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On the Gowers U2 and U3 norms of Boolean functions and their restriction to hyperplanes

DISCRETE APPLIED MATHEMATICS (2023)

Further cryptographic properties of the multiplicative inverse function

Deng Tang et al.

Summary: The paper discusses the importance of differential analysis in block ciphers, focusing on cryptographic properties of the multiplicative inverse function and the potential bias in its second order differential spectrum. It also highlights the significance of analyzing the Gowers uniformity norm of S-boxes for higher order approximations. The findings provide improved bounds on the nonlinearity profile of the multiplicative inverse function and may have implications for the non-randomness of a block cipher.

DISCRETE APPLIED MATHEMATICS (2022)

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Article Computer Science, Theory & Methods

GOWERS U2 NORM AS A MEASURE OF NONLINEARITY FOR BOOLEAN FUNCTIONS AND THEIR GENERALIZATIONS

Sugata Gangopadhyay et al.

Summary: This paper investigates the Gowers U-2 norm for generalized Boolean functions and Z-bent functions, providing a framework for employing the norm in the context of generalized Boolean functions. The paper also introduces Z-bent functions and focuses on their U-2 norms, giving an alternate proof to a known theorem and finding necessary and sufficient conditions for a function obtained by gluing Z-bent functions to be bent in terms of the Gowers U-2 norms of its components.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS (2021)

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Article Computer Science, Theory & Methods