The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and encryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security, security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.
The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and encryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security, security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.
In the quantum era, the advent of quantum computers poses significant threats to the security of current cryptosystems. Therefore, designing quantum-resistant cryptoschemes becomes important to guarantee information security. This work concentrates on the development of the post-quantum public key encryption (PKE) scheme. Non-commutative cryptography (NCC) has entered the field of post-quantum cryptography. We utilize the TSPEM problem with asymmetric structures (which serve as a potential candiate for resisting quantum attacks) to construct two PKE schemes which are demonstrated to be CPA security under the DTSPEM assumption. By representing the plaintext as a matrix, these schemes can effectively encrypt a significant amount of information in a single operation. Assuming an equal amount of messages for encryption, the proposed schemes acheive superior efficiency compared to existing PKE schemes. Structurally, our systems exhibit a level of synchronization and coexistence due to the distinct public keys $ (P) $ and ciphertexts $ (C_{1}) .Theefficiencyanalysisisconductedbycomparingknownschemesfromtheaspectofspecificcryptographicindicators.Generally,theproposedonesofferseveraladvantagesincludingprovablesecurity,highefficiency,potentialquantum−resistant,andrelativeeaseofimplementation;alongwithsynchronizationandcoexistence.OurinvestigationhasestablishedthefeasibilityofconstructingPKEschemesbasedontheTSPEMproblem,specificallyforasymmetriccommunicationscenarios.ThepreliminaryresultspavethewayforfurtherexplorationoftheTSPEMproblem ' $s potential in developing other cryptosystems suitable for quantum computing environments.
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.
Public key cryptography is extensively used for encryption, signing contracts and secure exchanges over the unreliable network.The findings of Shor in 1994, of a powerful algorithm which was based on quantum mechanics for computing discrete logarithms and factoring large integers sabotaged the security presumptions upon which the currently used public key cryptographic protocols are based, like ElGamal, RSA and ECC.However, few cryptosystems, known as post quantum cryptosystems, while not currently in wide use are considered to be resistant to such attacks.In this paper, a quantum version of ElGamal Cryptosystem is proposed whose security relies on the commutative rotation transformations and measurements in computational basis of qubits.An understanding of the new scheme over the quantum channels is provided.The proposed cryptosystem allows the party to send messages in the form of qubits over a quantum channel.Also the proposed protocol provides an opportunity for two parties to exchange keys which is considered as one of the major concerns while developing post quantum cryptosystems.
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.
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.
A Virtual Private Network (VPN) ensures the confidentiality and integrity of data transferred between two endpoints, even if the means of transport are insecure. One popular protocol is Internet Protocol Security (IPSec) which operates at OSI layer 3 and protects all protocols at higher layers. Cryptographic keys in IPSec are negotiated using the Internet Key Exchange (IKE) protocol. IKE negotiates security parameters for IPSec sessions. In particular, the IKEv2 protocol uses the Elliptic Curve Diffie-Hellman (ECDH) algorithm to establish a secret key shared between two nodes on a network. Although solving such a problem remains difficult with current computing power, it is believed that generic quantum computers will be able to solve this problem, which implies that the security of IKEv2 is compromised. There are, however, several cryptographic systems that are trusted to be resistant to attacks by quantum computers. This family of cryptosystems is known as quantum-resistant cryptography (QRC). In this paper, after highlighting the requirements for a secure key exchange protocol, we briefly review the QRC solutions that have been proposed in the recent literature.