一类有限域丢番图方程的解及其应用  

Solution to a Class of Diophantine Equations over a Finite Field and Its Application

作　　者：陈持协[1] 王标[1] 方颖珏[2] 巩小星 

机构地区：[1]国际关系学院信息科技系,北京100091 [2]深圳大学数学与计算科学学院,深圳518060

出　　处：《计算机系统应用》2015年第12期256-259,共4页Computer Systems & Applications

基　　金：中央高校基本科研业务费专项资金项目(3262015T48;KYF-2012-T09);北京市科技新星计划项目(XX2014B052);大学生学术支持项目(3262014S190)

摘　　要：对一类有限域线性丢番图方程c≡x+by(mod N)进行了研究,求出了其通解及域中有效解的对数,并证明其能将部分曲线密码方案求解用户私钥的计算量降低为N/z,z为子群<-b>的最小非零元.指出了5个应用该类型方程曲线密码方案,最后以一个环Zn上广义圆锥曲线多重数字签名方案私钥的求解为例进行说明.This paper focuses on c≡x＋by（mod N）, the linear Diophantine equations over a finite field, and derives the general solution and the amount of solutions in the domain from the equations. Then demonstrates that this solution can partly reduce the amount of calculation which derive the signer＇s private key in some curve cryptography schemes to N/z （z is the smallest non-zero element of subgroup 〈-b〉 ）. Finally, lists five curve cryptography schemes that based on this type of equation, and takes the solution of the private key of a digital multi-signature scheme on the generalized conic curve over Zn as an example to introduce the topic.

关 键 词：有限域 丢番图方程 通解 曲线密码学 私钥 

分 类 号：O156.7[理学—数学]