Paper 2014/011

Construction of New Families of ‎MDS‎ Diffusion Layers

S. M. Dehnavi, A. Mahmoodi Rishakani, M. R. Mirzaee Shamsabad, Hamidreza Maimani, and Einollah Pasha


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.

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Secret-key cryptography
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MDS&#8206&#8206Linearized&#8206&#8206Nonlinear&#8206&#8206Diffusion Layer&#8206&#8206Linerar Branch &#8206N&#8206umber&#8206&#8206Differential Branch Number
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std_dehnavism @ khu ac ir
2014-12-09: last of 11 revisions
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      author = {S.  M.  Dehnavi and A.  Mahmoodi Rishakani and M.  R.  Mirzaee Shamsabad and Hamidreza Maimani and Einollah Pasha},
      title = {Construction of New Families of ‎MDS‎ Diffusion Layers},
      howpublished = {Cryptology ePrint Archive, Paper 2014/011},
      year = {2014},
      note = {\url{}},
      url = {}
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