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Title:
Construction of New Families of MDS Diffusion Layers
Authors: S. M. Dehnavi, A. Mahmoodi Rishakani, M. R. Mirzaee Shamsabad, Hamidreza Maimani, Einollah Pasha
Abstract:Diffusion layers are crucial components of symmetric ciphers. These components, along with suitable Sboxes, can make symmetric ciphers resistant against statistical attacks like linear and differential cryptanalysis. Conventional MDS diffusion layers, which are defined as matrices over finite fields, have been used in symmetric ciphers such as AES, Twofish and SNOW. In this paper, we study linear, linearized and nonlinear MDS diffusion layers. We investigate linearized diffusion layers, which are a generalization of conventional diffusion layers; these diffusion layers are used in symmetric ciphers like SMS4, Loiss and ZUC. We introduce some new families of linearized MDS diffusion layers and as a consequence, we present a method for construction of randomized linear diffusion layers over a finite field. Nonlinear MDS diffusion layers are introduced in Klimov’s thesis; we investigate nonlinear MDS diffusion layers theoretically, and we present a new family of nonlinear MDS diffusion layers. We show that these nonlinear diffusion layers can be made randomized with a low implementation cost. An important fact about linearized and nonlinear diffusion layers is that they are more resistant against algebraic attacks in comparison to conventional diffusion layers. A special case of diffusion layers are (0,1)-diffusion layers. This type of diffusion layers are used in symmetric ciphers like ARIA. We examine (0,1)-diffusion layers and prove a theorem about them. At last, we study linearized MDS diffusion layers of symmetric ciphers Loiss, SMS4 and ZUC, from the mathematical viewpoint.
ePrint: https://eprint.iacr.org/2014/011
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