NDLI: New differentially 4-uniform permutations by modifying the inverse function on subfields

Please wait, while we are loading the content...

New differentially 4-uniform permutations by modifying the inverse function on subfields

Content Provider	Springer Nature Link
Author	Peng, Jie Tan, Chik How
Copyright Year	2016
Abstract	Permutations over $\mathbb {F}_{2^{2k}}$ with low differential uniformity, high algebraic degree and high nonlinearity are of great cryptographic importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers with SPN (Substitution Permutation Network) structure. A well known example is that the S-box of the famous Advanced Encryption Standard (AES) is derived from the inverse function on $\mathbb {F}_{2^{8}}$ , which has been proved to be a differentially 4-uniform permutation with the optimal algebraic degree and known best nonlinearity. Recently, Zha et al. proposed two constructions of differentially 4-uniform permutations over $\mathbb {F}_{2^{2k}}$ , say G $_{ t }$ and G $_{ s, t }$ with T r(s $^{−1}$) = 1, by applying affine transformations to the inverse function on some subfields of $\mathbb {F}_{2^{2k}}$ (Zha et al. Finite Fields Appl. 25, 64–78, 2014). In this paper, we generalize their method by applying other types of EA (extended affine) equivalent transformations to the inverse function on some subfields of $\mathbb {F}_{2^{2k}}$ and present two new constructions of differentially 4-uniform permutations, say F $_{ α }$ and F $_{ β, α }$ with T r(β $^{−1}$) = 1. Furthermore, we prove that all the functions G $_{ t }$ with different t are CCZ (Carlet-Charpin-Zinoviev) equivalent to our subclass F $_{0}$, while all the functions G $_{ s, t }$ with different t are CCZ-equivalent to our subclass F $_{ s,0}$. In addition, both our two constructions give many new CCZ-inequivalent classes of such functions, as checked by computer in small numbers of variables. Moreover, all these newly constructed permutations are proved to have the optimal algebraic degree and high nonlinearity.
Starting Page	363
Ending Page	378
Page Count	16
File Format	PDF
ISSN	19362447
Journal	Cryptography and Communications
Volume Number	9
Issue Number	3
e-ISSN	19362455
Language	English
Publisher	Springer US
Publisher Date	2016-01-15
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	S-box Differentially 4-uniform permutation Algebraic degree Nonlinearity CCZ-equivalent Cryptography Algebraic coding theory; cryptography Applications to coding theory and cryptography Data Structures, Cryptology and Information Theory Coding and Information Theory Communications Engineering, Networks Information and Communication, Circuits Mathematics of Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Theory and Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Differentially 4-uniform bijections by permuting the inverse function

Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1)

Permutation polynomials EA-equivalent to the inverse function over GF (2$^{ n }$)

A few more quadratic APN functions

Further results on differentially 4-uniform permutations over $\mathbb{F}_{2^{2m} } $

Differentially low uniform permutations from known 4-uniform functions

Functions of degree 4e that are not APN infinitely often

More constructions of differentially 4-uniform permutations on $${\mathbb {F}}_{2^{2k}}$$

Further results on differentially 4-uniform permutations over $\F_{2^{2m}}$

New differentially 4-uniform permutations by modifying the inverse function on subfields

Similar Documents

Differentially 4-uniform bijections by permuting the inverse function

Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1)

Permutation polynomials EA-equivalent to the inverse function over GF (2$^{ n }$)

A few more quadratic APN functions

Further results on differentially 4-uniform permutations over $\mathbb{F}_{2^{2m} } $

Differentially low uniform permutations from known 4-uniform functions

Functions of degree 4e that are not APN infinitely often

More constructions of differentially 4-uniform permutations on $${\mathbb {F}}_{2^{2k}}$$

Further results on differentially 4-uniform permutations over $\F_{2^{2m}}$

New differentially 4-uniform permutations by modifying the inverse function on subfields