The Construction Of Zero-sum Distinguishers For Type-2 And Type-3 Generalised Feistel Structures

This paper use the properties of higher-order integral and the propagation characteristics of the integral properties to construct zero-sum distinguishers for Type-2 and Type-3generalized Feistel structures which start from the intermediate states.But the aim of the paper is not just to construct the zero-sum distinguishers,but to find the maximum round numbers of the the zero-sum distinguishers and the corresponding optimal integral paths for the structures.However,we discover that it is difficult to use a method to prove that the round numbers of the zero-sum distinguishers for the structures are at its maximum.Therefore,the paper propose the integral path search algorithms to automatically search the maximum round numbers of the zero-sum distinguishers and the corresponding optimal integral paths for the structures by constructing higher order integral distinguisher in the forward and backward part.The complexity of Type-2 and Type-3 generalized Feistel structures with different characters is also analyzed on this basis.The thesis consists of four chapters and is organized as follows.Chapter 1 introduces the research background of the thesis,the related concepts.Chapter 2 introduces Type-2 and Type-3 generalized Feistel structure and propose the integral path search algorithm for the two structures.Chapter 3 lists the maximum round numbers of the zero-sum distinguishers and the numbers of the corresponding optimal integral paths for Type-2 and Type-3 generalized Feistel structure,and also lists optimal integral paths of the zero-sum distinguishers for the structures with 6 and 8 words.The summary of this paper is proposed in Chapter 4,we put forward some suggestions and the direction of efforts.