基于有限域上圆锥曲线的分组加密算法及实现

J4 ›› 2012, Vol. 50 ›› Issue (01): 54-58.

基于有限域上圆锥曲线的分组加密算法及实现

刘海峰¹, 吴鹏², 马令坤²

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

收稿日期:2011-05-04 出版日期:2012-01-26 发布日期:2012-03-06
通讯作者: 吴鹏 E-mail:394846603@qq.com

Implementation of Group Encryption AlgorithmBased on Conic Curve over Finite Fields

LIU Haifeng¹, WU Peng², MA Lingkun²

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

Received:2011-05-04 Online:2012-01-26 Published:2012-03-06
Contact: WU Peng E-mail:394846603@qq.com

摘要/Abstract

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.

关键词: 圆锥曲线, 点阵群, 分组加密, 有限域

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.

Key words: conic curve, matrix groups of points, group encryption, finite field

中图分类号:

O236.2

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]. J4, 2012, 50(01): 54-58.

LIU Haifeng, WU Peng, MA Lingkun. Implementation of Group Encryption AlgorithmBased on Conic Curve over Finite Fields[J]. J4, 2012, 50(01): 54-58.

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