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A comparison of Carlet's second-order nonlinearity bounds |
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| Authors: | Sihem Mesnager Gavin McGrew Dayton Steele Katherine Marsten |
| Affiliation: | 1. Department of Mathematics, University of Paris VIII, CNRS, UMR 7539 LAGA and Telecom ParisTech, Paris, France;2. Department of Math and Computer Science, University of Richmond, Richmond, USA |
| Abstract: | Carlet provides two bounds on the second-order nonlinearity of Boolean functions. We construct a family of Boolean functions where the first bound (the presumed weaker bound) is tight and the second bound is strictly worse than the first bound. We show that the difference between the two bounds can be made arbitrarily large. |
| Keywords: | Nonlinearity Boolean functions derivative concatenation |