Research On Clustering Effect Of Differential Paths For Block Ciphers

In recent years,due to the limited computing resources of terminal devices,cryptographic algorithms are developing towards the lightweight direction that consumes little hardware and software resources.Under this trend,lightweight block cipher is proposed for security encryption of micro computing devices.Although the algorithm has the characteristics of strong flexibility,low cost and easy implementation,its security is still an important research topic.Differential analysis is one of the most effective and classic methods to measure whether a block cipher is secure.This paper uses automated search tools to analyze the clustering effect of differential paths for CRAFT and SPECK lightweight block cipher.The main work is as follows:（1）The optimal differential characteristics for full-round CRAFT is given by using SAT,the branch and bound algorithm,and the sequential encoding method.To our knowledge,we are the first ones to achieve the full-round on searching of the optimal differential characteristics for CRAFT.With the method above,the paper finds the optimal probability2^-64 of 9-round.Moreover,to improve the differential probability,the paper proposes the lists and binary matrices method to compute the number of the differential trails with the same input difference and the same output difference and find 10494784 optimum trails and 5543168 trails with probability2^-71by manual.Compared with traditional methods,the proposed algorithm greatly reduces the computational complexity and memory capacity required by trails search,and greatly improves the efficiency of key-recover attack.On the basis of the 9-round differential distinguishers,the paper extends the attacked rounds by repeating the iterative truncated differential,which also ensures the optimal probability of the corresponding round for one of these distinguishers.Simultaneously,the number of the multiple differential trails is obtained by repeating the matrix A many times to have a good performance on the trail search cost,which presents the cyclic differential propagation.It is also the first time to give the calculation of CRAFT full rounds differential trails.（2）The paper gives the SAT models about the modular addition operation.Based on the new modeling rules,the optimal differential probability of full rounds for SPECK32 and partial rounds for SPECK48 is obtained.At the same time,the paper analyzes the clustering effect of the differential characteristic of SPECK32 and SPECK48.And,we obtain the differential probability2^-33.4378 for 10-round SPECK32 and the differential probability2^-46.3853 of 12-round for SPECK48,which is the best result for 12 rounds as far as we known.