Mathematics and Statistics Vol. 10(6), pp. 1320 - 1325
DOI: 10.13189/ms.2022.100618
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Transparency Order and Cross-Correlation Analysis of Boolean Functions

Mayasar Ahmad Dar ¹, Hiral Raja ², Afshan Butt ³, Deepmala Sharma ^1,*
1 Department of Mathematics, National Institute of Technology, Raipur(C.G)-492010, India
² Department of Mathematics, Dr. C. V. Raman University, Kota Bilaspur, India
³ Department of Mathematics, Bhilai Institute of Technology, Raipur, India

ABSTRACT

Transparency order is considered to be a cryptographically significant property that characterizes the resistance of S-boxes in opposition to differential power analysis attacks. The S-box having low transparency order is more resistant to these attacks. Until now, little attempts have been noticed to examine theoretically the transparency order and its relationship with other cryptographic properties. All constructions associated with transparency order are relying on search algorithms. In this paper, we discuss the new interpretation of bent functions in terms of their transparency order. Using the concept of vector concatenation and correlation characteristics, we find the transparency order of Boolean functions. The notion of complementary transparency order is given. For a pair of Boolean functions, we interpret complementary transparency order by their Walsh-Hadamard transform. We establish a relationship of transparency order with cross-correlation for a pair of Boolean functions. We find a relationship of transparency order with −variable decomposition bent functions. We generalize the bounds on sum-of-squares of autocorrelation in terms of transparency order of Boolean functions using Walsh-Hadamard spectra. Further the transparency order of a function fulfilling the propagation criterion about a linear subspace is evaluated.

KEYWORDS
Transparency order, Cross-Correlation, Boolean functions, Walsh-Hadamard Transform

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mayasar Ahmad Dar , Hiral Raja , Afshan Butt , Deepmala Sharma , "Transparency Order and Cross-Correlation Analysis of Boolean Functions," Mathematics and Statistics, Vol. 10, No. 6, pp. 1320 - 1325, 2022. DOI: 10.13189/ms.2022.100618.

(b). APA Format:
Mayasar Ahmad Dar , Hiral Raja , Afshan Butt , Deepmala Sharma (2022). Transparency Order and Cross-Correlation Analysis of Boolean Functions. Mathematics and Statistics, 10(6), 1320 - 1325. DOI: 10.13189/ms.2022.100618.