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Highly resistant Boolean functions for cryptography
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2013-12-30
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Highly resistant Boolean functions for cryptography
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APN functions
Let us consider a (vectorial) Boolean function f : F
m
2
−→ F
m
2
.
Definition
The function f is said to be APN (almost perfect nonlinear)
if for every a 6= 0 in F
m
2
and b ∈ F
m
2
,
there exists at most 2 elements x of F
m
2
such that
f (x + a) + f (x) = b.
If we use the function f in a S-box of a cryptosystem, they are the
functions which resist the best to differential cryptanalysis.
4
APN functions
Let us consider a (vectorial) Boolean function f : F
m
2
−→ F
m
2
.
Definition
The function f is said to be APN (almost perfect nonlinear)
if for every a 6= 0 in F
m
2
and b ∈ F
m
2
,
there exists at most 2 elements x of F
m
2
such that
f (x + a) + f (x) = b.
If we use the function f in a S-box of a cryptosystem, they are the
functions which resist the best to differential cryptanalysis.
4
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