Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is built. It is therefore imperative to find other means of implementing secure protocols. This thesis aims to contribute to the understanding of both the physical limitations, as well as the possibilities of cryptography in the quantum setting. In particular, we investigate several questions that are crucial to the security of quantum protocols: How can we find good uncertainty relations for a large number of measurement settings? How does the presence of entanglement affect classical protocols? And, what limitations does entanglement impose on implementing quantum protocols? Finally, can we circumvent some of those limitations using realistic assumptions?
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is built. It is therefore imperative to find other means of implementing secure protocols. This thesis aims to contribute to the understanding of both the physical limitations, as well as the possibilities of cryptography in the quantum setting. In particular, we investigate several questions that are crucial to the security of quantum protocols: How can we find good uncertainty relations for a large number of measurement settings? How does the presence of entanglement affect classical protocols? And, what limitations does entanglement impose on implementing quantum protocols? Finally, can we circumvent some of those limitations using realistic assumptions?
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 aim of this thesis is to study quantum computers and their impact on public-key cryptography. Crucial part of the work is dedicated to theoretical basis and definitions necessary for understanding the basic principles of quantum computers. The further chapters describe Shor's algorithm, explain the part of integer factoring problem in the security of current public key cryptographic algorithms, and show how to break the most widely used assymetric algorithm RSA by means of effective factoring. Last chapter provides comparison of classical factoring algorithms with Shors algorithm, mentions cryptography resistant to quantum computer attacks and discusses the current state of development in the field of qunatum computing. The conclusion summarizes both potential and real impact of quantum computers on public-key cryptography.
Quantum computing is a big change in the way computers work, and it promises to be much faster than traditional systems. This new technology brings both huge benefits and huge problems, especially when it comes to cryptographic security measures. Classical encryption algorithms, like RSA and ECC, depend on the fact that some math problems are hard, like discrete logarithms and integer factorization. Quantum algorithms, like Shor's algorithm, can solve these problems quickly. Because of this, the development of scalable quantum computers poses a danger to the basic safety of the cryptography methods that are widely used today. This short summary looks at the big effects that quantum computing will have on the safety of cryptography. It looks at the security holes that quantum algorithms create and stresses how important it is to find answers for post-quantum cryptography (PQC). PQC wants to make programs that can't be broken by quantum attacks. This will make sure that digital interactions can still be private, secure, and real in a world powered by quantum computers. Also, switching to PQC comes with a lot of problems, such as implementing algorithms, making sure they are all the same, and getting people to use them in a lot of different technology environments. The abstract talks about current research projects and foreign partnerships that aim to standardize and implement PQC. It stresses how important it is to plan ahead to reduce the risks of the future.
The advent of a full-scale quantum computer will severely impact most currently-used cryptographic systems.The most well-known aspect of this impact lies in the computational-hardness assumptions that underpin the security of most current public-key cryptographic systems: a quantum computer can factor integers and compute discrete logarithms in polynomial time, thereby breaking systems based on these problems.However, simply replacing these problems by other which are (believed to be) impervious even to a quantum computer does not completely solve the issue.Indeed, many security proofs of cryptographic systems are no longer valid in the presence of a quantum-capable attacker; while this does not automatically implies that the affected systems would be broken by a quantum computer, it does raises questions on the exact security guarantees that they can provide.This overview document aims to analyze all aspects of the impact of quantum computers on cryptographic, by providing an overview of current quantum-hard computational problems (and cryptographic systems based on them), and by presenting the security proofs that are affected by quantum-attackers, detailing what is the current status of research on the topic and what the expected effects on security are.
Quantum computing can be regarded as a disruptive enabling technology that can pose a threat to traditional cryptography as it invented new approaches to encrypt data. This paper will compare the level of security that accompanies quantum algorithms as well as the level of efficiency. Specifically, we examine the impact of efficient quantum computing on traditional cryptography and propose techniques against quantum invasions. Four quantum algorithms are analyzed for their efficiency and security benefits in the post-quantum era: Grover’s Algorithm, Shor’s Algorithm, The Quantum Key Distribution (QKD), Lattice-based cryptography. The results reveal that Grover’s algorithm improves search time complexity from O(n) to O(√n), which is advantageous over large data sets. As it will be clear shortly, Shor’s algorithm challenges RSA encryption because it outperforms classical algorithms in factoring large integers. QKD presents secure key exchange protocols that cannot be breached notwithstanding the attempts made using quantum computing. Lattice-based schemes are quantum-resistant alternatives based on the security of certain hard mathematical problems. Based on our experimental results, computational efficiency can be improved, but new cryptographic systems will have to be developed for the mitigation of quantum-related vulnerabilities. This research shows the importance of quantum-resistant cryptographic techniques to ensure data security in the emerging quantum computing era.
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.