Flexible and Compact MLWE-Based KEM

Wenqi Liang, Zhaoman Liu, Xuyang Zhao, Yafang Yang () and Zhichuang Liang ()
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Wenqi Liang: School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China
Zhaoman Liu: School of Computer Science, Fudan University, Shanghai 200433, China
Xuyang Zhao: School of Computer Science, Fudan University, Shanghai 200433, China
Yafang Yang: School of Computer Science, Fudan University, Shanghai 200433, China
Zhichuang Liang: School of Computer Science, Fudan University, Shanghai 200433, China

Mathematics, 2024, vol. 12, issue 11, 1-14

Abstract: In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically structured learning with errors (LWE) problem over power-of-two cyclotomics has been one of the most widely used hardness assumptions for lattice-based cryptographic schemes. However, power-of-two cyclotomic rings may be exploited in the inflexibility of selecting parameters. Recently, trinomial cyclotomic rings of the form Z q [ x ] / ( x n − x n / 2 + 1 ) , where n = 2 k 3 l , k ≥ 1 , l ≥ 0 , have received widespread attention due to their flexible parameter selection. In this paper, we propose Tyber, a variant scheme of the NIST-standardized KEM candidate Kyber over trinomial cyclotomic rings. We provide three parameter sets, aiming at the quantum security of 128, 192, and 256 bits (actually achieving 129, 197, and 276 bits) with matching and negligible error probabilities. When compared to Kyber, our Tyber exhibits stronger quantum security, by 22, 31, and 44 bits, than Kyber for three security levels.

Keywords: lattice-based cryptography; post-quantum cryptography; module learning with errors; Kyber; trinomial cyclotomics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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