辫群上的扭结共轭搜索问题和密码体制研究

通过分析辫群的相关性质及群上的判定问题，结合扭结共轭问题、子群成员判断问题及根搜索问题，提出一种辫群上的公钥加密协议和签名协议，对两者的安全性进行分析，证明敌手无法从公钥中恢复密钥，因此协议可以抵抗长度攻击、惟密钥攻击、一般选择消息攻击、定向选择消息攻击和适应性选择消息攻击。

Research on Twisted Conjugacy Search Problem and Cryptosystems on Braid Group

By analyzing the properties of braid group and some decision problems on braid group, this paper proposes a protocol by applying twisted conjugacy search problem, subgroup membership decision problem and root search problem on to specific subgroups of braid groups where the subgroups enjoy unsolvable word problem. Security analysis shows that the protocol can resist length attack, key-only attack, chosen message attack and chosenplaintext attack and so on.