of postquantum cryptography due to its resistance to quantum attacks. This research presents a robust lattice-based cryptographic framework for global cybersecurity. By tackling the shortest vector problem (SVP) and closest vector problem (CVP) through efficient algorithms, the proposed model ensures secure encryption and decryption processes that scale for global communication systems. The findings demonstrate the model's resilience against both classical and quantum attacks, positioning it as a critical solution for the future of secure digital infrastructure.
The lattice-based encryption paradigm (LBE) represents a new security model emphasizing flexible development, high levels of security, and efficient computations. It is now becoming more commonly seen as an alternative to other systems of post-quantum cryptography due to its foundations for both security (i.e., there is a high degree of confidence that lattice-based cryptography is secure) and efficiency with respect to computation. The theoretical basis for this report is related to the difficulty of solving the short vector problem (SVP) and other cryptographic hard problems concerning lattices. The report focuses on the hardness of lattice-based cryptography relative to three sub-components of the theoretical work: the relationship between geometric number theory and lattice-based systems, the application of AI to help determine parameters and the efficiencies of finding new lattice reduction algorithms, and finally estimating the difficulty to solve lattice problems. This report reviews the inherent difficulty of short vector problems (SVPs) and other kinds of SVPs, such as the closest vector problem. The report analyzes how to reduce both the time and space complexities for classical and quantum computing solutions through the discovery of new techniques based upon number-theoretic concepts. The report also discusses a number of examples, including digital signature products, encryption systems and homomorphic encryption systems as primitive constructions of cryptography based on lattices or through the properties of the lattice structures. Finally, based on number-theoretical relationships among complex numbers, the report provides a new theoretical approach to the construction of lattice-based systems and their strength relative to other types of cryptographic systems via the provision of theoretical bounds related to the lengths of lattice basis vectors.As a result of this research into bridging the divide between theoretical and practical cryptography, the results show that lattice-based systems have the capability of providing the strength to withstand quantum attacks. Through this research study, there is an improvement in how we understand mathematically the difficulty of lattices and how to create post-quantum secure cryptographic techniques through the use of lattices...
The advent of quantum computing poses an existential threat to contemporary public-key cryptographic systems, which rely on the computational hardness of problems such as integer factorization and discrete logarithms. Shor's algorithm, capable of solving these problems efficiently on a sufficiently powerful quantum computer, necessitates a paradigm shift towards post-quantum cryptography (PQC). This paper proposes a unified security framework that bridges the conceptual gap between traditional number-theoretic hardness assumptions and the lattice-based problems central to PQC. We delve into the foundational mathematical problems, comparing the security arguments of factoring and discrete logarithm problems with the Shortest Vector Problem (SVP) and its variants in lattices. The framework emphasizes a consistent methodology for assessing quantum resistance, facilitating a more holistic understanding of cryptographic security in the post-quantum era. By analyzing the inherent complexities and interconnections of these hard problems, we aim to provide a structured approach to evaluate and design quantum-resistant cryptographic schemes, fostering robust and future-proof digital security infrastructure. This work contributes to the ongoing efforts in PQC standardization by offering a comparative lens for diverse cryptographic primitives.
Abstract Due to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a quantum computer (post-quantum cryptography algorithms). The security of many well-known post-quantum cryptosystems based on lattice theory depends on the complexity of solving the shortest vector problem (SVP). In this paper, a model of quantum oracle developed from Grover’s algorithm is described to implement a hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used for attacks on cryptosystems whose security depends on solving the SVP. Upper bounds for the number of qubits and the depth of the circuit were obtained for two implementations of the proposed quantum oracle model: minimizing the number of qubits and minimizing the circuit depth. The complexity of implementing the proposed quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed.
This paper explores the intersection of Quantum Key Distribution (QKD) and Lattice Cryptography, two innovative fields in modern cryptography. The quantum realm provides unique opportunities for secure communication through principles like superposition and entanglement, while lattice-based cryptography offers promising post-quantum secure solutions. We delve into three prominent QKD protocols—BB84, B92, and EPR—and examine foundational aspects of Lattice Cryptography, including Learning With Errors (LWE) and the Shortest Vector Problem (SVP). By bridging quantum and classical cryptographic concepts, this paper contributes to the evolving landscape of secure communication in an era where the threat of quantum computing looms. This paper will further discuss how to make a QKD work along with SVP, so that we can convert a shared key algorithm(QKD) to a Public Key Cryptography for more safety. This paper will mostly deal with QKD protocol-BB84 and Shortest Vector Problems along with some basic requirements to understand these two algorithms.