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MORUS算法是已进入CAESAR竞赛第二轮评选的一个基于流密码的认证加密算法,研究算法的混乱与扩散性质对于评估其安全性来说十分必要.本文首次从完全性和差分扩散性两个角度对MORUS算法初始化过程的混乱与扩散性质进行了研究.我们首先研究了MORUS-640-128的完全性,得到算法输出密钥流和内部状态达到完全性的步数下界分别为4步和6步.利用此性质,我们对3步简化版MORUS-640-128进行了差分-区分攻击和密钥分割攻击.其中,差分-区分攻击仅需2个选择IV就能以0.999985的区分优势完成攻击;密钥分割攻击需要110个选择IV,能以99.8%的成功率恢复全部128比特初始密钥,计算复杂度为O(2~(106.8)).结合完全性算法,本文提出了改进的差分自动推演算法,并对4步简化版MORUS-640-128进行了差分-区分攻击,攻击所需的数据量和区分优势分别为2105和0.999665.上述攻击均是首次针对MORUS算法的安全性分析结果,对其初始化过程的设计有一定的参考意义.
The MORUS algorithm is a stream cipher-based authentication encryption algorithm which has entered the second round of CAESAR competitions. It is necessary to study the chaos and diffusion nature of the algorithm to evaluate its security.This paper firstly presents two aspects: completeness and differential diffusion The chaos and diffusion properties of the MORUS algorithm initialization process are studied.First, we study the completeness of the MORUS-640-128, and get the lower bounds of the algorithm output keystream and the completeness of the internal states as 4 steps and 6 steps respectively Using this property, we make differential-differentiated attacks and key-segmentation attacks on the three-step MORUS-640-128.Among them, the differential-differentiated attacks can be attacked by 0.999985 with only 2 choices IV, The key segmentation attack needs 110 choices IV, and can recover all the 128-bit initial keys with the success rate of 99.8%, and the computational complexity is O (2 ~ (106.8)). Combined with the completeness algorithm, this paper proposes an improved differential automatic Deduction algorithm and the differential-differentiate attack on the 4-step simplified version MORUS-640-128, the amount of data required for the attack and the distinguishing advantages are respectively 2105 and 0.999665.The above attacks are the first for the MORUS algorithm The results of the analysis, the design of its initialization process has a certain reference value.