An attack on p-adic lattice public-key encryption cryptosystems and signature schemes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-03-18 DOI:10.1007/s10623-025-01618-8

Chi Zhang

引用次数: 0

Abstract

Lattices have many significant applications in cryptography. In 2021, the p-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem (CVP) in p-adic lattices. These problems are considered to be challenging and there are no known deterministic polynomial time algorithms to solve them. In this paper, we improve the LVP algorithm in local fields. The modified LVP algorithm is a deterministic polynomial time algorithm when the field is totally ramified and p is a polynomial in the rank of the input lattice. We utilize this algorithm to attack the above schemes so that we are able to forge a valid signature of any message and decrypt any ciphertext. Although these schemes are broken, this work does not mean that p-adic lattices are not suitable in constructing cryptographic primitives. We propose some possible modifications to avoid our attack at the end of this paper.

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对 p 演算网格公钥加密密码系统和签名方案的攻击

格在密码学中有许多重要的应用。在2021年，引入了p进签名方案和公钥加密密码系统。它们基于p进格中的最长向量问题（LVP）和最近向量问题（CVP）。这些问题被认为是具有挑战性的，并且没有已知的确定性多项式时间算法来解决它们。本文对局部域的LVP算法进行了改进。改进的LVP算法是一个确定的多项式时间算法，当域是完全分叉时，p是输入格中秩的多项式。我们利用此算法攻击上述方案，以便我们能够伪造任何消息的有效签名并解密任何密文。虽然这些方案被破坏了，但这并不意味着p进格不适合构造密码原语。在本文的最后，我们提出了一些可能的修改来避免我们的攻击。

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

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.