Research on the Confusion and Diffusion Properties of the Initialization of MORUS
Zhang Pe · 2015
MORUS is an authenticated stream cipher, which has been selected as a second-round candidate of CAESAR competition. To study the confusion and diffusion properties of MORUS is essential for its security evaluation. This paper studies the confusion and diffusion properties of the initialization of MORUS through completeness and difference diffusion for the first time. We first study the completeness of MORUS-640-128, and get that the lower bound of steps that the output keystream and internal state of MOURS need to reach completeness is 4 and 6 steps respectively. With this property we propose a differential-distinguish attack and a divide-and-conquer attack on 3-step MORUS. Specifically, the differential-distinguish attack requires just 2 chosen IVs and the distinguishing advantage is 0.999985. The divide-and-conquer attack needs 110 chosen IVs to recover the whole 128 key bits with a success rate of 99.8% and a computational complexity of O(2~(106.8)). Combining the completeness algorithm, we propose an improved differential technique based on automatic deduction, and can attack 4-step MORUS effectively. This attack requires 2105 chosen IVs with a distinguishing advantage of 0.999665. These attacks are the first security analysis results of MORUS and have some reference significance for the design of its initialization process.