A New Construction of (m+k,m)-Functions with Low Differential Uniformity

Tailin NIU; Xi CHEN; Longjiang QU; Chao LI

doi:10.1587/transfun.2019EAL2030

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A New Construction of (m+k,m)-Functions with Low Differential Uniformity

Tailin NIU, Xi CHEN, Longjiang QU, Chao LI

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(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 U_i 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<2^k+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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.6 pp.850-855

Publication Date: 2020/06/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2019EAL2030

Type of Manuscript: LETTER

Category: Cryptography and Information Security

Authors

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

Keyword

substitution boxes, Feistel structures, differential uniformity

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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 U_i 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<2^k+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 U_i 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<2^k+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 U_i 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<2^k+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 -