基于Clifford半群上幂等元问题的密钥建立协议的研究

密钥建立协议是为了以后的密码学应用而使一个秘密密钥对两方或更多方都可用的过程。目前大多数密钥建立协议都是基于有限域上的算术。本文采用半群作为平台,推广了Iris Anshel等提出的代数密钥建立协议模型。在定义了可计算的Clifford半群上的多重同时幂等元搜索问题(MSISP)后,提出基于此问题的密钥建立协议。证明了若Clifford半群上的多重同时幂等元搜索问题(MSISP)是困难的,那么可以利用MSISP来构造密钥建立协议。

Study on Key Establishment Protocol Based on Idempotent Problem in Clifford Semigroup

A key establishment protocol is a protocol whereby a shared secret becomes available to two or more parties,for subsequent cryptographic applications.Most of the methods currently in use are based on arithmetic over finite fields.Using semigroup,this paper generalizes the algebraic key establishment protocol presented by Iris Anshel et al.After defining the multiple simultaneous idem-potent search problem(MSISP) on computational Clifford semigroups,we propose a key establishment protocol based on MSISP.It is proved that:if the MSISP is hard then the Clifford semigroup can be used to construct the key establishment protocol.