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Beierle, Christof; Carlet, Claude
Designs, codes and cryptography, 02/2023, Volume: 91, Issue: 2Journal Article
In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over F 2 5 give rise to a quadratic APN function in dimension 6 having maximum possible linearity of 2 5 (that is, minimum possible nonlinearity 2 4 ). In this article, we show that the case of n ≤ 5 is quite special in the sense that Gold APN functions in dimension n > 5 cannot be extended to quadratic APN functions in dimension n + 1 having maximum possible linearity. In the second part of this work, we show that this is also the case for APN functions of the form x ↦ x 3 + μ ( x ) with μ being a quadratic Boolean function.
