Todays most efficient and widely used cryptographic standards such as RSA rely on the difficulty of factoring large numbers to resist cryptanalysis. Asymmetric cryptography is used in a plethora of sensitive operations from online bank transactions to international e-commerce, and the Department of Defense also uses asymmetric cryptography to transmit sensitive data. Quantum computers have the potential to render obsolete widely deployed asymmetric ciphers essential to the secure transfer of information. Despite this, alternatives are not in place. The goal of this study is to understand the alternatives to classical asymmetric cryptography that can be used as substitutes should quantum computers be realized. This study explores quantum-resistant alternatives to traditional ciphers and involves experimenting with available implementations of ciphers described the post-quantum literature as well as developing our own implementations based on descriptions of algorithms in the literature. This study provides an original implementation of hash-based digital signature and detailed instructions on its use as well as customization of the NTRU lattice-based cryptography suite, including the use of NTRU and AES together in a hybrid cryptographic protocol. This thesis will make recommendations on future work necessary to prepare for the emergence of large-scale, fault-tolerant quantum computers.
Todays most efficient and widely used cryptographic standards such as RSA rely on the difficulty of factoring large numbers to resist cryptanalysis. Asymmetric cryptography is used in a plethora of sensitive operations from online bank transactions to international e-commerce, and the Department of Defense also uses asymmetric cryptography to transmit sensitive data. Quantum computers have the potential to render obsolete widely deployed asymmetric ciphers essential to the secure transfer of information. Despite this, alternatives are not in place. The goal of this study is to understand the alternatives to classical asymmetric cryptography that can be used as substitutes should quantum computers be realized. This study explores quantum-resistant alternatives to traditional ciphers and involves experimenting with available implementations of ciphers described the post-quantum literature as well as developing our own implementations based on descriptions of algorithms in the literature. This study provides an original implementation of hash-based digital signature and detailed instructions on its use as well as customization of the NTRU lattice-based cryptography suite, including the use of NTRU and AES together in a hybrid cryptographic protocol. This thesis will make recommendations on future work necessary to prepare for the emergence of large-scale, fault-tolerant quantum computers.
As quantum computing technology evolves, it poses greater risks to current cryptography schemes such as RSA and Elliptic Curve Cryptography (ECC), widely used to secure digital communications These classical algorithms are based on mathematical problems that quantum algorithms such as Shore-Grover deal with. Both, can resolve much faster, making them vulnerable to quantum attack This has given rise to post-quantum cryptography (PQC), which focuses on developing quantum-resistant algorithms to protect data in the future of quantum computers classical cryptography Can Break This paper aims to provide a comprehensive insight into quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariable polynomial methods. It examines the efficiency, benefits, and challenges associated with implementing these algorithms in real-world applications. By comparing key parameters such as key size, encryption/decryption speed, and signature size, this study examines the relative strengths and limitations of post-quantum algorithms to their classical counterparts The results show that lattice-based algorithms , such as NTRU and Kyber, offer promising solutions with relative efficiency and manageable key sizes, making them potential candidates for quantum-resistant cryptography but other approaches , such as SPHINCS+ (hash-based) and McEliece (code-based), large -Face challenges of key size and slow encryption speed, which may limit their usefulness in some applications Despite these challenges, quantum post-cryptography is necessary to secure the future of digital communications.
The rapid advancement of quantum computing presents a significant challenge to classical cryptographic systems that underpin modern digital security infrastructures. In particular, RSA-2048 encryption, widely deployed in banking and financial institutions for secure transactions, relies on the computational hardness of integer factorization. However, the emergence of quantum algorithms—especially Shor’s algorithm—poses a fundamental threat to RSA security by enabling polynomial-time factorization of large integers on sufficiently powerful quantum computers. This case study investigates the vulnerability of RSA-2048 within a banking environment, analyzing the mathematical foundations of the threat, potential timelines for quantum feasibility, and associated cybersecurity risks. The study further examines the implications for financial data protection, digital signatures, and secure communication channels. In response to these emerging risks, the paper explores post-quantum cryptographic alternatives, including lattice-based, hash-based, and code-based schemes, and evaluates their suitability for banking applications. The findings emphasize the urgency of transitioning toward quantum-resistant cryptographic frameworks and propose strategic recommendations for proactive cryptographic migration to ensure long-term data confidentiality and system resilience.
This dissertation analyzes the impact of quantum computing on the security of classical cryptographic systems, with a focus on the vulnerability of the RSA algorithm. RSA cryptography is based on the difficulty of factoring large prime numbers, a task considered computationally very difficulty for classical computers. However, with quantum computing, especially through Shor’s algorithm—this barrier can be overcome. Shor’s algorithm allows factorization in polynomial time, which would completely compromise the security of RSA.The dissertation presents the theoretical foundations of both cryptography and quantum computing, explaining key concepts such as qubits, superposition, entanglement, and quantum parallelism. It details the operation of Shor’s algorithm, from identifying the period of the modular exponential function to applying the Quantum Fourier Transform (QFT) and phase estimation to obtain the prime factors of a composite number.In addition to the theoretical component, the work includes practical implementations of the algorithm in both classical and simulated quantum environments, using IBM’s Qiskit library. Finally, it discusses post-quantum cryptography as a secure alternative in light of technological advancements, highlighting methods based on lattices, codes, hash functions, and multivariate systems.The conclusion emphasizes the urgency of adopting cryptographic systems resistant to quantum computing, as ongoing advances increasingly make the breaking of RSA a realistic threat. Post-quantum cryptography is mentioned as a necessary response to the challenge posed by quantum computing.In conclusion, although current quantum computers do not yet have sufficient power to break RSA in practice, technological progress is steadily bringing that scenario closer. Therefore, it is essential to develop and adopt quantum-resistant cryptographic systems to ensure information security in the coming decades.
