Propagation characteristics of \(x\mapsto x^{-1}\) and Kloosterman sums
type: Item
instance of: scholarly article
title: Propagation characteristics of \(x\mapsto x^{-1}\) and Kloosterman sums
zbMATH Open document ID: 1148.11041
author: Pascale Charpin
author: Tor Helleseth
author: Victor A. Zinoviev
published in: Finite Fields and their Applications
publication date: 2008-09-25T00:00:00Z
review text: The inverse permutation \(\sigma: x \mapsto x^{-1}\) appears in the design of the AES cryptosystem. This permutation is considered as a very good mapping. In this paper, the authors study the permutation \(\sigma: x \mapsto x^{-1}\) on the field of order \(2^n\) by means of their component functions \(f_\lambda\). It is proved that the weights of derivatives of \(f_\lambda\) can be expressed in terms of Kloosterman sums. The authors compute some indicators of the propagation characteristics of \(\sigma\) \((\mathcal{M}(\sigma)\) and \(\mathcal{V}(\sigma))\) and they prove that the mapping \(\sigma: x \mapsto x^{-1}\) has good propagation characteristics with respect to these indicators. Moreover, they deduce several new formulas on Kloosterman sums, by using classical formulas which link any Boolean function with its derivatives.
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 5347274
zbMATH Keywords: inverse permutation
zbMATH Keywords: Boolean functions
zbMATH Keywords: vectorial mapping
zbMATH Keywords: cryptographic criteria
zbMATH Keywords: Kloosterman sum
zbMATH Keywords: Melas codes
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: j.ffa.2005.08.007
OpenAlex ID: W2069017437
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DOI: 10.1016/J.FFA.2005.08.007
description: scientific article; zbMATH DE number 5347274