Pub Date : 2023-08-12DOI: 10.1007/s12095-023-00660-4
Ana Sălăgean, Percy Reyes-Paredes
Abstract The algebraic degree is an important parameter of Boolean functions used in cryptography. When a function in a large number of variables is not given explicitly in algebraic normal form, it is usually not feasible to compute its degree, so we need to estimate it. We propose a probabilistic test for deciding whether the algebraic degree of a Boolean function f is below a certain value k . If the degree is indeed below k , then f will always pass the test, otherwise f will fail each instance of the test with a probability $$textrm{dt}_k(f)$$ dtk(f) , which is closely related to the average number of monomials of degree k of the polynomials which are affine equivalent to f . The test has a good accuracy only if this probability $$textrm{dt}_k(f)$$ dtk(f) of failing the test is not too small. We initiate the study of $$textrm{dt}_k(f)$$ dtk(f) by showing that in the particular case when the degree of f is actually equal to k , the probability will be in the interval (0.288788, 0.5], and therefore a small number of runs of the test will be sufficient to give, with very high probability, the correct answer. Exact values of $$textrm{dt}_k(f)$$ dtk(f) for all the polynomials in 8 variables were computed using the representatives listed by Hou and by Langevin and Leander.
代数度是密码学中布尔函数的一个重要参数。当含有大量变量的函数没有以代数范式显式给出时，通常无法计算其次数，因此需要对其进行估计。我们提出了一个判别布尔函数f的代数度是否低于某一值k的概率检验。如果阶数确实低于k，则f总能通过测试，否则f每次测试失败的概率为$$textrm{dt}_k(f)$$ dt k (f)，这与f的仿射等价多项式的k阶单项式的平均个数密切相关。只有当测试失败的概率$$textrm{dt}_k(f)$$ dt k (f)不太小时，测试才具有良好的准确性。我们开始研究$$textrm{dt}_k(f)$$ dt k (f)，通过表明在f的度实际上等于k的特殊情况下，概率将在(0.288788,0.5)区间内，因此少量的测试运行将足以以非常高的概率给出正确答案。使用Hou和Langevin和Leander列出的代表，计算8个变量中所有多项式的精确值$$textrm{dt}_k(f)$$ dt k (f)。
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Pub Date : 2023-07-29DOI: 10.1007/s12095-023-00662-2
Marko Djurasevic, Domagoj Jakobovic, Luca Mariot, Stjepan Picek
Abstract Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one should consider and cryptographic properties that need to be fulfilled makes the search for new Boolean functions still a very active domain. There are several options to construct appropriate Boolean functions: algebraic constructions, random search, and metaheuristics. In this work, we concentrate on metaheuristic approaches and examine the related works appearing in the last 25 years. To the best of our knowledge, this is the first survey work on this topic. Additionally, we provide a new taxonomy of related works and discuss the results obtained. Finally, we finish this survey with potential future research directions.
{"title":"A survey of metaheuristic algorithms for the design of cryptographic Boolean functions","authors":"Marko Djurasevic, Domagoj Jakobovic, Luca Mariot, Stjepan Picek","doi":"10.1007/s12095-023-00662-2","DOIUrl":"https://doi.org/10.1007/s12095-023-00662-2","url":null,"abstract":"Abstract Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one should consider and cryptographic properties that need to be fulfilled makes the search for new Boolean functions still a very active domain. There are several options to construct appropriate Boolean functions: algebraic constructions, random search, and metaheuristics. In this work, we concentrate on metaheuristic approaches and examine the related works appearing in the last 25 years. To the best of our knowledge, this is the first survey work on this topic. Additionally, we provide a new taxonomy of related works and discuss the results obtained. Finally, we finish this survey with potential future research directions.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135444409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-18DOI: 10.1007/s12095-023-00634-6
Li-An Chen, Robert S. Coulter
We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order 3 mod 4, irrespective of the field size. Computational results are also given.
