CONSTRUCTION OF NEW FAMILIES OF MDS DIFFUSION LAYERS

Abstract. Diusion layers are crucial components of sym-metric ciphers. These components, along with suitable Sboxes, can make symmetric ciphers resistant against sta-tistical attacks like linear and dierential cryptanalysis. Conventional MDS diusion layers, which are dened as matrices over nite elds, have been used in symmetric ci-phers such as AES, Twosh and SNOW. In this paper, we study linear, linearized and nonlinear MDS diusion lay-ers. We investigate linearized diusion layers, which are a generalization of conventional diusion layers; these diu-sion layers are used in symmetric ciphers like SMS4, Loiss and ZUC. We introduce some new families of linearized MDS diusion layers and as a consequence, we present a method for construction of randomized linear diusion layers over a nite eld. Nonlinear MDS diusion layers are introduced in Klimov's thesis; we investigate nonlinear MDS diusion layers theoretically, and we present a new family of nonlinear MDS diusion layers. We show that these nonlinear diusion layers can be made randomized with a low implementation cost. An important fact about linearized and nonlinear diusion layers is that they are more resistant against algebraic attacks in comparison to conventional diusion layers. A special case of diusion layers are (0,1)-diusion layers. This type of diusion lay-ers are used in symmetric ciphers like ARIA. We examine (0,1)-diusion layers and prove a theorem about them. At last, we study linearized MDS diusion layers of symmet-ric ciphers Loiss, SMS4 and ZUC, from the mathematical viewpoint