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- W4385438390 abstract "Let $F$ be a finite field, let $f$ be a function from $F$ to $F$, and let $a$ be a nonzero element of $F$. The discrete derivative of $f$ in direction $a$ is $Delta_a f colon F to F$ with $(Delta_a f)(x)=f(x+a)-f(x)$. The differential spectrum of $f$ is the multiset of cardinalities of all the fibers of all the derivatives $Delta_a f$ as $a$ runs through $F^*$. The function $f$ is almost perfect nonlinear (APN) if the largest cardinality in the differential spectrum is $2$. Almost perfect nonlinear functions are of interest as cryptographic primitives. If $d$ is a positive integer, the power function over $F$ with exponent $d$ is the function $f colon F to F$ with $f(x)=x^d$ for every $x in F$. There is a small number of known infinite families of APN power functions. In this paper, we re-express the exponents for one such family in a more convenient form. This enables us to give the differential spectrum and, even more, to determine the sizes of individual fibers of derivatives." @default.
- W4385438390 created "2023-08-01" @default.
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- W4385438390 date "2023-07-28" @default.
- W4385438390 modified "2023-10-18" @default.
- W4385438390 title "Almost perfect nonlinear power functions with exponents expressed as fractions" @default.
- W4385438390 doi "https://doi.org/10.48550/arxiv.2307.15657" @default.
- W4385438390 hasPublicationYear "2023" @default.
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