{"title":"Bounds on the differential uniformity of the Wan-Lidl polynomials","authors":"Li-An Chen, Robert S. Coulter","doi":"10.1007/s12095-023-00634-6","DOIUrl":"https://doi.org/10.1007/s12095-023-00634-6","url":null,"abstract":"We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order 3 mod 4, irrespective of the field size. Computational results are also given.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"469 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135244738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-13DOI: 10.1007/s12095-022-00625-z
Gustavo Banegas, Ricardo Villanueva-Polanco
Abstract This paper presents a general strategy to recover a block cipher secret key in the cold boot attack setting. More precisely, we propose a key-recovery method that combines key enumeration algorithms and Grover’s quantum algorithm to recover a block cipher secret key after an attacker has procured a noisy version of it via a cold boot attack. We also show how to implement the quantum component of our algorithm for several block ciphers such as AES, PRESENT and GIFT, and LowMC. Additionally, since evaluating the third-round post-quantum candidates of the National Institute of Standards and Technology (NIST) post-quantum standardization process against different attack vectors is of great importance for their overall assessment, we show the feasibility of performing our hybrid attack on Picnic, a post-quantum signature algorithm being an alternate candidate in the NIST post-quantum standardization competition. According to our results, our method may recover the Picnic private key for all Picnic parameter sets, tolerating up to 40 % of noise for some of the parameter sets. Furthermore, we provide a detailed analysis of our method by giving the cost of its resources, its running time, and its success rate for various enumerations.
{"title":"On recovering block cipher secret keys in the cold boot attack setting","authors":"Gustavo Banegas, Ricardo Villanueva-Polanco","doi":"10.1007/s12095-022-00625-z","DOIUrl":"https://doi.org/10.1007/s12095-022-00625-z","url":null,"abstract":"Abstract This paper presents a general strategy to recover a block cipher secret key in the cold boot attack setting. More precisely, we propose a key-recovery method that combines key enumeration algorithms and Grover’s quantum algorithm to recover a block cipher secret key after an attacker has procured a noisy version of it via a cold boot attack. We also show how to implement the quantum component of our algorithm for several block ciphers such as AES, PRESENT and GIFT, and LowMC. Additionally, since evaluating the third-round post-quantum candidates of the National Institute of Standards and Technology (NIST) post-quantum standardization process against different attack vectors is of great importance for their overall assessment, we show the feasibility of performing our hybrid attack on Picnic, a post-quantum signature algorithm being an alternate candidate in the NIST post-quantum standardization competition. According to our results, our method may recover the Picnic private key for all Picnic parameter sets, tolerating up to 40 % of noise for some of the parameter sets. Furthermore, we provide a detailed analysis of our method by giving the cost of its resources, its running time, and its success rate for various enumerations.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135906260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-03DOI: 10.1007/s12095-021-00487-x
S. Dougherty, J. Gildea, Adrian Korban, S. Șahinkaya
{"title":"G-codes, self-dual G-codes and reversible G-codes over the ring Bj,kdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}${m","authors":"S. Dougherty, J. Gildea, Adrian Korban, S. Șahinkaya","doi":"10.1007/s12095-021-00487-x","DOIUrl":"https://doi.org/10.1007/s12095-021-00487-x","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"23 1","pages":"601 - 616"},"PeriodicalIF":0.0,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86158811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-07DOI: 10.1007/s12095-020-00466-8
P. Stănică, Aaron Geary
{"title":"The c-differential behavior of the inverse function under the EA-equivalence","authors":"P. Stănică, Aaron Geary","doi":"10.1007/s12095-020-00466-8","DOIUrl":"https://doi.org/10.1007/s12095-020-00466-8","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"3 1","pages":"295 - 306"},"PeriodicalIF":0.0,"publicationDate":"2021-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141201918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-06DOI: 10.1007/s12095-020-00427-1
Marco Calderini
{"title":"On the EA-classes of known APN functions in small dimensions","authors":"Marco Calderini","doi":"10.1007/s12095-020-00427-1","DOIUrl":"https://doi.org/10.1007/s12095-020-00427-1","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"112 1","pages":"821 - 840"},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-04DOI: 10.1007/s12095-020-00432-4
Xiaoqiang Wang, Dabin Zheng
{"title":"The subfield codes of several classes of linear codes","authors":"Xiaoqiang Wang, Dabin Zheng","doi":"10.1007/s12095-020-00432-4","DOIUrl":"https://doi.org/10.1007/s12095-020-00432-4","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"124 21","pages":"1111 - 1131"},"PeriodicalIF":0.0,"publicationDate":"2020-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-04DOI: 10.1007/s12095-020-00432-4
Xiaoqiang Wang, Dabin Zheng
{"title":"The subfield codes of several classes of linear codes","authors":"Xiaoqiang Wang, Dabin Zheng","doi":"10.1007/s12095-020-00432-4","DOIUrl":"https://doi.org/10.1007/s12095-020-00432-4","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"124 17","pages":"1111 - 1131"},"PeriodicalIF":0.0,"publicationDate":"2020-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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