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REESSE3+算法是2014年由苏盛辉教授提出的一个8轮迭代的分组密码算法.由于REESSE3+算法受到了来学嘉教授提出的IDEA算法的启发,采用了混合3个不相容的群运算来保证其安全性,因此对于REESSE3+算法在遇到差分攻击时的安全性问题,本文采用了来学嘉教授提出的马尔可夫密码模型进行论证.马尔可夫密码模型通过马尔可夫密码所对应的概率转移矩阵或其对应的马尔可夫链来得到该马尔可夫密码在面对差分攻击时是否是安全的,或者至少需要多少轮迭代才能安全.在本文中我们首先给出了REESSE3+(m)算法的定义,然后我们证明了REESSE3+(m)是属于马尔可夫密码的,并且我们还给出了REESSE3+(16)算法所对应的概率转移矩阵的生成算法,再通过REESSE3+(16)算法所对应的概率转移矩阵证明了REESSE3+(16)算法需要16轮迭代才能抵抗差分攻击.由于REESSE3+算法只有8轮迭代,所以在分组长度为16位时,该算法是不能抵抗差分攻击的;之后我们证明了REESSE3+算法所对应的概率转移矩阵具有非对称性,并且其对应的马尔可夫链具有非周期性,结合IDEA算法的证明过程,我们推测REESSE3+算法在16轮迭代后是足够抵抗差分攻击的,至于REESSE3+算法中给出的8轮迭代的安全性还有待进一步考证.
The REESSE3 + algorithm is an 8-iteration block cipher algorithm proposed by Professor Su Shenghui in 2014. As the REESSE3 + algorithm is inspired by the IDEA algorithm proposed by Professor Xuejia, three groups of incompatible operations are mixed to ensure its security Therefore, this paper uses the Markov cipher model proposed by Professor Xuejia to prove the safety of REESSE3 + algorithm in differential attacks.Markov cipher model uses the probability transfer matrix corresponding to Markov cipher Or its corresponding Markov chain to find out whether the Markov cipher is safe in the face of differential attacks or at least the number of iterations needed to be safe.In this paper we first give the definition of REESSE3 + (m) algorithm , And then we prove that REESSE3 + (m) belongs to Markov cipher, and we also give a generation algorithm of probability transfer matrix corresponding to REESSE3 + (16) algorithm, and then transfer the probability corresponding to REESSE3 + (16) The matrix proves that REESSE3 + (16) algorithm needs 16 rounds of iterations to resist differential attacks. Because REESSE3 + algorithm has only 8 rounds of iterations, so the packet length is 16 bits , We prove that the matrix of probability transfer corresponding to REESSE3 + algorithm is asymmetric and the corresponding Markov chain has aperiodicity. Combined with the proof of IDEA algorithm, we infer that REESSE3 + The algorithm is sufficient to resist differential attacks after 16 rounds of iteration, and the safety of 8 rounds of iterations given in the REESSE3 + algorithm remains to be further verified.