On the Diffusion Property of Iterated Functions

For vectorial Boolean functions, the behavior of iteration has consequence in the diffusion property of the system. We present a study on the diffusion property of iterated vectorial Boolean functions. The measure that will be of main interest here is the notion of the degree of completeness, which has been suggested by the NESSIE project. We provide the first to the best of our knowledge two constructions of n,i¾źn-functions having perfect diffusion property and optimal algebraic degree. We also obtain the complete enumeration results for the constructed functions.

[1]  H. Feistel.  Cryptography and Computer Privacy , 1973 .

[2]  Willi Meier,et al.  Algebraic Immunity of S-Boxes and Augmented Functions , 2007, FSE.

[3]  Claude Carlet,et al.  Vectorial Boolean Functions for Cryptography , 2006 .

[4]  John B. Kam,et al.  Structured Design of Substitution-Permutation Encryption Networks , 1979, IEEE Transactions on Computers.

[5]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[6]  Josef Pieprzyk,et al.  Rotation-Symmetric Functions and Fast Hashing , 1998, J. Univers. Comput. Sci..

[7]  R. Forre,et al.  Methods and instruments for designing S-boxes , 1990, Journal of Cryptology.

[8]  Gregory V. Bard,et al.  Algebraic Cryptanalysis , 2009 .

[9]  Josef Pieprzyk,et al.  Fast Hashing and Rotation-Symmetric Functions , 1999 .

[10]  Alexander Maximov,et al.  Classes of Plateaued Rotation Symmetric Boolean Functions under Transformation of Walsh Spectra , 2004, IACR Cryptol. ePrint Arch..

[11]  Josef Pieprzyk,et al.  Cryptanalysis of Block Ciphers with Overdefined Systems of Equations , 2002, ASIACRYPT.

[12]  Joan Daemen,et al.  Cipher and hash function design strategies based on linear and differential cryptanalysis , 1995 .

[13]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[14]  Rudolf Lide,et al.  Finite fields , 1983 .

[15]  Pulak Mishra,et al.  Mergers, Acquisitions and Export Competitive- ness: Experience of Indian Manufacturing Sector , 2012 .

[16]  Claude Carlet,et al.  Boolean Functions for Cryptography and Error-Correcting Codes , 2010, Boolean Models and Methods.

[17]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[18]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[19]  Vincent Rijmen,et al.  Comments by the NESSIE Project on the AES Finalists , 2000 .