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.
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.
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 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.
Since the launch of the post-quantum cryptography standardization project by NIST, post-quantum cryptography has become a prominent research area. Non-commutative cryptography constructed using NP-complete problems is widely regarded resistant to quantum computing attacks, so it has become an important branch of post-quantum cryptography. Nonetheless, the existing non-commutative cryptographic protocol still exhibits certain shortcomings. In this paper, a non-commutative combinatorial semigroup with matrix power function is constructed from a modified medial semigroup by the method of semidirect product, and then a key exchange protocol is developed on it to provide a kind of novel non-commutative cryptographic protocol. Due to the non-commutativity of cryptographic platform, the proposed protocol could perform well in respect of antiquantum computing attack, which is superior to traditional cryptographic protocol. In addition, the security analysis shows that the protocol has significant advantages in resisting algebraic and brute force attacks, as well as aganist quantum cryptanalysis; the complexity analysis demonstrates that computation and storage complexities are of polynomial order, ensuring efficient operation even for large matrix sizes.
This paper presents an enhanced post-quantum key agreement protocol based on Rényi entropy, addressing vulnerabilities in the original construction while preserving information-theoretic security properties. We develop a theoretical framework leveraging entropy-preserving operations and secret-shared verification to achieve provable security against quantum adversaries. Through entropy amplification techniques and quantum-resistant commitments, the protocol establishes 2128 quantum security guarantees under the quantum random oracle model. Key innovations include a confidentiality-preserving verification mechanism using distributed polynomial commitments, tightened min-entropy bounds with guaranteed non-negativity, and composable security proofs in the quantum universal composability framework. Unlike computational approaches, our method provides information-theoretic security without hardness assumptions while maintaining polynomial complexity. Theoretical analysis demonstrates resilience against known quantum attack vectors, including Grover-accelerated brute force and quantum memory attacks. The protocol achieves parameterization for 128-bit quantum security with efficient O(n2) communication complexity. Extensions to secure multiparty computation and quantum network applications are established, providing a foundation for long-term cryptographic security.
Quantum-safe public key exchange protocols face significant challenges in hardware- and software-based approaches. Quantum key distribution, which relies on specialized quantum hardware, presents a significant barrier to widespread adoption due to its high cost and limited scalability. Conversely, software-based solutions using post-quantum algorithms introduce complications, such as increased resource demands and larger cipher-texts. Furthermore, the security of these post-quantum algorithms remains relatively untested, which has led to the emerging trend of hybrid deployment, combining clas-sical and quantum-resistant techniques to hedge against potential vulnerabilities. Recently, Arqit proposed a quantum-secure symmet-ric key agreement (SKA) protocol, claiming that it is lightweight and scalable [1] to address these problems. However, their proprietary solution is not available for independent analysis. To evaluate the performance and scalability of quantum-secure SKA techniques, we develop variations of the SKA protocol using open-source and accessible components in this work. To analyze quantum-secure SKA scheme, we imple-mented an SKA technique that involves a hybrid mech-anism, leveraging secret strings distributed through a combination of existing classical and quantum public key pairs during the initial key exchange. We analyze our scheme and demonstrate that it incurs minimal performance overhead, with only 99ms for purely quantum SKA and 199ms for the hybrid version, compared to the classical SKA protocol. We also show that our scheme remains robust under various network conditions, including delays, packet losses, and bandwidth variations, maintaining small and consistent overheads. We also show that this solution is scalable, with an overhead of only one second for every additional five concurrent users. This performance improves significantly with increased computational resources-achieving a 50-60% improvement when scaling from two to four CPUs. Additionally, our security evaluations confirm that the protocol provides consistent and sufficient randomness throughout the key agreement process, ensuring quantum-resistance at every stage.
The rise of Web 3.0 has propelled the Internet to new heights of development. However, post-quantum protocols are in high demand to ensure the utmost security to keep pace with the advancements. Our solution is upgrading the traditional synchronous authenticated identity identification and key agreement protocol. Specifically, we have developed an asymmetric key version of the quantum-safe Needham-Schroeder protocol. The proposed protocol achieves forward secrecy, which the classical Needham-Schroeder lacks. Using the highly flexible universal composability framework (iUC), we have analyzed the security of the protocol and achieved mutual authentication and session key security for an unbounded number of sessions. Our informal security analysis confirms that the proposed protocol resists known attacks such as replay and masquerading. Besides, it satisfies security goals, including known-key secrecy and ephemeral secret key leakage. Our modular solution can upgrade practical applications that rely on the traditional Needham-Schroeder protocol and its derivatives to the post-quantum era.