Abstract
Plenty of lattice-based cryptosystems use ternary or quinary sparse short vectors to accelerate the computing procedure. The hybrid attack, proposed by Howgrave-Graham, utilizes the sparsity of the short non-zero vector. Some improved hybrid attack presents a state-of-the-art performance in solving SVPs with ternary short vectors. However, the efficiency of the hybrid attack decreases when the short vector becomes quinary. Although there are several works for the ternary case, few of them focus on the situation that the infinite norm is larger than 1.
In this paper, we propose a new attack for lattice-based schemes using quinary short vectors, called the ESHybrid attack. Our attack is based on the structure of the hybrid attack, with the Meet-LWE algorithm [25] that replaces the traditional meet-in-the-middle structure. To solve the open question that Meet-LWE can not be applied to the hybrid attack, we propose the Error-Splitting (ES) technique. This technique utilizes the structure of quinary vectors and also makes the Meet-LWE procedure faster. We give a complete analysis of the complexity of this algorithm. The evaluation from practical parameter sets ensures that our ESHybrid attack is faster than the ordinary lattice reduction approach and the existing hybrid attack.
This work was done when all authors belonged to The University of Tokyo, and was supported by JST CREST Grant Number JPMJCR2113, Japan.
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Zhu, H., Kamada, S., Kudo, M., Takagi, T. (2023). Improved Hybrid Attack via Error-Splitting Method for Finding Quinary Short Lattice Vectors. In: Shikata, J., Kuzuno, H. (eds) Advances in Information and Computer Security. IWSEC 2023. Lecture Notes in Computer Science, vol 14128. Springer, Cham. https://doi.org/10.1007/978-3-031-41326-1_7
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