The use of public key cryptosystems range from securely encrypting emails and files to creating digital signatures for non-repudiation. The security of public key cryptosystems is based on computationally "unsolvable" complex mathematical problems. This tends to change with the introduction of quantum computers that undoubtedly pose a threat to the current schemes. In response to that extensive research has been conducted that resulted in several cryptosystems that are believed to be quantum resistant. This thesis presents a concise overview of multiple hash-based signature schemes and provides a comparative description and analysis of them. The comparisons are based on different signature scheme properties, such as key sizes, signature sizes and security level provided. The proposed quantum resistant schemes are also compared to the standard schemes used today, such as RSA and ECDSA.
The use of public key cryptosystems range from securely encrypting emails and files to creating digital signatures for non-repudiation. The security of public key cryptosystems is based on computationally "unsolvable" complex mathematical problems. This tends to change with the introduction of quantum computers that undoubtedly pose a threat to the current schemes. In response to that extensive research has been conducted that resulted in several cryptosystems that are believed to be quantum resistant. This thesis presents a concise overview of multiple hash-based signature schemes and provides a comparative description and analysis of them. The comparisons are based on different signature scheme properties, such as key sizes, signature sizes and security level provided. The proposed quantum resistant schemes are also compared to the standard schemes used today, such as RSA and ECDSA.
The standard public-key cryptosystems used today relies mathematical problems that require a lot of computing force to solve, so much that, with the right parameters, they are computationally unsolvable. But there are quantum algorithms that are able to solve these problems in much shorter time. These quantum algorithms have been known for many years, but have only been a problem in theory because of the lack of quantum computers. But with recent development in the building of quantum computers, the cryptographic world is looking for quantum-resistant replacements for today’s standard public-key cryptosystems. Public-key cryptosystems based on lattices are possible replacements. This thesis presents several possible candidates for new standard public-key cryptosystems, mainly NTRU and ring-LWE-based systems. The latticebased cryptosystems are shown to be very fast and have strong, provable security against quantum computers, but are a lot more complicated than RSA and Diffie-Hellman.
The boom of quantum computing has brought both benefits and threats to cyber-physical systems. The primary purpose of the paper is to highlight the possible threats by quantum computers, and to provide a comparative study of the on-going quantum-resistant post-quantum cryptography suitable for current network infrastructure. Asymmetric key cryptography, mainly the widely adopted RSA and ECC algorithms, has been compromised by quantum algorithms such as the Shor’s algorithm. Moreover, symmetric algorithms such as AES are weakened by brute force attacks using Grover’s algorithm. Thus, researchers are developing public key algorithms based on hard mathematical models that provide resistance against quantum attacks and can be deployed in classical hardware. We categorize the well-known post-quantum schemes based on (1) their security goals: confidentiality and integrity, and (2) their mathematical problems: code-based, lattice-based, super-singular elliptic curve isogeny based, multivariate and hash-based algorithm. Hash-based post- quantum cryptography is further categorized into two: stateless and stateful signature scheme. Furthermore, the chapter compares the algorithms based on the key sizes, ciphertext sizes, signature sizes, computation, and time cost. The paper also presents the challenges faced by the post-quantum algorithms, and it outlines directions for further research to improve the algorithms. Moreover, various cyber-physical fields, including industrial control systems, mainly nuclear power plants, water management plants, and even space stations and their infrastructure, rely on classical cryptography. Thus, the paper presents a generic hybrid cryptosystem based on classical and post-quantum cryptography to enhance resistance against classical and quantum attacks.
One emerging threat to Public Key Infrastructures is the possible development of large-scale quantum computers, which would be able to break the public-key cryptosystems used today. Several possibly post-quantum secure cryptographic algorithms have been proposed but so far they have not been used in many practical settings. The purpose of this thesis was to find post-quantum digital signature algorithms that might be suitable for use in Public Key Infrastructures today. To answer the research question, an extensive literature study was conducted where relevant algorithms were surveyed. Algorithms with high-grade implementations in different cryptographic libraries were benchmarked for performance. Hash-based XMSS and SPHINCS, multivariate-based Rainbow and lattice-based BLISS-B were benchmarked and the results showed that BLISS-B offered the best performance, on par with RSA and ECDSA. All the algorithms did however have relatively large signature sizes and/or key sizes. Support for post-quantum digital signature algorithms in Public Key Infrastructure products could easily be achieved since many algorithms are implemented in cryptographic libraries. The algorithms that could be recommended for use today were SPHINCS for high-security applications and possibly BLISS-B for lower security applications requiring higher efficiency. The biggest obstacles to widespread deployment of post-quantum algorithms was deemed to be lack of standardisation and either inefficient operations compared to classical algorithms, uncertain security levels, or both.
