A sharper lower bound on Rankin's constant

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2023-08-01 DOI:10.1016/j.ipl.2023.106379

Kang Li , Fengjun Xiao , Bingpeng Zhou , Jinming Wen

引用次数: 0

Abstract

Rankin's constant is an important lattice constant which has applications in many fields including cryptography and communications. In spite of its importance, few of exact values of Rankin's constant are known. In this paper, we develop a lower bound on Rankin's constant $γ_{2 k, k}$ which corresponds to the half volume problem. Compared with the previous best lower bound developed by Wen et al., ours is more than $\frac{\sqrt{k}}{2}$ times better. This improved lower bound on Rankin's constant directly leads to a sharper lower bound on Schnorr's constant and helps to better understand the intrinsic limitations of the 2k-block-Rankin reduction.

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Rankin常数的一个更尖锐的下界

兰金常数是一个重要的格常数，在密码学和通信等领域有着广泛的应用。尽管兰金常数很重要，但它的确切值却鲜为人知。本文给出了与半体积问题相对应的Rankin常数γ2k，k的下界。与Wen等人提出的最优下界相比，我们的最优下界提高了k2倍以上。Rankin常数的这个改进的下界直接导致Schnorr常数的一个更尖锐的下界，并有助于更好地理解2k块Rankin约简的内在局限性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.