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Security and Communication Networks

Module-LWE-Based Key Exchange Protocol Using Error Reconciliation Mechanism

Wenjuan Jia, Guanhao Xue, Baocang Wang, Yupu Hu

Published Feb 1, 2022• 2 citations
Publisher

Abstract

Lattice-based key exchange protocols have attracted tremendous attention for its post-quantum security. In this work, we construct a Module-LWE-based key exchange protocol using Peikert’s error reconciliation mechanism. Compared with Kyber.KE, our key exchange protocol reduces the total communication cost by 96-byte, i.e., 3.2% ∼ 6.1%, under the different parameter sets, and without reducing the post-quantum security levels. Moreover, our key exchange protocol slightly reduces the probability of session key agreement failure and the time consumed by modular multiplication of numbers and ring elements by approximately 30%. Thus, the key exchange protocol in this paper is more suitable for the lightweight communication systems.

DOI
10.1155/2022/8299232

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•Jan 1, 2015•1 citation
Lattice-based key exchange protocols have attracted tremendous attention for its post-quantum security. In this work, we construct a Module-LWE-based key exchange protocol using Peikert’s error reconciliation mechanism. Compared with Kyber.KE, our key exchange protocol reduces the total communication cost by 96-byte, i.e., 3.2% ∼ 6.1%, under the different parameter sets, and without reducing the post-quantum security levels. Moreover, our key exchange protocol slightly reduces the probability of session key agreement failure and the time consumed by modular multiplication of numbers and ring elements by approximately 30%. Thus, the key exchange protocol in this paper is more suitable for the lightweight communication systems.
The widespread use of Internet of Things devices alongside advances in quantum computing presents urgent challenges for secure communication. RSA and ECC have become inadequate, prompting the need for Post-quantum Cryptography (PQC). This work introduces a novel reconciliation-based Module-LWE key exchange protocol that eliminates the traditional encapsulation-decapsulation structure in schemes like Kyber.KE, thereby reducing computational cycles, communication size, and memory footprint. Unlike Kyber and NewHope, the proposed design employs modular rounding with Peikert reconciliation, optimizing the entire key exchange process without requiring additional randomness or ciphertext transmission. By leveraging Peikert’s error reconciliation technique and modular rounding, the proposed protocol achieves a 15% reduction in computational cycles, a 78-byte reduction in communication size, and a 10% decrease in memory usage. Using Open Quantum Safe (OQS) benchmark data, we evaluate performance across Kyber512, Kyber768, and Kyber1024 levels, demonstrating the protocol’s superior energy efficiency and lightweight design. These improvements position our protocol as a secure, efficient, and scalable solution for post-quantum key exchange in resource-constrained environments such as embedded systems and IoT networks.
We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice E8E_8E8​, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus q with comparable error probability. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.
We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional latticeE8E_{8}E8​, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulusqqqwith comparable error probability and similar requirements in terms of bandwidth. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.
In the last decade, there has been significant progress in the development of quantum computers, with massive investments by major tech companies. It is assumed that once large-scale quantum computers are built, many commonly used public key cryptosystems will no longer be secure. To prevent quantum attacks, researchers are already working on the design of post-quantum cryptographic protocols, and the US National Institute of Standards and Technology (NIST) is holding an international competition to select new cryptographic standards.Lattice-based cryptographic constructions are promising candidates because they offer strong theoretical security guarantees and can be implemented efficiently. One of the most widely used cryptographic primitives based on lattices is the Learning With Errors (LWE) problem introduced by Regev. Later works have proposed structured variants of LWE such as Ring-LWE and Module-LWE, which allow for a more compact representation.In this thesis, we consider two lattice-based NIST candidates for Key Encapsulation Mechanisms (KEMs) and propose new error correction and reconciliation techniques in order to improve their efficiency, their security, as well as their reliability.Unlike some previous works on error correction for lattice-based protocols, we provide rigorous error probability bounds.We first consider FrodoKEM, a lattice-based cryptosystem based on LWE, and introduce a modified error correction mechanism to improve its performance. Our encoder maps the secret key block-wise into a scaled version of the 8-dimensional Gosset lattice E_8. We propose three sets of parameters for our modified implementation. The first implementation outperforms FrodoKEM in terms of plausible security; the second allows to reduce the bandwidth by halving the modulus, and the third allows to increase key sizes.The second KEM we are considering is KyberKEM, which is based on Module-LWE. We propose a reconciliation technique using the lattice E_8, and show that our scheme can outperform KyberKEM in terms of security with comparable error probability and similar bandwidth requirements. We also investigate the use of higher dimensional lattices for reconciliation.
Module Learning with Errors (M-LWE) based key reconciliation mechanisms (KRM) can be viewed as quantizing an M-LWE sample according to a lattice codebook. This paper describes a generic M-LWE-based KRM framework, valid for any dimensional lattices and any modulusqqqwithout a dither. Our main result is an explicit upper bound on the decryption failure rate (DFR) of M-LWE-based KRM. This bound allows us to construct optimal lattice quantizers to reduce the DFR and communication cost simultaneously. Moreover, we present a KRM scheme using the same security parameters(q,k,η1,η2)(q, k, \eta_{1}, \eta_{2})(q,k,η1​,η2​)as in Kyber. Compared with Kyber, the communication cost is reduced by up to 36.47% and the DFR is reduced by a factor of up to 299. The security arguments remain the same as Kyber.
Using the hard assumption of Ring-Decision Learning With Errors (Ring-DLWE) in the lattice, a new Authenticated Key Exchange (AKE) scheme is proposed, which is based on the Peikert's reconciliation technique. Under the standard model, the proposed scheme is provably secure in the CK model, which is additionally achieves weak Perfect Forward Secrecy (wPFS). Compared with the current Key Exchange (KE) schemes based on the LWE, the proposed scheme not only protects the shared session key with balanced key derivation function but also resists quantum attacks because of the hard assumption on lattice problem.