TY - JOUR
T1 - On perfect nonlinear functions (Π)
AU - Zhang, Xiyong
AU - Guo, Hua
PY - 2008/8
Y1 - 2008/8
N2 - Perfect nonlinear functions are of importance in cryptography. By using Galois ring, relative trace and investigating the character values of corresponding relative difference sets, we present a construction of perfect nonlinear functions from ℤ42m to ℤ_4m, where m is a divisor of 2m, and a construction of perfect nonlinear functions from ℤ_p2n to ℤ_p2m where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from ℤ_2p2 to ℤ_2p if and only if p = 2, and there doesn't exist a perfect nonlinear function from ℤ_2kl2n to ℤ_2klm if m > n and l(l is odd) is self-conjugate modulo 2 k (k 1).
AB - Perfect nonlinear functions are of importance in cryptography. By using Galois ring, relative trace and investigating the character values of corresponding relative difference sets, we present a construction of perfect nonlinear functions from ℤ42m to ℤ_4m, where m is a divisor of 2m, and a construction of perfect nonlinear functions from ℤ_p2n to ℤ_p2m where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from ℤ_2p2 to ℤ_2p if and only if p = 2, and there doesn't exist a perfect nonlinear function from ℤ_2kl2n to ℤ_2klm if m > n and l(l is odd) is self-conjugate modulo 2 k (k 1).
KW - Galois ring
KW - Perfect nonlinear function
KW - Relative difference set
KW - Relative trace
UR - https://www.scopus.com/pages/publications/48349127142
U2 - 10.1007/s00200-008-0065-1
DO - 10.1007/s00200-008-0065-1
M3 - 文章
AN - SCOPUS:48349127142
SN - 0938-1279
VL - 19
SP - 293
EP - 309
JO - Applicable Algebra in Engineering, Communications and Computing
JF - Applicable Algebra in Engineering, Communications and Computing
IS - 4
ER -