Cryptography has evolved from ancient substitution ciphers to modern mathematical algorithms including Rivest–Shamir–Adleman (RSA), elliptic curve cryptography (ECC), and advanced encryption standard (AES) that form the core of security systems, along with the major information security objectives: confidentiality, integrity, authenticity, availability, accountability, nonrepudiation, and privacy and their practical applications in protocols such as transport layer security (TLS), Internet Protocol Security (IPsec), and Secure/Multipurpose Internet Mail Extensions (S/MIME). The security of RSA, ECC, and symmetric-key ciphers has been threatened by quantum computers that exploit Shor’s and Grover’s algorithms. In response to this quantum threat, NIST has standardized post-quantum cryptographic PQC) algorithms: ML-KEM, a lattice-based key encapsulation mechanism and ML-DSA, a lattice-based digital signature scheme. This chapter surveys the development of cryptographic systems from transposition ciphers to post-quantum cryptography, examining their mathematical foundations, operational mechanisms, and respective security properties. In addition to these, the PQC algorithms have been implemented in TLS 1.3, and a comparative analysis has been performed. The study traces the history of cryptography while understanding post-quantum standards as the necessary foundation for long-term information security in the quantum era.
Cryptography has evolved from ancient substitution ciphers to modern mathematical algorithms including Rivest–Shamir–Adleman (RSA), elliptic curve cryptography (ECC), and advanced encryption standard (AES) that form the core of security systems, along with the major information security objectives: confidentiality, integrity, authenticity, availability, accountability, nonrepudiation, and privacy and their practical applications in protocols such as transport layer security (TLS), Internet Protocol Security (IPsec), and Secure/Multipurpose Internet Mail Extensions (S/MIME). The security of RSA, ECC, and symmetric-key ciphers has been threatened by quantum computers that exploit Shor’s and Grover’s algorithms. In response to this quantum threat, NIST has standardized post-quantum cryptographic PQC) algorithms: ML-KEM, a lattice-based key encapsulation mechanism and ML-DSA, a lattice-based digital signature scheme. This chapter surveys the development of cryptographic systems from transposition ciphers to post-quantum cryptography, examining their mathematical foundations, operational mechanisms, and respective security properties. In addition to these, the PQC algorithms have been implemented in TLS 1.3, and a comparative analysis has been performed. The study traces the history of cryptography while understanding post-quantum standards as the necessary foundation for long-term information security in the quantum era.
The ongoing development of powerful quantum computers poses a significant threat to the security of conventional encryption methods such as Rivest Shamir Adleman (RSA) and Elliptic Curve Cryptography (ECC). With algorithms such as Shor's Algorithm, quantum computers can solve the mathematical problems on which these methods are based and thus break them within a few hours. This work highlights this development's challenges and examines post-quantum cryptography (PQC) as a solution. PQC offers quantum-safe encryption based on mathematical problems that are difficult to solve, even for quantum computers. The text analyzes lattice, hash, and isogeny-based approaches and introduces the new NIST standards, including Kyber, Dilithium, and Sphinx+. It also discusses practical challenges in implementing quantum-safe systems, including performance degradation and cryptographic agility. It concludes with recommendations for migrating to PQC to ensure long-term security in an era increasingly characterized by quantum computing.
Traditionally, information security needed encryption, authentication, key management, non-repudiation and authorization which were being met using several techniques. Standardization of algorithms by National Institute of Standards and Technology (NIST) has facilitated international communication for banking and information transfer using these standards. Encryption can be carried out using Advanced Encryption Standard (AES) using variable block lengths (128, 192 or 256 bits) and variable key lengths (128, 192 or 256 bits). Solutions for light weight applications such as those for Internet of Things (IoT) are also being standardized. Message integrity is possible using host of hash algorithms such as SHA-1, SHA-2 etc., and more recently using SHA-3 algorithm. Authentication is possible using well known Rivest-Shamir-Adleman (RSA) algorithm needing 2048/4096 bit operations. Elliptic Curve Cryptography (ECC) is also quite popular and used in several practical systems such as WhatsApp, Blackberry etc. Key exchange is possible using Diffie-Hellman algorithm and its variations. Digital Signatures can be carried out using RSA algorithm or Elliptic Curve Digital Signature Algorithm (ECDSA) or DSA (Digital Signature Algorithm). All these algorithms derive security from difficulty in solving some mathematical problems such as factorization problem or discrete logarithm problem. Though published literature gives evidence of solving factorization problem upto 768 bits only, it is believed that using Quantum computers, these problems could be solved by the end of this decade. This is due to availability of the pioneering work of Shor and Grover [1]. For factoring an integer of N bits, Shor’s algorithm takes quantum gates. As such, there is ever growing interest in being ready for the next decade with algorithms that may resist attacks in the quantum computer era. NIST has foreseen this need and has invited proposals from researchers all over the world. In the first round, about 66 submissions were received which have been scrutinized for completeness of submissions , novelty of the approach and security and 25 of these were promote to second round to improve based on the comments received on the first round submission. These will be analyzed for security and some will be selected for final recommendation for use by industry. These are for encryption/decryption, key agreement, hashing and Digital Signatures for both hardware and software implementations. In this paper, we present a brief survey of the state of the art in post-Quantum Cryptography (PQC) followed by study of one of technique referred to as Learning With Errors (LWE) in some detail.
