{"title":"可逆二元矩阵中可逆子矩阵最大比例的求值","authors":"Jiayi Hu","doi":"10.1145/3545839.3545843","DOIUrl":null,"url":null,"abstract":"The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.","PeriodicalId":249161,"journal":{"name":"Proceedings of the 2022 5th International Conference on Mathematics and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evaluation of the maximum proportion of invertible submatrices in invertible binary matrices\",\"authors\":\"Jiayi Hu\",\"doi\":\"10.1145/3545839.3545843\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.\",\"PeriodicalId\":249161,\"journal\":{\"name\":\"Proceedings of the 2022 5th International Conference on Mathematics and Statistics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2022 5th International Conference on Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3545839.3545843\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2022 5th International Conference on Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3545839.3545843","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Evaluation of the maximum proportion of invertible submatrices in invertible binary matrices
The research on all-or-nothing transform in cryptography leads to the problem that, for a given positive integer , what is the density of invertible submatrices of any invertible matrix? For binary matrices, previous work shows that in the case , , where denotes the maximum proportion of invertible submatrices in invertible matrices. In this paper we study the case . It is proved that and an upper bound of is given as well.
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