Cryptography, the practice of concealing messages for private exchange, has evolved significantly to address the challenges posed by new communication methods. In today`s digital world, cryptography has become the cornerstone of cybersecurity, using advanced mathematics like number theory and computational complexity to protect digital information through algorithms. The upcoming arrival of quantum computers poses a serious threat to traditional cryptographic methods, especially those based on asymmetric key cryptography. Quantum Safe Cryptography (QSC) represents the next step in information security, designed to develop cryptographic systems that can withstand attacks from both quantum and classical computers. As quantum computing moves from theory to reality, it`s becoming clear that current cryptographic methods based on integer factorization and discrete logarithm problems are vulnerable to quantum algorithms like Shor`s algorithm. This study highlights the security risks that quantum computing poses to existing encryption methods and proposes a comprehensive approach to quantum-safe cryptography. The transition to quantum-resistant algorithms involves replacing vulnerable cryptographic systems with alternatives that can resist quantum computational attacks. Current analysis shows that while asymmetric key cryptography faces immediate vulnerability, symmetric key algorithms and hash functions remain relatively secure in the near term with appropriate adjustments. Quantum cryptography, which directly uses quantum mechanical principles, offers highly secure encryption mechanisms, notably Quantum Key Distribution (QKD). This research aims to enhance the security of digital infrastructure against quantum threats by evaluating hybrid cryptographic implementations that combine classical and quantum-resistant approaches for optimal security.
With the rapid advancement regarding quantum computing, traditional cryptographic systems face an existential threat because of their reliance concerning mathematical challenges which may be addressed effectively solved using quantum algorithms like the one developed by Shor. This imminent risk has driven extensive research into quantum-resistant cryptography (PQC), that seeks to develop encryption methods resilient against attacks powered by quantum computing. This study offers a thorough literature survey on high-level security techniques in quantum security for PQC, analysing past and current research efforts in this domain. We first examine the vulnerabilities of classical cryptographic protocols, including public-key encryption methods such as RSA (developed by Rivest, Shamir, and Adleman) and ECC (which uses elliptic curve mathematics), and traditional cryptographic hashing methods, against quantum adversaries. The study then explores the foundational approaches to quantum-secure cryptography, including lattice-based, hash-based, multivariate polynomial, code-based, and isogeny-based encryption methods that possess emerged as promising candidates for standardization. The survey highlights key challenges in the real-world application of PQC, including performance trade-offs, key size overhead, and deployment complexities. We conclude by identifying future research directions during the creation of scalable, efficient, and provably secure cryptographic methods designed to withstand quantum attacks techniques. As the shift toward the quantum-resilient era approaches, this survey aims to provide a clear and structured comprehension of the evolving the domain of quantum security for PQC.
Quantum computers are moving closer to reality, and with that comes a serious concern for today's public-key cryptography. Many of the encryption and digital signature systems we rely on now, such as RSA and ECC, may no longer be secure in the future. Because of this, researchers are actively looking for new methods that can protect digital communication in the post-quantum era. One of the most promising directions is lattice-based cryptography. This paper gives a simple and focused review of lattice-based signature schemes. It brings together the main ideas from the existing literature and explains how these schemes are built, why they are considered secure, and what makes them practical. The review mainly discusses schemes based on hard lattice problems such as SIS and LWE. To make the comparison clearer, a table is also included that compares different signature schemes in terms of key size, signature size, security level, and computational efficiency. Overall, this study shows why lattice-based signature schemes are becoming an important part of modern cryptographic research and why they may play a major role in securing digital systems against future quantum threats.