对HB~#协议的代数分析

Algebraic Analysis on HB~# Authentication Protocol

HB协议是一类对计算要求极低的认证协议,能够抵抗量子攻击,非常适合于移动和物联网环境,而这种无线通信环境要求HB协议应该具有抗中间人攻击的能力.基于此,设计了一种对HB~#协议进行中间人攻击的代数分析方法,在这种代数攻击中,认证密钥可以被快速地恢复.这一攻击方法建立在Z2中一类多元二次方程组的解的基础之上,首先找到了这类方程组有解的充分必要条件和求解算法,然后利用这一结果对HB~#协议进行中间人攻击.

HB-like protocols are such a kind of authentication protocols that require low computational resource and promise to resist quantum attacks. They are especially suitable for mobile applications and the Internet of Things （IoT）. However, the wireless communications in these environments have compelled that HB-like protocols should be able to resist the man-in-the-middle （MIM） attacks. In this vein, this paper proposes an algebraic MIM attack to a recently presented HB^# authentication protocol which is claimed to resist MIM attacks. During this attack, the authentication keys can be totally recovered efficiently. The proposed attacking method is based on the solutions to a system of quadratic equations of muhi-variables over Z2. Hence, the necessary and sufficient conditions for this system of equations being solvable have been found in advance. Then, an algebraic attack to HB^# protocol has been presented accordingly.