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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Constructions of Almost Resilient Functions
verfasst von : Pin-Hui Ke, Tai-Lin Liu, Qiao-Yan Wen
Erschienen in: Cryptology and Network Security
Verlag: Springer Berlin Heidelberg
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The relation between almost resilient function and its component functions is investigated in this paper. We prove that if each nonzero linear combination of
f
1
,
f
2
,⋯,
f
m
is an
ε
-almost(
n
,1,
k
)-resilient function, then
F
=(
f
1
,
f
2
,⋯,
f
m
) is a
$\frac{2^{m}-1}{2^{m}-1}\epsilon$
-almost(
n
,
m
,
k
)-resilient function. In the case
ε
equals 0, the theorem gives another proof of Linear Combination Lemma for resilient functions. As applications of this theorem, we introduce a method to construct a balanced
$\frac{9}{2}\epsilon$
-almost (3
n
,2,2
k
+1)-resilient function from a balanced
ε
-almost (
n
,1,
k
)-resilient function and present a method of improving the degree of the constructed functions with a small trade-off in the nonlinearity and resiliency. At the end of this paper, the relation between balanced almost CI function and its component functions are also concluded.