Cryptography Reference
In-Depth Information
K
key hypothesis
...
...
k
j(1≤j≤K)
P
1
P
2
...
P
X
Ref
1
Ref
2
...
Ref
X
Centering References
Ref
r(1≤r≤X)
PCA
PC
1
PC
2
...
PC
X
Selection of
m
first
PC
(
CEV
criterion)
F
k
j
Indicator Computation
...
...
Best key
=
argmax
(
)
F
k
j
, (1 ≤ j ≤ k)
Fig. 1.
FPCA description
Then, we propose to compute an indicator
F
k
j
that is defined as follows:
h
(
W, C
m
)
)
m
m
X
F
CS
k
j
c
i
=
(
λ
m
·
)=
(
λ
m
·
(
w
i
·
)
,
(2)
m
=1
m
=1
i
=1
where
m
is the number of retained principal components,
λ
m
is the eigenvalue
corresponding to
PC
m
,
h
is a linear combination function with
C
m
=
i
=1
is the centred coordinate vector of references when projected to
PC
m
and
W
=
{
c
i
}
{
i
=1
is the associated weight vector. Actually, this indicator takes two factors
into consideration: the dispersion and the position of references in the new system
coordinate which is composed by the principal components. The dispersion is
quantified by the value of the eigenvalues
λ
m
and the position by the vector of
weights
W
. The best key guess corresponds to the highest value of
F
k
j
w
i
}
regarding
all key hypotheses (
argmax
(
F
k
j
)).
One other alternative is to consider only the factor of dispersion. This is useful
in the case that the position factor is unknown. In fact, the dispersion factor
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