密钥交换协议中本原根的快速更新算法

Diffie-Hellman密钥交换协议可以使通信双方在不可信信道上建立共享密钥，从而实现安全通信。提出该协议的安全性建立在DH安全大素数P及其本原根g的基础上。证明了形如P=2q+1(其中q=4i+1是大素数)的DH安全大素数P有q-1个本原根，由P的最小本原根2可以快速生成其余本原根，并提出快速生成安全大素数P及其本原根g更新的算法。

Rapidly Updating Algorithm of Primitive Root in Key Exchange Protocol

Diffie-Hellman key exchange is a cryptographic protocol which allows two parties to jointly establish a shared secret key over an insecure communications channel, whose security is based on the DH large safe prime P and primitive root g. It proves that the number of primitive root of P is q-1, if P is derived from the serial P=2q+1(q from q=4i+1), every primitive root of P can be generated from the primitive root 2 rapidly and conveniently. A rapid algorithm of DH large safe prime generation and the updating of its primitive root are proposed.