基于椭圆曲线同源的公钥密码机制  

Public-key Cryptosystem Based on Elliptic Curve Isogenies

作　　者：胡进[1] 何德彪[1] 陈建华[1] 黄尹[1] 

机构地区：[1]武汉大学数学与统计学院,武汉430072

出　　处：《北京工业大学学报》2011年第6期916-920,共5页Journal of Beijing University of Technology

基　　金：国家'八六三'计划资助项目(2001AA141010)

摘　　要：针对RSA公钥密码系统和椭圆曲线密码系统基于的数学难题均不能抵抗量子计算机攻击问题,提出了一种能构造公钥密码系统的数学难题———椭圆曲线同源星上的计算问题.解决该数学难题的时间复杂度为指数级,该数学难题能抵抗量子计算机攻击.在此数学难题基础上构造了一个公钥密码机制ECIIES(elliptic curveisogenies integrated encryption scheme),ECIIES是在基本Elgamal机制基础上,通过对中间变量和密文作校验来抵抗自主消息攻击.在随机模型下证明了ECIIES在自主选择消息攻击下是不可区分安全的.To the question of the mathematical problems of RSA public-key cryptosystem and elliptic curve cryptosystem can＇t be against quantum computer,a mathematical problem,suitable for constructing public-key cryptosystem,is proposed： computing an isogeny between the given elliptic curves.The computational complexity for solving this problem is exponential.The problem is hard for solving with a quantum computer.A public-key cryptosystem scheme named ECIIES is proposed for an isogeny crypto system.ECIIES which based on the basic Elgamal scheme,can be against chosen ciphertext attacks by using a MAC function about intermediate variables and ciphertext.At last,the scheme ECIIES is proved to be IND-CCA2 security in the random oracle model.

关 键 词：公钥密码系统 量子计算机 同源 椭圆曲线 自主选择消息攻击 随机模型 

分 类 号：TN918[电子电信—通信与信息系统]