{"title":"Quantum algorithm for discrete logarithm problem for matrices over finite group rings","authors":"A. Myasnikov, A. Ushakov","doi":"10.1515/gcc-2014-0003","DOIUrl":null,"url":null,"abstract":"Abstract. We propose a polynomial time quantum algorithm for solving the discrete logarithm problem (DLP) in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis and V. Shpilrain [Groups Complex. Cryptol. 5 (2013), 97–115]. Our result implies that the Kahrobaei–Koupparis–Shpilrain protocol does not belong to the realm of post-quantum cryptography.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"1 1","pages":"31 - 36"},"PeriodicalIF":0.1000,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2014-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 21
Abstract
Abstract. We propose a polynomial time quantum algorithm for solving the discrete logarithm problem (DLP) in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis and V. Shpilrain [Groups Complex. Cryptol. 5 (2013), 97–115]. Our result implies that the Kahrobaei–Koupparis–Shpilrain protocol does not belong to the realm of post-quantum cryptography.
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