Analysis of MORUS Against Collision Attack
Funds:
The National Natural Science Foundation of China (61572516, 61272041, 61272488)
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摘要: MORUS算法是CAESAR競賽第3輪的候選認(rèn)證加密算法之一，該文評估了MORUS-640-128算法對碰撞攻擊的安全性。由碰撞關(guān)系確定一系列非線性方程，采用分塊分析的方法，從非線性方程中找到消息字差分間的信息泄漏規(guī)律，首次給出了算法在兩步后發(fā)生碰撞的必要條件集，確定了輸入差分的字分布情況。在此基礎(chǔ)上，將碰撞的必要條件轉(zhuǎn)化成偽布爾函數(shù)最優(yōu)化問題，利用混合整數(shù)規(guī)劃模型進(jìn)行求解。實(shí)驗(yàn)結(jié)果顯示算法發(fā)生碰撞時，輸入差的漢明重量至少為28，其碰撞概率小于2-140 ，得到了比文獻(xiàn)[7]更緊致的概率上界(原為2-130)。結(jié)果表明MORUS-640-128算法具備良好的抗碰撞攻擊能力。Abstract: MORUS is an authenticated stream cipher, which is selected is third-round candidate of the ongoing CAESAR competition. In this work, the security of MORUS-640-128 against collision attack is evaluated. The partition method is utilized to find the information leakage between the word differences of message in the nonlinear function determined by the collision. The necessary conditions of collision after two steps are proposed for the first time. The distribution of input difference is determined. Furthermore, necessary conditions are turned into Pseudo-Boolean optimization problems. With the usage of mixed integer programming, it is found that the weight of message difference must be higher than 28 with the collision probability less than 2-140 , which is a better upper bound than ref. [7] 2-130. The result shows that MORUS-640-128 has a good performance on resistance against collision attack.
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Key words:
- CAESAR competition /
- MORUS /
- Collision attack /
- Lower bound of difference weight
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