On propagation characteristics of resilient functions
(2003) 9th Annual International Workshop, SAC 2002 2595. p.175-195- Abstract
- In this paper we derive several important results towards a better understanding of propagation characteristics of resilient Boolean functions. We first introduce a new upper bound on nonlinearity of a given resilient function depending on the propagation criterion. We later show that a large class of resilient functions admit a linear structure; more generally, we exhibit some divisibility properties concerning the Walsh-spectrum of the derivatives of any resilient function. We prove that, fixing the order of resiliency and the degree of propagation criterion, a high algebraic degree is a necessary condition for construction of functions with good autocorrelation properties. We conclude by a study of the main constructions of resilient... (More)
- In this paper we derive several important results towards a better understanding of propagation characteristics of resilient Boolean functions. We first introduce a new upper bound on nonlinearity of a given resilient function depending on the propagation criterion. We later show that a large class of resilient functions admit a linear structure; more generally, we exhibit some divisibility properties concerning the Walsh-spectrum of the derivatives of any resilient function. We prove that, fixing the order of resiliency and the degree of propagation criterion, a high algebraic degree is a necessary condition for construction of functions with good autocorrelation properties. We conclude by a study of the main constructions of resilient functions. We notably show how to avoid linear structures when a linear concatenation is used and when the recursive construction introduced in [11] is chosen. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/309966
- author
- Charpin, P and Pasalic, Enes LU
- organization
- publishing date
- 2003
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Boolean functions, linear space, resiliency, nonlinearity, propagation characteristics
- host publication
- Lecture Notes in Computer Science (Selected Areas in Cryptography. Revised Papers)
- volume
- 2595
- pages
- 175 - 195
- publisher
- Springer
- conference name
- 9th Annual International Workshop, SAC 2002
- conference location
- St. John's, Newfoundland, Canada
- conference dates
- 2002-08-15 - 2002-08-16
- external identifiers
-
- wos:000182919400013
- scopus:35248894976
- ISSN
- 0302-9743
- 1611-3349
- DOI
- 10.1007/3-540-36492-7_13
- language
- English
- LU publication?
- yes
- id
- 5c4eeb9c-328a-462f-89ff-0068202aa9f9 (old id 309966)
- date added to LUP
- 2016-04-01 11:53:50
- date last changed
- 2024-01-08 00:38:24
@inproceedings{5c4eeb9c-328a-462f-89ff-0068202aa9f9,
abstract = {{In this paper we derive several important results towards a better understanding of propagation characteristics of resilient Boolean functions. We first introduce a new upper bound on nonlinearity of a given resilient function depending on the propagation criterion. We later show that a large class of resilient functions admit a linear structure; more generally, we exhibit some divisibility properties concerning the Walsh-spectrum of the derivatives of any resilient function. We prove that, fixing the order of resiliency and the degree of propagation criterion, a high algebraic degree is a necessary condition for construction of functions with good autocorrelation properties. We conclude by a study of the main constructions of resilient functions. We notably show how to avoid linear structures when a linear concatenation is used and when the recursive construction introduced in [11] is chosen.}},
author = {{Charpin, P and Pasalic, Enes}},
booktitle = {{Lecture Notes in Computer Science (Selected Areas in Cryptography. Revised Papers)}},
issn = {{0302-9743}},
keywords = {{Boolean functions; linear space; resiliency; nonlinearity; propagation characteristics}},
language = {{eng}},
pages = {{175--195}},
publisher = {{Springer}},
title = {{On propagation characteristics of resilient functions}},
url = {{http://dx.doi.org/10.1007/3-540-36492-7_13}},
doi = {{10.1007/3-540-36492-7_13}},
volume = {{2595}},
year = {{2003}},
}