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A Proposal of Invariant Operations on Maximally Asymmetric Functions for Their Efficient Generation
Rie Kometani, Shinobu Nagayama, Martin Lukac, Masato Inagi and Shin’ichi Wakabayashi
Maximally asymmetric functions (MAFs) can be promising in various applications, such as cryptography and telecommunications, because of their interesting characteristics. However, not only a way to realize MAFs but also even their efficient generation methods have not been known. This paper proposes some operations on MAFs to generate more than one MAF efficiently. Since the proposed operations are invariant with respect to the asymmetry of functions, they can efficiently produce another MAF from a given MAF. This paper also presents equivalence classes in MAFs based on the operations. By demonstrating that the number of equivalence classes in MAFs is small, the paper shows that most of MAFs can be generated by only applying the proposed operations without generating them from scratch.
Keywords: Maximally asymmetric functions, discrete functions, invariant operations, benchmark generation, equivalence classes