| Walsh transforms and cryptographic applications in bias computing |
| Lu, Y; Desmedt, Y
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| 2016
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| 发表期刊 | CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
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| ISSN | 1936-2447
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| 卷号 | 8期号:3页码:435-453 |
| 摘要 | Walsh transform is used in a wide variety of scientific and engineering applications, including bent functions and cryptanalytic optimization techniques in cryptography. In linear cryptanalysis, it is a key question to find a good linear approximation, which holds with probability (1+d)/2 and the bias d is large in absolute value. Lu and Desmedt (2011) take a step toward answering this key question in a more generalized setting and initiate the work on the generalized bias problem with linearly-dependent inputs. In this paper, we give fully extended results. Deep insights on assumptions behind the problem are given. We take an information-theoretic approach to show that our bias problem assumes the setting of the maximum input entropy subject to the input constraint. By means of Walsh transform, the bias can be expressed in a simple form. It incorporates Piling-up lemma as a special case. Secondly, as application, we answer a long-standing open problem in correlation attacks on combiners with memory. We give a closed-form exact solution for the correlation involving the multiple polynomial of any weight for the first time. We also give Walsh analysis for numerical approximation. An interesting bias phenomenon is uncovered, i.e., for even and odd weight of the polynomial, the correlation behaves differently. Thirdly, we introduce the notion of weakly biased distribution, and study bias approximation for a more general case by Walsh analysis. We show that for weakly biased distribution, Piling-up lemma is still valid. Our work shows that Walsh analysis is useful and effective to a broad class of cryptanalysis problems.; Walsh transform is used in a wide variety of scientific and engineering applications, including bent functions and cryptanalytic optimization techniques in cryptography. In linear cryptanalysis, it is a key question to find a good linear approximation, which holds with probability (1+d)/2 and the bias d is large in absolute value. Lu and Desmedt (2011) take a step toward answering this key question in a more generalized setting and initiate the work on the generalized bias problem with linearly-dependent inputs. In this paper, we give fully extended results. Deep insights on assumptions behind the problem are given. We take an information-theoretic approach to show that our bias problem assumes the setting of the maximum input entropy subject to the input constraint. By means of Walsh transform, the bias can be expressed in a simple form. It incorporates Piling-up lemma as a special case. Secondly, as application, we answer a long-standing open problem in correlation attacks on combiners with memory. We give a closed-form exact solution for the correlation involving the multiple polynomial of any weight for the first time. We also give Walsh analysis for numerical approximation. An interesting bias phenomenon is uncovered, i.e., for even and odd weight of the polynomial, the correlation behaves differently. Thirdly, we introduce the notion of weakly biased distribution, and study bias approximation for a more general case by Walsh analysis. We show that for weakly biased distribution, Piling-up lemma is still valid. Our work shows that Walsh analysis is useful and effective to a broad class of cryptanalysis problems. |
| 收录类别 | SCI
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| 关键词 | Walsh Transform
Linear Cryptanalysis
Bias Analysis
Maximum Entropy Principle
Piling-up Lemma
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| 部门归属 | Chinese Acad Sci, Inst Software, Beijing, Peoples R China. Univ Texas Dallas, Richardson, TX 75083 USA. UCL, London, England.
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| 语种 | 英语
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| WOS记录号 | WOS:000384758600007
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| 引用统计 |
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| 内容类型 | 期刊论文
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| URI标识 | http://ir.iscas.ac.cn/handle/311060/17316
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| 专题 | 中国科学院软件研究所
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推荐引用方式
GB/T 7714 |
Lu, Y,Desmedt, Y. Walsh transforms and cryptographic applications in bias computing[J]. CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES,2016,8(3):435-453.
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| APA |
Lu, Y,&Desmedt, Y.(2016).Walsh transforms and cryptographic applications in bias computing.CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES,8(3),435-453.
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| MLA |
Lu, Y,et al."Walsh transforms and cryptographic applications in bias computing".CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 8.3(2016):435-453.
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