改进的多变量哈希函数

Improved Multivariate Hash Function

针对基于MI算法提出的一种多变量哈希函数进行研究,对该算法的安全性进行分析,找到其破解方法,并在此基础上对该算法进行改进。改进算法在保持了原有算法的所有优点的基础上对这种碰撞攻击免疫。还对该改进算法进行了原像攻击、第二原像攻击、差分攻击和代数攻击方面的安全性分析。同时建立数学模型,并通过实验测试了该改进算法的雪崩效应及其稳定性。实验结果表明,该算法满足严格雪崩效应原则,具有理想的、稳定的雪崩效应。

A multivariate hash function based on multivariate public key cryptographic algorithm MI was researched and its security was alaalyzed so that the method to broke the hash function was found. For this reason, the improved hash function was proposed. The improved hash function can keep all advantages of the original hash function. Further more it is immune on the collision. Its preimage attack, second preimage attack, differential attack and algebraic attack were also analyzed in this paper. The avalanche effect and its stability of the improved hash function were tested on the basis of a mathematical modeL The experiment data shows the improved hash function meets the strict avalanche criterion and its avalanche effect is perfect and stable.