相关随机分析线性子空间的伪适应性零知识证明

非交互式零知识(non-interactive zero-knowledge, NIZK)证明是零知识证明的一种, 它也是密码学协议中的一个重要工具. 非交互式零知识证明系统有着很多的应用, 可以将其应用在数字签名方案、公钥密码体制以及密钥分配体制等. 矩阵运算具有非交换属性, 基于非交换代数结构的公钥密码算法, 目前还没有量子计算算法, 因此, 基于矩阵的零知识证明具有抗量子计算攻击的潜力. Kiltz等人在EUROCRYPT 2015上构造了一个线性空间的伪适应性非交互式零知识证明(quasi-adaptive NIZK, QANIZK), 同时将该技巧推广到保持线性同态结构的签名方案....

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Published inJournal of Cryptologic Research Vol. 5; no. 2; p. 101
Main Authors Jin-Hui, LIU, YU, Yong, YANG, Bo, Wan-Qing, WU, 刘金会, 禹 勇, 杨 波, 吴万青
Format Journal Article
LanguageChinese
Published Beijing Chinese Association for Cryptologic Research, Journal of Cryptologic Research 01.01.2018
Subjects
Algorithms
Cryptography
Digital signatures
Randomness
Subspaces
Vector spaces
Online AccessGet full text
ISSN2097-4116
DOI10.13868/j.cnki.jcr.000223

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Abstract 非交互式零知识(non-interactive zero-knowledge, NIZK)证明是零知识证明的一种, 它也是密码学协议中的一个重要工具. 非交互式零知识证明系统有着很多的应用, 可以将其应用在数字签名方案、公钥密码体制以及密钥分配体制等. 矩阵运算具有非交换属性, 基于非交换代数结构的公钥密码算法, 目前还没有量子计算算法, 因此, 基于矩阵的零知识证明具有抗量子计算攻击的潜力. Kiltz等人在EUROCRYPT 2015上构造了一个线性空间的伪适应性非交互式零知识证明(quasi-adaptive NIZK, QANIZK), 同时将该技巧推广到保持线性同态结构的签名方案. 针对这类方案, 本文主要介绍了一种相关随机攻击方法, 分别对线性空间的具有适应性合理性的QANIZK, 简单的具有适应性一次模拟合理性的QANIZK和QANIZK构造进行了相关随机分析. 在对方案的相关随机分析过程中, 首先给定一个合理的假设, 分析方案的公私密钥对, 通过求解代数方程组, 获取一些等价密钥, 进而伪造签名. 然后, 分别介绍攻击方法相关的算法描述, 有效性分析和攻击成功的概率. 最后说明攻击方法的合理性并提出进一步的分析研究.
AbstractList 非交互式零知识(non-interactive zero-knowledge, NIZK)证明是零知识证明的一种, 它也是密码学协议中的一个重要工具. 非交互式零知识证明系统有着很多的应用, 可以将其应用在数字签名方案、公钥密码体制以及密钥分配体制等. 矩阵运算具有非交换属性, 基于非交换代数结构的公钥密码算法, 目前还没有量子计算算法, 因此, 基于矩阵的零知识证明具有抗量子计算攻击的潜力. Kiltz等人在EUROCRYPT 2015上构造了一个线性空间的伪适应性非交互式零知识证明(quasi-adaptive NIZK, QANIZK), 同时将该技巧推广到保持线性同态结构的签名方案. 针对这类方案, 本文主要介绍了一种相关随机攻击方法, 分别对线性空间的具有适应性合理性的QANIZK, 简单的具有适应性一次模拟合理性的QANIZK和QANIZK构造进行了相关随机分析. 在对方案的相关随机分析过程中, 首先给定一个合理的假设, 分析方案的公私密钥对, 通过求解代数方程组, 获取一些等价密钥, 进而伪造签名. 然后, 分别介绍攻击方法相关的算法描述, 有效性分析和攻击成功的概率. 最后说明攻击方法的合理性并提出进一步的分析研究.
Author YU, Yong
Wan-Qing, WU
Jin-Hui, LIU
YANG, Bo
刘金会
禹 勇
吴万青
杨 波
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SubjectTerms Algorithms
Cryptography
Digital signatures
Randomness
Subspaces
Vector spaces
Title 相关随机分析线性子空间的伪适应性零知识证明
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