| 基于有限域上圆锥曲线的分组加密算法及实现 |
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| 引用本文： | 刘海峰,吴鹏,马令坤. 基于有限域上圆锥曲线的分组加密算法及实现[J]. 吉林大学学报(理学版), 2012, 50(1): 54-58 |
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| 作者姓名： | 刘海峰 吴鹏 马令坤 |
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| 作者单位： | 1. 陕西科技大学 理学院, 西安 710021； 2. 陕西科技大学 电气与信息工程学院, 西安 710021 |
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| 基金项目： | 国家自然科学基金(批准号:60972152);陕西省教育厅专项科研项目(批准号:11JK1015) |
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| 摘 要： | 运用群论的概念构造圆锥曲线的点阵群, 将其应用于改进的Hill加密算法中, 构建了基于圆锥曲线点列的分组密码系统, 并从明文嵌入和阶的运算两方面比较了椭圆曲线和圆锥曲线密码体制, 分析了改进的Hill加密算法的安全性. 实例结果表明, 圆锥曲线分组密码系统具有易于设计和应用的优点.
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| 关 键 词： | 圆锥曲线 点阵群 分组加密 有限域 |
| 收稿时间： | 2011-05-04 |
Implementation of Group Encryption Algorithm Based on Conic Curve over Finite Fields |
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| LIU Hai-feng,WU Peng,MA Ling-kun. Implementation of Group Encryption Algorithm Based on Conic Curve over Finite Fields[J]. Journal of Jilin University: Sci Ed, 2012, 50(1): 54-58 |
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| Authors: | LIU Hai-feng WU Peng MA Ling-kun |
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| Affiliation: | 1. Faculty of Science, Shaanxi University of Science and Technology, Xi’an 710021, China； 2. College of Electric and Information Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China |
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| Abstract: | Matrix group of conic curve points was first created according to group theory and applied to the improved algorithm of Hill cipher as an instance.A group encryption system based on conic curve point sequence was constructed.Comparison of conic curve cryptography with ECC was made in the aspects of plaintext embedment and order-calculation.Safety performance of improved Hill encryption algorithm was discussed,too.The instance demonstrates the advantages of conic curve group cryptosystem in the aspects of design and application.The algorithm has a definite practical value and popularizing significance. |
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| Keywords: | conic curve matrix groups of points group encryption finite field |
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