TY - JOUR
T1 - On the Differential Spectrum and the APcN Property of a Class of Power Functions over Finite Fields
AU - Tu, Ziran
AU - Li, Nian
AU - Wu, Yanan
AU - Zeng, Xiangyong
AU - Tang, Xiaohu
AU - Jiang, Yupeng
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - In this paper, we investigate the power function F (x) = xd over the finite field F 24n, where n is a positive integer and d = 23n +22n +2n -1. We prove that this power function is APcN with respect to all c ϵ F 24n /{1} satisfying c22n+1 = 1, and we determine its c-differential spectrum. To the best of our knowledge, this is the second class of APcN power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.
AB - In this paper, we investigate the power function F (x) = xd over the finite field F 24n, where n is a positive integer and d = 23n +22n +2n -1. We prove that this power function is APcN with respect to all c ϵ F 24n /{1} satisfying c22n+1 = 1, and we determine its c-differential spectrum. To the best of our knowledge, this is the second class of APcN power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.
KW - Differential spectrum
KW - c-differential uniformity
KW - differential uniformity
KW - power function
UR - https://www.scopus.com/pages/publications/85136882205
U2 - 10.1109/TIT.2022.3198133
DO - 10.1109/TIT.2022.3198133
M3 - 文章
AN - SCOPUS:85136882205
SN - 0018-9448
VL - 69
SP - 582
EP - 597
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 1
ER -