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Known inifinte families of quadratic APN polynomials over GF(2^n)
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Revision as of 11:57, 5 December 2018 by
Nikolay
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N
∘
{\displaystyle N^{\circ }}
Functions
Conditions
References
C1-C2
x
2
s
+
1
+
u
2
k
−
1
x
2
i
k
+
2
m
k
+
s
{\displaystyle x^{2^{s}+1}+u^{2^{k}-1}x^{2^{ik}+2^{mk+s}}}
n
=
p
k
,
gcd
(
k
,
3
)
=
gcd
(
s
,
3
k
)
=
1
,
p
∈
{
3
,
4
}
,
i
=
s
k
mod
p
,
m
=
p
−
i
,
n
≥
12
,
u
primitive in
F
2
n
∗
{\displaystyle n=pk,\gcd(k,3)=\gcd(s,3k)=1,p\in \{3,4\},i=sk\mod p,m=p-i,n\geq 12,u{\text{ primitive in }}\mathbb {F} _{2^{n}}^{*}}
[1]
↑
L. Budaghyan, C. Carlet, G. Leander,
Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
, IEEE Trans. Inform. Theory 54(9), 2008, pp. 4218-4229
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