Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Researchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers, thereby ensuring the security of data transmissions over public networks. A critical component of this security is the key agreement protocol, which allows two parties to establish a shared secret key over an insecure channel. This paper introduces two novel post-quantum key agreement protocols that can be easily implemented on standard computers using rectangular or rank-deficient matrices, exploiting the generalizations of the matrix power function, which is a generator of NP-hard problems. We provide basic concepts and proofs, pseudocodes, and examples, along with a discussion of complexity.
Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Researchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers, thereby ensuring the security of data transmissions over public networks. A critical component of this security is the key agreement protocol, which allows two parties to establish a shared secret key over an insecure channel. This paper introduces two novel post-quantum key agreement protocols that can be easily implemented on standard computers using rectangular or rank-deficient matrices, exploiting the generalizations of the matrix power function, which is a generator of NP-hard problems. We provide basic concepts and proofs, pseudocodes, and examples, along with a discussion of complexity.
We present an improved post-quantum version of Sakalauskas matrix power function key agreement protocol, using rectangular matrices instead of the original square ones. Sakalauskas matrix power function is an efficient and secure way to generate a shared secret key, and using rectangular matrices provides additional flexibility and security. This method reduces the computational complexity by allowing smaller random integer matrices while maintaining a high level of security. We dont rely on matrices with special formatting to achieve commutativity, instead, we use full random values on those structures, increasing their entropy. Another advantage of using rectangular matrices over key agreement protocols is that they offer better protection against various linearization attacks.
Quantum cryptography has emerged as a revolutionary technology for ensuring secure communication in the era of quantum computing. While existing research primarily focuses on theoretical frameworks and small-scale experimental setups, significant challenges remain in practical implementation, scalability, and security vulnerabilities. This study aims to bridge the gap between theory and real-world deployment by developing robust quantum cryptographic protocols that address key challenges such as noise management, side-channel attacks, and Trojan horse attacks. Additionally, we propose an optimized quantum key distribution (QKD) mechanism that ensures secure communication over long distances under realistic conditions. Our research integrates post-quantum cryptography with quantum cryptographic techniques to provide a hybrid security model that is resilient against both classical and quantum computing threats. By leveraging commercially available quantum hardware and advanced randomness extraction methods, this study contributes to the development of scalable, secure, and efficient quantum communication networks. The findings of this research will play a crucial role in advancing secure digital communication systems and fortifying data security in the post-quantum era.
Quantum cryptography has emerged as a revolutionary technology for ensuring secure communication in the era of quantum computing. While existing research primarily focuses on theoretical frameworks and small-scale experimental setups, significant challenges remain in practical implementation, scalability, and security vulnerabilities. This study aims to bridge the gap between theory and real-world deployment by developing robust quantum cryptographic protocols that address key challenges such as noise management, side-channel attacks, and Trojan horse attacks. Additionally, we propose an optimized quantum key distribution (QKD) mechanism that ensures secure communication over long distances under realistic conditions. Our research integrates post-quantum cryptography with quantum cryptographic techniques to provide a hybrid security model that is resilient against both classical and quantum computing threats. By leveraging commercially available quantum hardware and advanced randomness extraction methods, this study contributes to the development of scalable, secure, and efficient quantum communication networks. The findings of this research will play a crucial role in advancing secure digital communication systems and fortifying data security in the post-quantum era.
We present in this paper an algorithm for exchanging session keys, coupled with a hashing encryption module. We show schemes designed for their potential invulnerability to classical and quantum attacks. In turn, if the parameters included were appropriate, brute-force attacks exceed the (five) security levels used in the NIST competition of new post-quantum standards. The original idea consists of products of rectangular matrices in Zp as public values and whose factorization is proved to be an NP-complete problem. We present running times as a function of the explored parameters and their link with operational safety. To our knowledge there are no classical and quantum attacks of polynomial complexity available at hand, remaining only the systematic exploration of the private-key space.
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.
With the rise of new advancements in quantum computing, more attention is given to the development of post-quantum security primitives and protocols. Recently, several authentication, key agreement and signature schemes relying on the hardness of the Inhomogeneous Small Inter Solution (ISIS) and its variants have been defined in literature. The advantage of these schemes is that they are simple, easy to implement and possess a reasonable communication and computation cost, compared to other post-quantum alternatives. Unfortunately, we show serious attacks on six different categories of these schemes, corresponding with more than ten publications in recent highly reputed journals. These vulnerabilities pose serious risks to consumer electronics, including IoT devices, smart home systems, and wearable technologies, where secure communication and authentication are vital. Exploitation of these vulnerabilities could lead to unauthorized access, device tampering, and data breaches, significantly impacting user trust and device functionality. Finally, we discuss the feasibility of defining post-quantum secure key exchange protocols, based on the ISIS problem and propose a high level approach to derive secure post-quantum protocols.