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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
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(m+k,m)-fonctionne avec de bonnes propriétés cryptographiques lorsque 1≤k<m jouent un rôle important dans plusieurs chiffrements par blocs. Dans cet article, basé sur la méthode introduite par Carlet et al. en 2018, on construit des familles infinies de (m+k,m) -fonctions avec une faible uniformité différentielle en construisant une classe de sous-ensembles spéciaux disjoints par paires dans $gf_2^k$. Une telle classe de sous-ensembles Ui sont choisis pour générer des multiensembles tels que tous les éléments de $gf_2^k$ apparaissent autant de fois que possible dans chacun de ces multiensembles. Nous construisons explicitement ce type de sous-ensembles spéciaux par des polynômes linéarisés, et fournissons différentiellement Δ-uniforme (m+k,m)-fonctions avec Δ<2k+1,k≤m-2. Plus précisément, lorsque k=m-2, l'uniformité différentielle de nos fonctions est inférieure à la fonction construite par Carlet et al. Les fonctions construites offrent plus de choix pour la conception des chiffrements de Feistel.
Tailin NIU
National University of Defense Technology
Xi CHEN
National University of Defense Technology
Longjiang QU
National University of Defense Technology,the State Key Laboratory of Cryptology
Chao LI
National University of Defense Technology
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Tailin NIU, Xi CHEN, Longjiang QU, Chao LI, "A New Construction of (m+k,m)-Functions with Low Differential Uniformity" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 6, pp. 850-855, June 2020, doi: 10.1587/transfun.2019EAL2030.
Abstract: (m+k,m)-functions with good cryptographic properties when 1≤k<m play an important role in several block ciphers. In this paper, based on the method introduced by Carlet et al. in 2018, we construct infinite families of (m+k,m)-functions with low differential uniformity by constructing a class of pairwise disjoint special subsets in $gf_2^k$. Such class of subsets Ui are chosen to generate multisets such that all elements in $gf_2^k$ appears as many times as possible in each of these multisets. We construct explicitly such kind of special subsets by linearized polynomials, and provide differentially Δ-uniform (m+k,m)-functions with Δ<2k+1,k≤m-2. Specifically when k=m-2, the differential uniformity of our functions are lower than the function constructed by Carlet et al. The constructed functions provide more choices for the design of Feistel ciphers.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2030/_p
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@ARTICLE{e103-a_6_850,
author={Tailin NIU, Xi CHEN, Longjiang QU, Chao LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Construction of (m+k,m)-Functions with Low Differential Uniformity},
year={2020},
volume={E103-A},
number={6},
pages={850-855},
abstract={(m+k,m)-functions with good cryptographic properties when 1≤k<m play an important role in several block ciphers. In this paper, based on the method introduced by Carlet et al. in 2018, we construct infinite families of (m+k,m)-functions with low differential uniformity by constructing a class of pairwise disjoint special subsets in $gf_2^k$. Such class of subsets Ui are chosen to generate multisets such that all elements in $gf_2^k$ appears as many times as possible in each of these multisets. We construct explicitly such kind of special subsets by linearized polynomials, and provide differentially Δ-uniform (m+k,m)-functions with Δ<2k+1,k≤m-2. Specifically when k=m-2, the differential uniformity of our functions are lower than the function constructed by Carlet et al. The constructed functions provide more choices for the design of Feistel ciphers.},
keywords={},
doi={10.1587/transfun.2019EAL2030},
ISSN={1745-1337},
month={June},}
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TY - JOUR
TI - A New Construction of (m+k,m)-Functions with Low Differential Uniformity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 850
EP - 855
AU - Tailin NIU
AU - Xi CHEN
AU - Longjiang QU
AU - Chao LI
PY - 2020
DO - 10.1587/transfun.2019EAL2030
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2020
AB - (m+k,m)-functions with good cryptographic properties when 1≤k<m play an important role in several block ciphers. In this paper, based on the method introduced by Carlet et al. in 2018, we construct infinite families of (m+k,m)-functions with low differential uniformity by constructing a class of pairwise disjoint special subsets in $gf_2^k$. Such class of subsets Ui are chosen to generate multisets such that all elements in $gf_2^k$ appears as many times as possible in each of these multisets. We construct explicitly such kind of special subsets by linearized polynomials, and provide differentially Δ-uniform (m+k,m)-functions with Δ<2k+1,k≤m-2. Specifically when k=m-2, the differential uniformity of our functions are lower than the function constructed by Carlet et al. The constructed functions provide more choices for the design of Feistel ciphers.
ER -