用循环矩阵求解多项式的块同构问题

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
Yasufumi Hashimoto
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引用次数: 0

摘要

多项式同构问题(IP问题)是研究多元公钥密码系统(后量子密码学的主要候选方案之一)对密钥恢复攻击的安全性的重要问题。近年来,人们提出了几种基于IP问题本身或其推广的方案。在PQCrypto 2020上,Santoso介绍了多项式同构问题的推广,称为多项式块同构问题(BIP问题),并在此问题的基础上提出了一种新的带循环矩阵的Diffie-Hellman型加密方案(BIPC问题)。最近,Ikematsu等人提出了一种称为线性堆栈攻击的攻击,以恢复Santoso加密方案的等效密钥。虽然这种攻击降低了方案的安全性,但它无助于解决BIPC问题本身。本文利用循环矩阵的共轭性,通过简化BIPC问题,给出了如何直接求解BIPC问题的方法。事实上,我们用该参数实验解决了BIPC问题,该参数在Santoso安全分析中具有256位安全性,在线性堆栈攻击中具有72.7位安全性,大约10分钟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solving the Problem of Blockwise Isomorphism of Polynomials with Circulant Matrices
The problem of Isomorphism of Polynomials (IP problem) is known to be important to study the security of multivariate public key cryptosystems, one of the major candidates of post-quantum cryptography, against key recovery attacks. In these years, several schemes based on the IP problem itself or its generalization have been proposed. At PQCrypto 2020, Santoso introduced a generalization of the problem of Isomorphism of Polynomials, called the problem of Blockwise Isomorphism of Polynomials (BIP problem), and proposed a new Diffie-Hellman type encryption scheme based on this problem with Circulant matrices (BIPC problem). Quite recently, Ikematsu et al. proposed an attack called the linear stack attack to recover an equivalent key of Santoso's encryption scheme. While this attack reduced the security of the scheme, it does not contribute to solving the BIPC problem itself. In the present paper, we describe how to solve the BIPC problem directly by simplifying the BIPC problem due to the conjugation property of circulant matrices. In fact, we experimentally solved the BIPC problem with the parameter, which has 256 bit security by Santoso's security analysis and has 72.7bit security against the linear stack attack, by about 10 minutes.
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来源期刊
CiteScore
1.10
自引率
20.00%
发文量
137
审稿时长
3.9 months
期刊介绍: Includes reports on research, developments, and examinations performed by the Society''s members for the specific fields shown in the category list such as detailed below, the contents of which may advance the development of science and industry: (1) Reports on new theories, experiments with new contents, or extensions of and supplements to conventional theories and experiments. (2) Reports on development of measurement technology and various applied technologies. (3) Reports on the planning, design, manufacture, testing, or operation of facilities, machinery, parts, materials, etc. (4) Presentation of new methods, suggestion of new angles, ideas, systematization, software, or any new facts regarding the above.
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