Tables

Known instances of APN functions over $\mathbb {F} _{2^{n}}$

• Known infinite families of APN power functions over GF(2^n)
• Known infinite families of quadratic APN polynomials over GF(2^n)
• Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8
• CCZ-inequivalent APN functions from the known APN classes over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{F}_{2^n}} for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 \le n \le 11}
• Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials and Hexanomials with coefficients in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{F}_2} CCZ-inequivalent to the infinite monomial families over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{F}_{2^n}} for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 \le n \le 11}
• Walsh spectra of quadratic APN functions over GF(2^8)
• Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)
• Some APN functions CCZ-equivalent to ----- and CCZ-equivalent to the Gold functions over GF(2^n)
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• New APN polynomials (up to CCZ-equivalence) over GF(2^11)