{"title":"有限群环上矩阵离散对数问题的量子算法","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":"{\"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}","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
摘要
摘要提出了一种求解有限群环上矩阵离散对数问题的多项式时间量子算法。这个问题的难度最近被用于D. Kahrobaei, C. Koupparis和V. Shpilrain [Groups Complex]提出的密钥交换协议的设计中。密码学，5(2013)，97-115。我们的结果表明Kahrobaei-Koupparis-Shpilrain协议不属于后量子密码学领域。
Quantum algorithm for discrete logarithm problem for matrices over finite group rings
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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