Measuring the Sum-of-Squares Indicator of Boolean Functions in Encryption Algorithm for Internet of Things

Zhou, Yu; Wei, Yongzhuang; Zhang, Fengrong

doi:10.1155/2019/1348639

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…The below given theorem is the inference of the Theorem 20 [19] in a modified form in terms of transparency order by using sum-of-squares-of-modulus indicator. Theorem 20 [19] has various other cryptographic constituents having similar cryptographic characteristics.…”

Section: Transparency Order and Cross-correlation Theoremmentioning

confidence: 99%

Transparency Order and Cross-Correlation Analysis of Boolean Functions

Dar¹,

Raja²,

Butt³

et al. 2022

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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 (n − 2)−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.

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Section: Transparency Order and Cross-correlation Theoremmentioning

confidence: 99%

Transparency Order and Cross-Correlation Analysis of Boolean Functions

Dar¹,

Raja²,

Butt³

et al. 2022

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“…For more research on the autocorrelation function and the cross-correlation function of Boolean functions, refer to reference [14].…”

Section: Preliminariesmentioning

confidence: 99%

On the Modified Transparency Order of $(n, m)$ -Functions

Zhou¹,

Wei

Zhang

et al. 2021

Security and Communication Networks

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The concept of transparency order is introduced to measure the resistance of n , m -functions against multi-bit differential power analysis in the Hamming weight model, including the original transparency order (denoted by TO ), redefined transparency order (denoted by RTO ), and modified transparency order (denoted by MTO ). In this paper, we firstly give a relationship between MTO and RTO and show that RTO is less than or equal to MTO for any n , m -functions. We also give a tight upper bound and a tight lower bound on MTO for balanced n , m -functions. Secondly, some relationships between MTO and the maximal absolute value of the Walsh transform (or the sum-of-squares indicator, algebraic immunity, and the nonlinearity of its coordinates) for n , m -functions are obtained, respectively. Finally, we give MTO and RTO for (4,4) S-boxes which are commonly used in the design of lightweight block ciphers, respectively.

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