In this paper, we discuss the challenges of quantum computing to traditional cryptography and the latest development of post-quantum cryptography as a coping strategy. As quantum computing advances, cryptographic algorithms that rely on the complexity of classical computers, such as RSA and ECC, are at risk of failing, which has prompted the cryptography community to seek new encryption solutions. Post-quantum cryptography focuses on encryption technology and develops resistance to quantum computing attacks. It studies encryption schemes based on lattice theory, multivariate polynomials, coding theory, and hash functions. In addition, lattice-based cryptography is critical. It builds multiple algorithms, including RLWE and NTRU, focusing on LWE and SIS issues, demonstrating strong potential in a quantum computing environment. In terms of signature algorithms, Dilithium and Falcon lattice-based schemes are the focus of standardization. In the simulation analysis of these algorithms, we evaluated their security, efficiency, and compatibility, laying the theoretical and practical foundation for the cryptosystem transformation in the post-quantum era.
Quantum computing represents a transformative advancement in computational power, with profound implications for cryptographic systems. This paper explores the intersection of quantum computing and cryptography, examining the potential for quantum computers to both break traditional cryptographic algorithms and enable new forms of secure communication. Classical cryptographic systems, such as RSA and ECC, rely on the computational difficulty of problems like integer factorization and discrete logarithms. However, quantum algorithms, notably Shor's algorithm, can solve these problems exponentially faster than the best-known classical algorithms, posing a significant threat to the security of current cryptographic practices. This vulnerability necessitates the development and implementation of quantum-resistant algorithms to ensure data security in a post-quantum world. The paper reviews the state-of-the-art in quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariate polynomial cryptography. These algorithms are analyzed for their security properties, efficiency, and practicality for real-world deployment. Additionally, the paper discusses the ongoing standardization efforts led by organizations such as NIST, which are crucial for establishing widely accepted quantum-safe cryptographic protocols. Beyond the threat posed by quantum computing, this paper also highlights the potential benefits quantum computing can bring to cryptographic systems. Quantum Key Distribution (QKD) is one such advancement, offering theoretically unbreakable encryption by leveraging the principles of quantum mechanics. QKD enables secure communication channels that are immune to any computational advances, including those of quantum computers, by ensuring that any attempt at eavesdropping can be detected. The practical implementation challenges of QKD and other quantum cryptographic protocols are also addressed, including issues related to transmission distance, error rates, and integration with existing communication infrastructures. Experimental results from recent QKD trials are presented, showcasing significant progress in extending the viability of quantum-secure communication over long distances. Furthermore, the paper delves into the hybrid approaches combining classical and quantum cryptographic techniques. These approaches aim to leverage the strengths of both paradigms to enhance security and performance. For instance, hybrid protocols might use classical encryption for bulk data transfer, supplemented by quantum techniques for key exchange, thereby ensuring robust security even against future quantum adversaries. In conclusion, while quantum computing poses substantial risks to existing cryptographic systems, it also offers novel opportunities for creating highly secure communication protocols. The transition to quantum-safe cryptography is imperative to protect sensitive information in the quantum era. This paper underscores the urgency of advancing quantum-resistant cryptographic research, promoting international collaboration for standardization, and exploring innovative applications of quantum technologies in cryptography. Continued research and development in these areas are essential to stay ahead of the evolving threat landscape and harness the full potential of quantum computing for secure communications.
The advent of quantum computing poses a significant challenge to conventional cryptographic methods such as RSA, Elliptic Curve Cryptography (ECC), and Diffie-Hellman key exchange. Quantum algorithms, particularly Shor’s algorithm, have the potential to break these encryption techniques, making it essential to develop cryptographic approaches that can withstand quantum threats. Post-quantum cryptography (PQC) has emerged as a crucial area of research, aiming to establish cryptographic mechanisms that remain secure even in the presence of quantum adversaries. This study presents a detailed comparative analysis of five primary categories of quantum-resistant cryptographic algorithms: lattice-based, code-based, hash-based, multivariate polynomial, and isogeny-based encryption schemes. Each of these approaches offers distinct advantages and challenges in terms of security, efficiency, and implementation feasibility. Among them, lattice-based cryptography has gained significant attention due to its robust security properties and computational efficiency, making it a strong candidate for standardization. Conversely, code-based cryptography provides high security but is hindered by its large key sizes, affecting its practical deployment. The research includes a real-time performance assessment of selected PQC algorithms, analyzing key factors such as encryption speed, key size, and computational demands. Furthermore, the study examines the challenges associated with transitioning from classical encryption standards to quantum-resistant frameworks, including compatibility constraints, computational overhead, and the necessity for global standardization. Potential mitigation approaches, such as hybrid cryptographic techniques that integrate both classical and post-quantum encryption models, are also explored. Our findings emphasize that while quantum-resistant cryptography is still evolving, early adoption of PQC frameworks is essential for safeguarding future communication networks. This paper provides valuable insights for researchers, cybersecurity professionals, and policymakers on strategic measures to implement quantum-secure encryption systems effectively.