一种新的等价于多项式离散对数的公钥密码体制研究  

Research on a New Public Key Cryptosystem Equivalent to Polynomial Discrete Logarithm

作　　者：景征骏[1,2] 蒋国平[3] 古春生[2] 

机构地区：[1]南京邮电大学计算机学院,江苏南京210023 [2]江苏技术师范学院计算机系,江苏常州213001 [3]南京邮电大学自动化学院,江苏南京210023

出　　处：《南京邮电大学学报（自然科学版）》2013年第1期6-9,共4页Journal of Nanjing University of Posts and Telecommunications：Natural Science Edition

基　　金：江苏省高校自然基金基础研究计划(08KJD510022);江苏省‘六大人才高峰’高层次人才计划(SJ209006);南京邮电大学引进人才计划(NY209021);江苏省普通高校研究生科技创新计划(cxzz11_0401)资助项目

摘　　要：有限域上的离散对数问题是公钥密码设计的重要研究内容之一。文中通过对有限域上不可约多项式性质的进一步研究,得出不可约多项式与其诱导出的友矩阵周期的相关定理,并利用有限域同构的性质构造了一种新的类ELGamal公钥密码体制。经论证,该方案的安全性等价于求解有限域上多项式离散对数问题的难解性。同时,分析了方案的加解密算法的性能,并进行了优化。新公钥体制下的密文膨胀率近似为1,在加密大批量数据时有较高的效率。Discrete logarithm problem on finite field is one of the important research topics of public key cryptography. Following an in-depth syudy on the nature of the irreducible polynomial over finite field, some theorems are provided on irreducible polynomial and its deduced friend matrix periodity and a new i- somorphism based ELGamal-type public key cryptosystem is constructed over finite field. It is demonstra- ted that the security of the new cryptosystem is equivalent to the intractability of polynomial discrete log- arithm problem over finite field. The performance of the encryption and de-encription algorithms is ana- lyzed and optimized. The ciphertext expantion rate of the new scheme is approximately 1, so it has higher efficiency while encrypting large amount of data.

关 键 词：公钥加密体制 有限域同构 多项式离散对数 

分 类 号：TN918[电子电信—通信与信息系统]