Abstract
We introduce a new transform on Boolean functions generalizing the Walsh-Hadamard transform. For Boolean functions \(q\) and \(f\), the q-transform of f measures the proximity of \(f\) to the set of functions obtained from \(q\) by change of basis. This has implications for security against certain algebraic attacks. In this paper we derive the expected value and second moment (Parseval’s equation) of the \(q\)-transform, leading to a notion of \(q\)-bentness. We also develop a Poisson Summation Formula, which leads to a proof that the \(q\)-transform is invertible.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
