Public-Key Cryptosystems and Signature Schemes from $$p$$ -Adic Lattices

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-03-01 DOI:10.1134/s2070046624010035

引用次数: 0

Abstract

In 2018, the longest vector problem and closest vector problem in local fields were introduced, as the $p$ -adic analogues of the shortest vector problem and closest vector problem in lattices of Euclidean spaces. They are considered to be hard and useful in constructing cryptographic primitives, but no applications in cryptography were given. In this paper, we construct the first signature scheme and public-key encryption cryptosystem based on $p$ -adic lattice by proposing a trapdoor function with the norm-orthogonal basis of $p$ -adic lattice. These cryptographic schemes have reasonable key size and the signature scheme is efficient, while the encryption scheme works only for short messages, which shows that $p$ -adic lattice can be a new alternative to construct cryptographic primitives and well worth studying.

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来自 $$p$$ 自适应网格的公钥密码系统和签名方案

摘要 2018年，引入了局部域中的最长向量问题和最近向量问题，作为欧几里得空间晶格中最短向量问题和最近向量问题的$p$ -adic类比。它们被认为很难，而且在构造密码基元时很有用，但在密码学中却没有应用。在本文中，我们通过提出具有 $p$ -adic 网格的规范正交基的陷阱门函数，构建了第一个基于 $p$ -adic 网格的签名方案和公钥加密密码系统。这些加密方案具有合理的密钥大小，签名方案也很有效，而加密方案只适用于短信息，这表明（p）-adic网格可以成为构建加密基元的一种新的替代方案，非常值得研究。

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

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.