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A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

Mao Mao, Shaowu, Zhang, Huanguo, Wu, Wanqing, Liu ., Jinhui, Li -, Shuanbao, Wang, Houzhen

Published Jan 1, 2014• 0 citations
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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.
Because of Shor’s method, it is expected that quantum computers will have the capability to decipher current public key encryption methods. Consequently, there is a need to replace existing public key cryptography with quantum-resistant cryptography, also known as post-quantum cryptography (PQC) algorithms. In the last twenty years, significant progress has been made in the field of PQC research, leading to the creation of various algorithms that are proven to be resistant to quantum attacks. Several organizations responsible for standardization have already selected and are in the process of standardizing specific PQC algorithms.In popular instant messaging and voice-over IP applications like Signal, Facebook Messenger, and WhatsApp, the Signal Protocol provides end-to-end encryption (E2EE) and additional security features such as forward secrecy, future secrecy, authentication, asynchronous communication, and deniability. The protocol utilizes the ECDH Curve25519 key exchange and hash-based key derivation algorithms to accomplish this. However, the ECDH key exchange is vulnerable to attacks from quantum computers, which can compromise the security of contemporary cryptographic techniques by obtaining the corresponding public keys. Therefore, there is a need to replace the ECDH key exchange with a quantum-safe key exchange scheme that is resistant to attacks from quantum computers.In this context, the focus is on investigating post-quantum cryptography (PQC) that can provide robust security against quantum computing threats and proposing an end-to-end encryption scheme.
To solve the problem that existing Authenticated Key Exchange(AKE) protocols have high computational complexity and cannot resist quantum attacks,this paper proposes an AKE protocol based on R-LWE problem on lattice.The KEM scheme constructed based on R-LWE problem is combined with the digital signature algorithm with the message recovery function to achieve authentication,and the Peikert-type error coordination mechanism is replaced by the encrypted construction method to obtain the random and uniform session key.Analysis results show that,compared with the protocol designed by BOS,et al.,the proposed protocol has lower computational complexity,significantly reduces traffic,and effectively resists quantum attacks.