{"title":"基于二次方程组硬度的隐群代数签名算法","authors":"N. Moldovyan","doi":"10.56415/qrs.v30.24","DOIUrl":null,"url":null,"abstract":"A new-type algebraic digital signature schemes on non-commutative associative algebras are developed using technique of performing exponentiation operations in a hidden group. The signature contains two elements: a randomization integer e and a vector S. The used verification equations are characterized in multiple entries of the signature element S. The post-quantum security of the introduced signature algorithms is provided by the computational difficulty of solving a system of many quadratic equations in many variables, like in the public-key multivariate cryptosystems. However in the former case the quadratic equations are set over the finite fields having the order of significantly larger size.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic signature algorithms with a hidden group group, based on hardness of solving systems of quadratic equations\",\"authors\":\"N. Moldovyan\",\"doi\":\"10.56415/qrs.v30.24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new-type algebraic digital signature schemes on non-commutative associative algebras are developed using technique of performing exponentiation operations in a hidden group. The signature contains two elements: a randomization integer e and a vector S. The used verification equations are characterized in multiple entries of the signature element S. The post-quantum security of the introduced signature algorithms is provided by the computational difficulty of solving a system of many quadratic equations in many variables, like in the public-key multivariate cryptosystems. However in the former case the quadratic equations are set over the finite fields having the order of significantly larger size.\",\"PeriodicalId\":38681,\"journal\":{\"name\":\"Quasigroups and Related Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quasigroups and Related Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56415/qrs.v30.24\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Algebraic signature algorithms with a hidden group group, based on hardness of solving systems of quadratic equations
A new-type algebraic digital signature schemes on non-commutative associative algebras are developed using technique of performing exponentiation operations in a hidden group. The signature contains two elements: a randomization integer e and a vector S. The used verification equations are characterized in multiple entries of the signature element S. The post-quantum security of the introduced signature algorithms is provided by the computational difficulty of solving a system of many quadratic equations in many variables, like in the public-key multivariate cryptosystems. However in the former case the quadratic equations are set over the finite fields having the order of significantly larger size.