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The Open Cybernetics & Systemics Journal

Diffie-Hellman Key Exchange Protocol Based on Ring-LWE

Zhimin Yu, Jing Zheng-Jun, Li Shi-Cun

Published Sep 10, 2015• 1 citation
Publisher

Abstract

In this paper, we first construct a one-round Diffie-Hellman key exchange protocol based on Ring-LWE.The security of our construction is based on the hardness of the Ring-LWE problem.Second, we adaptively extend our construction from Ring-LWE to LWE.Finally, we efficiently implement our key exchange protocols based on Ring-LWE and LWE.
DOI
10.2174/1874110x01509011033

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The necessity of a secure key exchange protocol arises from the critical need to establish encrypted communication over an untrusted network. Over time, a multitude of key exchange mechanisms have been developed to counteract adversarial threats. The Diffie-Hellman key exchange protocol (DHKE) is one of the most widely used protocols for symmetric key sharing. However, this protocol exhibits certain inherent limitations that attackers may exploit. It lacks authentication mechanism and is susceptible to Man-in-the-Middle (MITM) attacks and quantum attacks. To mitigate these vulnerabilities, we have designed a hybrid key exchange protocol combining DHKE with Learning With Errors (LWE), a lattice-based post-quantum primitive. This proposed protocol provides authentication via a Public Key Infrastructure (PKI) together with CRYSTALS-Dilithium digital signature, resilience against MITM attacks, and robustness against classical and quantum threats. We have done a security analysis using the Dolev-Yao threat model, extended to quantum-equipped attackers, and showed that the protocol achieves mutual authentication, session key secrecy, and forward secrecy under the hardness of LWE and DHKE. Lastly, we provided detailed parameter recommendations based on NIST standards and shed light on side-channel attacks.
The only known threat to some symmetric cryptographic schemes like DES is Grover’s algorithm that proposes a square root speed-up over classical brute force algorithms. NIST [14] points out that if the key sizes are sufficient, symmetric cryptographic schemes (specifically the Advanced Encryption Standard-AES) are resistant to quantum computers. The development of quantum computer is on full pace, hopefully it might be available in a decade. Thus, it is necessary to develop efficient quantum secure public key cryptosystems to provide safe key exchange in quantum era. In this paper we presented an efficient implementation of a Ring-Learning with errors public key cryptosystem whose security is based on intractability of hard problem on lattices. And comparative analysis of proposed cryptosystem with RSA, ECDH and LWE based key exchange protocols is presented.
Designing efficient key agreement protocols is a fundamental cryptographic problem. In this paper, we first define a security model for key agreement in certificateless cryptography that is an extension of earlier models. We note that the existing pairing free protocols are not secure in our model. We design an efficient pairing-free, single round protocol that is secure in our model based on the hardness assumption of the Computational Diffie Hellman (CDH) problem. We also observe that previously existing pairing-free protocols were secure based on much stronger assumptions such as the hardness of the Gap Diffie Hellman problem. We use a restriction of our scheme to design an efficient pairing-free single round identity based key agreement protocol that is secure in the id-CK+ model based on the hardness assumption of the CDH problem. Additionally, both our schemes satisfy several other security properties such as forward secrecy, resistance to reflection attacks etc.