一种改进的辫子群上的密钥协商协议

An Improved Key Agreement Protocol on Braid Groups

由Shor,Boneh和Liptonon等人发现的、可在量子多项式时间内解决大整数分解、离散对数和椭圆曲线上的离散对数问题的量子算法使得当前以这些“难解”问题为基础的传统公钥密码体制受到挑战。辫子群是一种新兴的适用于量子计算机时代的公钥密码平台,但是目前基于辫子群的密钥协商协议AAG、AAFG和BDH等都有不同程度的安全弱点。本文利用随机化辫子和非共轭变换技术,在AAG和AAFG密钥协商协议的基础上,提出了一种改进的辫子群上的密钥协商协议,用于在非保密信道上安全协商共享密钥。该协议可以抵抗目前已知的长度攻击、线性表示攻击和各种基于共轭搜索方法的攻击。

Shor,Boneh,Liptonon et al. present some remarkable quantum algorithms which can solve integer factoring problem, discrete logarithm problem and discrete logarithm problem on elliptic curves in quantum polynomial time. These quantum algorithms are great challenges to classical public key cryptographies based on the above-described hard problems. It seems that braid group is a kind of considerable public key cryptography platform, but current key agreement protocols, such as AAG,AAFG and BDH, all have different degrees of security weaknesses. This paper takes advantage of random braids and non-conjugate transformations to present an improved braid key agreement protocol relat ed to AAG and AAFG, which can make the two communication parties securely share a common key over any insecure channel. This protocol can resists current length-based attacks, linear representation attacks and other conjugacy search attacks.