Linear and differential cryptanalysis and their generalizations are the most important tools in ststistical analysis of symmetric ciphers.
These attacks make use of linear and differential properties of Sboxes and component functions of symmetric ciphers. In this
article, we investigate generalized statistical properties for Sboxes. We justify the application of linear, differential and differential-linear
cryptanalysis from the mathematical viewpoint. We verify some well-known Sboxes and vectotial Boolean functions by the proposed
criteria and show that these functions have larger biases compared with previous criteria presentesd up to now.
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