Generalized Maiorana–McFarland Construction of Resilient Boolean Functions With High Nonlinearity and Good Algebraic Properties

SAO 1-Resilient Functions With Lower Absolute Indicator in Even Variables

“…Conjecture 1 is still outstanding, which has been generalized by Zhang et al to the resilient functions. Zhang et al conjectured that the maximum nonlinearity of m-resilient Boolean functions in n variables (n ≥ 8) is upper bounded by 2 n−1 − 2 n/2−1 − 2 n/4 +m−1 , see [28,Conjecture] or [29,Conjecture 1], which is related to Conjecture 1 when m = 0 since N LN (n/2) ≤ 2 n/2−1 − 2 n/4−1 . Conjecture 2 was disproved only for even n = 10 [11] and 14 [1], and for odd n = 9, 11 [11], n = 15 [15] and n = 21 [9], [12] before.…”

The Existence of a Class of Balanced Multi‐output Rotation Symmetric Boolean Functions

“…It was shown that the substitution boxes(S-boxes) generated from the polynomials over F n 2 with coefficients in F 2 , and exponentiations over F n 2 are linearly equivalent to rotation symmetric Sboxes(RSSBs) [12] , and the class of RSSBs possess some good cryptographic properties such as low differentially uniform, high algebraic degree and high nonlinearity, which motivate us to find cryptographically desirable Sboxes in the class of RSSBs [12] . Up until to now, some papers were devoted to the study of RSSBs [12−15] , and Zhang et al [16] presented new results on resilient functions, and Du et al [9−11] studied the constructions of rotation symmetric resilient functions. However, the results on the existence and construction of RSSBs are quite rare, so how to construct balanced RSSBs and resilient RSSBs are of great significance.…”

Constructions of p‐variable 1‐resilient rotation symmetric functions over GF(p)

“…Zhang et al . made some progresses in resilient functions recently ; constructions and count of rotation symmetric resilient Boolean functions were proposed in . Correlation‐immune and resilient functions over finite fields had been studied extensively by many authors .…”