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.
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.
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 is an art of hiding the significant data or information with some other codes. It is a practice and study of securing information and communication. Thus, cryptography prevents third party intervention over the data communication. The cryptography technology transforms the data into some other form to enhance security and robustness against the attacks. The thrust of enhancing the security among data transfer has been emerged ever since the need of Artificial Intelligence field came into a market. Therefore, modern way of computing cryptographic algorithm came into practice such as AES, 3DES, RSA, Diffie-Hellman and ECC. These public-key encryption techniques now in use are based on challenging discrete logarithms for elliptic curves and complex factorization. However, those two difficult problems can be effectively solved with the help of sufficient large-scale quantum computer. The Post Quantum Cryptography (PQC) aims to deal with an attacker who has a large-scale quantum computer. Therefore, it is essential to build a robust and secure cryptography algorithm against most vulnerable pre-quantum cryptography methods. That is called ‘Post Quantum Cryptography’. Therefore, the present crypto system needs to propose encryption key and signature size is very large.in addition to careful prediction of encryption/decryption time and amount of traffic over the communication wire is required. The post-quantum cryptography (PQC) article discusses different families of post-quantum cryptosystems, analyses the current status of the National Institute of Standards and Technology (NIST) post-quantum cryptography standardisation process, and looks at the difficulties faced by the PQC community.
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 rise of the new paradigm (Quantum computing) in the recent years have created a major security challenge to classical and widely used primitive cryptography schemes such as ECC (Elliptic Curve Cryptography) and RSA (Rivest-Shamir-Adleman) Algorithm. These classical computing algorithms depend on the problems of discrete logarithm and integer factorization respectively. Recent advancements in quantum computing have made encryption schemes more vulnerable since they are weak to some quantum attacks, like Shor’s Algorithm and Grove’s Algorithm. Therefore the call for a new set of algorithms known as Post-Quantum cryptography (PQC) that would not be vulnerable to quantum attacks is imminent. NIST haven selected some candidates in the second round of Post-Quantum Cryptographic algorithms standardization project. This work’s goal is to review these algorithms under there types. A rigorous survey on each Post-Quantum Cryptography schemes and their underlying properties will be x-rayed while recommending areas for research in this new security paradigm.
Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.
The emergence of quantum computing is a serious threat to the principles of modern crypto-logical mathematics. The classical public-key cryptography, including Rivest-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC), and Diffie-Hellman are very safe against classical adversaries yet become susceptible to quantum algorithms, including the Shor algorithm, which can easily solve the underlying mathematical problems. This weakness is jeopardizing confidentiality and integrity of the world-wide systems of communication, money transactions, and essential structures, and requires the immediate creation of safe alternatives. The current literature on post-quantum cryptography (PQC) has covered various classes of algorithm, such as lattice-based, code-based, multivariate schemes, and isogeny-based schemes. Although lattice-based approaches like Nth Degree Truncated Polynomial Ring Unit (NTRU) and FrodoKEM can be highly theoretically resistant, they can be computationally and memory-intensive. Cryptosystems based on code such as Classic McEliece are secure but not practicable because they have huge public key sizes. Multivariate schemes like Rainbow, and isogeny-based schemes like Super singular Isogeny Key Encapsulation (SIKE) have been attacked recently by cryptanalytic attacks, and broken completely. Such restrictions open the necessity to find more efficient and secure quantum-resistant solutions.This research study postulates a hybrid post-quantum cryptographic (PQC) system that combines CRYSTALS-Kyber for encryption with CRYSTALS-Dilithium for digital signatures both of which are approved through the National Institute of Standards and Technology (NIST) PQC standardization program. The model will be such that it ensures quantum resistance but at the same time it will be scalable, efficient and compatible with the existing infrastructures. The test outcomes indicate that the hybrid PQC model is 35-45 percent faster to encrypt and decrypt, signature performance is enhanced by up to 40 percent, and the throughput is 20 times higher (98.7 Mbps) than the same base PQC scheme including Nth Degree Truncated Polynomial Ring Unit (NTRU), McEliece and Rainbow. These enhancements affirm that the suggested model provides a viable trade-off between the security, speed, and efficiency in terms of key size, which makes it a viable and a sound base to ensure secure communication in the quantum age.