Abstract It is viewed as revolutionary technology, offering incredible potential in terms of computing power within different scientific and industrial sectors. Quantum computers provide remarkable computing power; however, they also present significant security risks to existing public-key cryptography systems used to secure digital communication, online banking systems, government, medical applications, cloud computing systems, and IoT systems. Security of commonly used encryption schemes like RSA, DH, and ECC depends on mathematical problems that are impossible for classical computers to solve but can be easily resolved with the help of powerful enough quantum computers by using Shor’s algorithm. Furthermore, Grover’s algorithm makes exhaustive search attacks much faster, thus effectively lowering the security level of symmetric encryption schemes since it provides the speed-up for brute-force attacks. Post-Quantum Cryptography (PQC) turned out to be an effective and scalable method to protect digital data from attacks using quantum computing. In contrast to quantum cryptography, which requires a special quantum communication channel, PQC uses classical cryptographic algorithms that cannot be broken down by either classical or quantum computer due to certain mathematical problems. This research paper offers an extensive exploration of post-quantum cryptography through the analysis of the development of quantum computing, weaknesses of current cryptographic techniques, and mathematics behind quantum-resistant algorithms. Moreover, this paper explores the major classes of PQC techniques such as lattice-based, code-based, hash-based, multivariate, and isogeny-based cryptography and provides details about their security and application. Moreover, the report gives an overview of the NIST Post-Quantum Cryptography Standardization Project and analyzes recent standardizations of quantum-proof algorithms to be utilized in future digital infrastructures. Keywords: Post-Quantum Encryption, Quantum Security, Quantum-Proof Public-Key Cryptography, Lattice-Based Security Protocols, ML-KEM Key Encapsulation Mechanism, ML-DSA Digital Signature Algorithm, NIST Post-Quantum Cryptography, Contemporary Cybersecurity, Secure Communications, Cryptographic Algorithms.
The threats are existential to the traditional cryptosystems of public keys, including RSA, Diffie-Hellman, and elliptic curve cryptography (ECC), due to the rapid progress in quantum computing. Such algorithms as the Shor and Grover algorithms prove that as soon as large scale quantum computers are achieved, these classical cryptographic protocols will not provide any privacy and integrity to online communication. This has created an emergency to find post-quantum cryptography (PQC), or quantum-safe cryptography, which will resist attacks by both classical and quantum attackers. The paper is a review of the latest research and development in post-quantum cryptographic algorithms and their implementation in current security systems. We organize quantum-safe methods into significant organizations such as lattice-based, hash-based, multivariate polynomial-based and code-based encrypted communications. Each type has been evaluated critically based on computational efficiency, key sizes, speed of encryption/decryption and security proofs. The survey also examines the current standardization activities happening in the world and especially the U.S. National Institute of Standards and Technology (NIST) PQC competition, which lists candidate algorithms that have advanced to standard adoption. Besides this, the paper addresses hybrid cryptographic designs that use both classical and post-quantum bases in ensuring a seamless migration in the transition phase. Internet security protocols like TLS, VPNs and blockchain consensus as applications of PQC are examined in detail. Lastly, we pinpoint open research issues, which include creating lightweight PQC to support resource-constrained IoT devices, balancing performance and strong security assurances, and interoperability between the new PQC algorithms and existing infrastructures. Through detailed survey we inform the future of researchers, practitioners, and policymakers on the preparation of the post-quantum era of secure digital communications.
The transition to post-quantum cryptography (PQC) marks a pivotal shift in ensuring digital security, prompted by the potential of quantum computers to compromise classical systems such as Rivest-Shamir-Adlema and elliptic-curve cryptography. In response, NIST has standardized three foundational PQC algorithms: Module-lattice-based Key-encapsulation Mechanism for key establishment; Module-lattice-based Digital Signature, and Stateless Hash-based Digital Signature algorithms for digital signatures. Meanwhile, FALCON and Hamming Quasi-cyclic (HQC) schemes, both selected as finalists, are expected to join the standards soon. This paper presents a comprehensive survey of these NIST-selected PQC standards, with a dual focus on software implementations and hardware architecture designs. We analyze their mathematical frameworks, distinctive features, and optimization strategies related to performance, security, and resource efficiency. The software review examines algorithmic complexity, memory usage, and programming considerations, while the hardware review discusses FPGA and ASIC implementations, emphasizing modular arithmetic, polynomial operations, and resource efficiency challenges. A comparative analysis highlights the strengths and trade-offs of each algorithm, offering insights into their applicability across various platforms-from resource-constrained internet of things devices to high-performance computing environments. This study provides a foundational understanding of NIST’s selected PQC standards and their practical deployment in securing the post-quantum era.
Quantum computing poses an existential threat to classical public-key cryptography, particularly RSA and elliptic-curve systems, which form the backbone of secure communication, authentication, and digital trust. Once scalable quantum computers emerge, algorithms such as Shor’s will be capable of breaking these schemes, jeopardizing confidentiality and integrity across the internet and enterprise systems. Post-quantum cryptography (PQC) offers a viable defense, providing quantum-resistant algorithms that can be implemented on today’s hardware and protocols. Recent standardization milestones—including NIST’s approval of ML-KEM (Kyber) for key establishment, ML-DSA (Dilithium) and SLH-DSA (SPHINCS+) for signatures, and the selection of HQC as a complementary KEM—mark a turning point for practical adoption. This paper surveys the quantum threat model, algorithm families, performance trade-offs, and integration patterns such as hybrid modes and crypto-agile architectures. It further outlines a phased migration roadmap for enterprises, emphasizing harvest-now-decrypt-later risks and compliance imperatives. By bridging technical, operational, and policy perspectives, the study provides actionable guidance to prepare organizations for a secure and quantum-resilient future.