## Cryptology ePrint Archive: Report 2015/873

On the Diffusion Property of Iterated Functions

Jian Liu, Sihem Mesnager, and Lusheng Chen

Abstract: 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 $(n,n)$-functions having perfect diffusion property and optimal algebraic degree. We also obtain the complete enumeration results for the constructed functions.

Category / Keywords: Boolean functions; degree of completeness; perfect diffusion property; algebraic degree; balancedness.

Original Publication (in the same form): IMACC CONFERENCE 2015

Date: received 8 Sep 2015, last revised 14 Sep 2015

Contact author: smesnager at univ-paris8 fr

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2015/873

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