Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem
Advances in quantum computation threaten to break public key cryptosystems such as RSA, ECC, and E1Gamal that are based on the difficulty of factorization or taking a discrete logarithm, although up to now, no quantum algorithms have been found to be able to solve certain mathematical problems on no...
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| Veröffentlicht in: | Science China. Information sciences 2016-05, Vol.59 (5), p.129-139, Article 052109 |
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| creator | Liu, Jinhui Zhang, Huanguo Jia, Jianwei Wang, Houzhen Mao, Shaowu Wu, Wanqing |
| description | Advances in quantum computation threaten to break public key cryptosystems such as RSA, ECC, and E1Gamal that are based on the difficulty of factorization or taking a discrete logarithm, although up to now, no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures. Against this background, Raulynaitis et al. have proposed a novel asymmetric cipher protocol using a matrix decomposition problem. Their proposed scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we show that the asymmetric cipher of the non-commutative cryptography scheme is vulnerable to a linear algebra attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. We also propose an improvement to enhance the scheme of Raulynaitis et al. |
| doi_str_mv | 10.1007/s11432-015-5443-2 |
| format | Article |
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Against this background, Raulynaitis et al. have proposed a novel asymmetric cipher protocol using a matrix decomposition problem. Their proposed scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we show that the asymmetric cipher of the non-commutative cryptography scheme is vulnerable to a linear algebra attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. 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We also propose an improvement to enhance the scheme of Raulynaitis et al.</description><subject>Algorithms</subject><subject>Asymmetry</subject><subject>Computer Science</subject><subject>Computer systems</subject><subject>Cryptography</subject><subject>Decomposition</subject><subject>ElGamal</subject><subject>Encryption</subject><subject>Information Systems and Communication Service</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Matrices (mathematics)</subject><subject>Matrix algebra</subject><subject>Polynomials</subject><subject>Quantum computing</subject><subject>Research Paper</subject><subject>代数攻击</subject><subject>公钥密码体制</subject><subject>分解问题</subject><subject>密码协议</subject><subject>矩阵</subject><subject>离散对数问题</subject><subject>非对称密码</subject><issn>1674-733X</issn><issn>1869-1919</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9UE1LAzEQDaJgqf0B3oKeo_ncJEcpfkHBgwreQppm2y27m22yC-6_N2WL3pzLDMx78-Y9AK4JviMYy_tECGcUYSKQ4JwhegZmRBUaEU30eZ4LyZFk7OsSLFLa41yMYSrVDLwv49j1trX1mKoEQwltC20am8b3sXLQVd3OR9jF0AcXajikqt1CCxub199w411oupCqvgrtEbWufXMFLkpbJ7849Tn4fHr8WL6g1dvz6_JhhRxTRY8c0aq0Xm3WXHtJPOEbwUrGhMpGZP6RU-EUpmvBqcVKa8uoVdkLFUSxXHNwO93NuofBp97swxCzlWSozv5FgSXPKDKhXAwpRV-aLlaNjaMh2BzjM1N8JquaY3yGZg6dOClj262Pf5f_I92chHah3R4y71epKFTBqdSE_QDd43zD</recordid><startdate>20160501</startdate><enddate>20160501</enddate><creator>Liu, Jinhui</creator><creator>Zhang, Huanguo</creator><creator>Jia, Jianwei</creator><creator>Wang, Houzhen</creator><creator>Mao, Shaowu</creator><creator>Wu, Wanqing</creator><general>Science China Press</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>W92</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20160501</creationdate><title>Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem</title><author>Liu, Jinhui ; Zhang, Huanguo ; Jia, Jianwei ; Wang, Houzhen ; Mao, Shaowu ; Wu, Wanqing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-c198fae8db49e71e14d53f33580157000425c802b542a0899a32a816725183333</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algorithms</topic><topic>Asymmetry</topic><topic>Computer Science</topic><topic>Computer systems</topic><topic>Cryptography</topic><topic>Decomposition</topic><topic>ElGamal</topic><topic>Encryption</topic><topic>Information Systems and Communication Service</topic><topic>Linear algebra</topic><topic>Mathematical analysis</topic><topic>Matrices (mathematics)</topic><topic>Matrix algebra</topic><topic>Polynomials</topic><topic>Quantum computing</topic><topic>Research Paper</topic><topic>代数攻击</topic><topic>公钥密码体制</topic><topic>分解问题</topic><topic>密码协议</topic><topic>矩阵</topic><topic>离散对数问题</topic><topic>非对称密码</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jinhui</creatorcontrib><creatorcontrib>Zhang, Huanguo</creatorcontrib><creatorcontrib>Jia, Jianwei</creatorcontrib><creatorcontrib>Wang, Houzhen</creatorcontrib><creatorcontrib>Mao, Shaowu</creatorcontrib><creatorcontrib>Wu, Wanqing</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库-工程技术</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Science China. 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| subjects | Algorithms Asymmetry Computer Science Computer systems Cryptography Decomposition ElGamal Encryption Information Systems and Communication Service Linear algebra Mathematical analysis Matrices (mathematics) Matrix algebra Polynomials Quantum computing Research Paper 代数攻击 公钥密码体制 分解问题 密码协议 矩阵 离散对数问题 非对称密码 |
| title | Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem |
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