{"title":"通过扩展集构造Bent函数支撑的一种算法","authors":"Joseph Nelson, Chungath Srinivasan, K. V. Lakshmy","doi":"10.33889/ijmems.2023.8.5.060","DOIUrl":null,"url":null,"abstract":"Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 four-variable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions.","PeriodicalId":44185,"journal":{"name":"International Journal of Mathematical Engineering and Management Sciences","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Algorithm for Constructing Support of Bent Functions by Extending a Set\",\"authors\":\"Joseph Nelson, Chungath Srinivasan, K. V. Lakshmy\",\"doi\":\"10.33889/ijmems.2023.8.5.060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 four-variable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions.\",\"PeriodicalId\":44185,\"journal\":{\"name\":\"International Journal of Mathematical Engineering and Management Sciences\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Engineering and Management Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33889/ijmems.2023.8.5.060\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Engineering and Management Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33889/ijmems.2023.8.5.060","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
An Algorithm for Constructing Support of Bent Functions by Extending a Set
Boolean functions form the fundamental components of symmetric cryptographic systems, serving as the building blocks. Modifying bent functions makes it feasible to design Boolean functions with desired properties that exhibit high non-linearity. The current study offers a comprehensive analysis of bent functions through its support, culminating in the introduction of an algorithm for the systematic construction of four variable bent functions. This algorithm enables the complete generation of all 896 four-variable bent functions. Furthermore, we introduce a methodology for constructing n-variable bent functions (where n > 4), leveraging both the algorithm and an established secondary technique for bent function construction. Lastly, we examine the estimation of the count of bent functions by utilising certain properties associated with the support of bent functions.
期刊介绍:
IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.