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- W3013791688 abstract "We explicitly determine the binary representation of the inverse of all Kasami exponents $K_r=2^{2r}-2^r+1$ modulo $2^n-1$ for all possible values of $n$ and $r$. This includes as an important special case the APN Kasami exponents with $gcd(r,n)=1$. As a corollary, we determine the algebraic degree of the inverses of the Kasami functions. In particular, we show that the inverse of an APN Kasami function on $mathbb{F}_{2^n}$ always has algebraic degree $frac{n+1}{2}$ if $nequiv 0 pmod 3$. For $nnotequiv 0 pmod 3$ we prove that the algebraic degree is bounded from below by $frac{n}{3}$. We consider Kasami exponents whose inverses are quadratic exponents or Kasami exponents. We also determine the binary representation of the inverse of the Bracken-Leander exponent $BL_r=2^{2r}+2^r+1$ modulo $2^n-1$ where $n=4r$ and $r$ odd. We show that the algebraic degree of the inverse of the Bracken-Leander function is $frac{n+2}{2}$." @default.
- W3013791688 created "2020-04-03" @default.
- W3013791688 creator A5077216045 @default.
- W3013791688 date "2020-03-28" @default.
- W3013791688 modified "2023-09-27" @default.
- W3013791688 title "On the inverses of Kasami and Bracken-Leander exponents" @default.
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