TY - JOUR
T1 - Permutation Resemblance
AU - Chen, Li An
AU - Coulter, Robert S.
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2023/10/1
Y1 - 2023/10/1
N2 - Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.
AB - Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We prove several results concerning permutation resemblance and show how it can be used to produce low differentially uniform bijections. We also study the permutation resemblance of planar functions, which over fields of odd characteristic are known not to be bijections and to have the optimal differential uniformity.
KW - differential uniformity
KW - finite fields
KW - image sets
KW - Permutation resemblance
KW - planar functions
UR - http://www.scopus.com/inward/record.url?scp=85164425484&partnerID=8YFLogxK
U2 - 10.1109/TIT.2023.3292598
DO - 10.1109/TIT.2023.3292598
M3 - Article
AN - SCOPUS:85164425484
SN - 0018-9448
VL - 69
SP - 6711
EP - 6718
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 10
ER -