Bent Functions by Sihem Mesnager

Author:Sihem Mesnager
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.as will be discussed below, r max should be as small as possible for efficiency reasons, so the natural choice for the indices in a cyclotomic coset will be the coset leaders which are odd integers.

In fact, G a and H a are even Artin–Schreier curves. Theorems 11.1.7 and 11.1.8 state that there exist efficient algorithms to compute the cardinality of such curves as long as r max is supposed to be relatively small. The polynomial defining H a (respectively G a ) is indeed of degree r max + 2 (respectively r max ), so the curve is of genus (r max + 1)∕2 (respectively (r max − 1)∕2). The complexity for testing the hyper-bentness of a Boolean function in this family is then dominated by the computation of the cardinality of a curve of genus (r max + 1)∕2. Then, applying Theorem 11.1.8 gives the following time and space complexities in m and r max .

Theorem 11.3.2.

Let f a be a function in the family defined as above. Let moreover r max be the maximal index in R. Then the hyper-bentness of f a can be checked in

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