等价于Z^＊pq中离散对数问题的密钥交换体制  

A Secret Key Exchange Scheme Which Is Equivalent to the Discrete Logarithm for Z_(pq)￣*

作　　者：王小云[1] 

机构地区：[1]山东大学

出　　处：《通信学报》1995年第2期79-83,共5页Journal on Communications

摘　　要：对某类素数Ｐ，ＢｅｒｔｄｅｎＢｏｅｒ证明了Ｄｉｆｆｉｅ－Ｈｅｌｌｍａｎ密钥交换体制等价于Ｚｐ中的离散对数问题。在本文中，我们建立Ｚ（ｎ，ａ）中密钥交换体制，其中ｎ＝ｐｑ，ｐ、ｑ为两个未知的大的素因子，ａ为选定的Ｚｎ中的伪原根。同样，在一定的条件限制下，此体制的安全性等价于Ｚｎ，ａ中离散对数问题。其中ｐ、ｑ应满足：（１）λ（λ（ｎ））只含≤Ｂ的素因子；（２）ｎ／λ（λ（ｎ））≤Ｂ＇。其中Ｂ＝Ｑ（ｋ），Ｂ＇＝Ｑ＇（ｋ），Ｑ、Ｑ＇为次数≥１的正系数多项式，ｋ＝［ｌｏｇ２ｎ］。限制后的Ｚ（ｎ，ａ）中离散对数问题仍然是困难的。For some kinds of primes,Bert den Boer proved that Diffie-Hellman key exchange scheme is equivalent to the discrete logarithm problem for Z_p.In this paper,we construct a key exchange scheme for Z_(n,a)(n=p、q,p and q are unknown primes,a is a given pseudo-random generator)The security of the scheme is as strong as the discrete logarithm problem for Z_(n,a)if n satisfies the following conditions:(1)λ(λ(n)) has only small prime factors which are smaller than B;(2);B=Q(k),B'=Q'(k),Q、Q' are polynomials with positive coefficients and degree≥1,k=[log_2n].In this case,the discrete logarithm problem for Z_(n,a) is also difficult.

关 键 词：密钥交换体制 离散对数 伪原根 

分 类 号：TN918.2[电子电信—通信与信息系统] TN911.1[电子电信—信息与通信工程]