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ass
o
ciate
d
h
o
m
o
g
en
e
o
u
s
r
ec
u
r
r
en
ce
r
elatio
n
.
Her
e
th
e
co
n
ce
p
t
o
f
r
ec
u
r
r
en
c
e
r
elatio
n
is
u
s
ed
f
o
r
r
a
n
d
o
m
n
u
m
b
er
g
en
er
atio
n
wh
ich
is
u
s
ed
f
o
r
k
ey
g
en
er
atio
n
.
I
n
d
escr
ete
m
ath
e
m
atics
th
e
u
s
e
o
f
r
ec
u
r
r
en
ce
r
elatio
n
in
r
an
d
o
m
n
u
m
b
er
g
e
n
er
atio
n
[
9
-
11
]
is
a
n
ew
co
n
ce
p
t.
T
h
e
d
etails
alg
o
r
ith
m
is
g
iv
en
in
n
e
x
t
s
ec
tio
n
.
DNA
s
eq
u
en
ce
:
DNA
is
Deo
x
y
Neu
clic
Acid
[
12
]
t
h
at
is
th
e
s
tar
t
lin
e
o
f
a
ll
life
.
DNA
m
o
lecu
les
co
n
ta
in
s
tr
an
d
s
o
f
n
u
cleo
tid
es
th
at
ar
e:
Ad
en
in
e
(
A)
,
C
y
to
s
in
e
(
C
)
,
Gu
an
in
e
(
G)
an
d
T
h
y
m
in
e
(
T
)
.
T
h
e
D
NA
m
o
lecu
les
co
m
p
r
is
e
d
o
u
b
le
h
elix
s
tr
u
ctu
r
e
co
m
b
in
in
in
g
th
e
c
o
m
p
lem
e
n
t
ar
y
s
tr
an
d
s
A
to
T
an
d
G
to
C
.
T
h
e
m
ix
tu
r
e
o
f
b
its
r
ep
r
es
en
ts
t
h
ese
4
b
ases
as
s
h
o
wn
in
T
ab
le
1
.
I
n
co
r
p
o
r
ati
n
g
o
f
th
e
f
ea
tu
r
es
o
f
DNA
in
cr
y
p
to
g
r
ap
h
y
is
a
s
in
g
u
lar
co
n
ce
p
t
as
f
o
r
in
s
tan
ce
th
e
DNA
en
cr
y
p
tio
n
tech
n
i
q
u
e.
I
n
m
an
y
m
et
h
o
d
s
we
will
u
s
e
th
e
DNA
tr
aits
.
T
h
e
p
lain
t
ex
tu
al
co
n
ten
t
ca
n
b
e
co
n
v
e
r
ted
in
to
ASC
I
I
co
d
e
s
af
ter
wh
ich
in
to
b
in
a
r
y
co
d
e,
th
at
ca
n
th
en
b
e
r
ep
lace
d
th
r
o
u
g
h
DNA
b
ases
A,
T
,
G
an
d
C
[
1
3
,
1
4
].
T
ab
le
1
.
DNA
en
co
d
in
g
B
i
t
s
B
a
se
00
A
01
T
10
G
11
C
2.
RE
L
AT
E
D
B
ACK
G
RO
UN
D
WO
RK
S
Sh
am
ir
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
em
e
:
Sh
am
ir
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
em
e
is
b
ased
o
n
(
,
)
th
r
es
h
o
ld
p
r
im
ar
ily
b
ased
s
ec
r
et
s
h
ar
in
g
tech
n
iq
u
e
[
15
]
.
I
n
t
h
is
s
ch
em
e
a
(
−
1
)
d
eg
r
ee
p
o
ly
n
o
m
ial
is
i
m
p
o
r
tan
t.
T
h
e
p
o
ly
n
o
m
ial
f
ea
tu
r
e
o
f
o
r
d
er
(
−
1
)
is
b
u
ilt
as
f
o
llo
ws
-
(
)
=
(
0
+
1
1
+
2
2
+
3
3
+
⋯
+
−
1
−
1
)
.
W
h
er
e
0
th
e
s
ec
r
et
an
d
is
is
a
p
r
im
e
n
u
m
b
er
an
d
all
o
th
er
co
ef
f
icien
ts
ar
e
s
elec
ted
r
an
d
o
m
l
y
f
r
o
m
s
ec
r
et.
E
ac
h
o
f
th
e
n
s
h
ar
es
is
a
p
air
(
,
)
o
f
n
u
m
b
er
s
s
atis
f
y
in
g
(
)
=
an
d
>
0
,
1
≤
≤
an
d
0
<
1
<
2
<
3
<
.
.
.
<
≤
−
1
.
Giv
en
an
y
s
h
ar
es,
th
e
p
o
ly
n
o
m
ials
ar
e
u
n
i
q
u
ely
d
eter
m
in
ed
a
n
d
h
e
n
ce
th
e
s
ec
r
et
0
ca
n
b
e
c
o
m
p
u
te
d
v
ia
L
a
g
r
a
n
g
e’
s
in
ter
p
o
latio
n
.
B
lak
ey
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
e
m
e
:
B
lak
ey
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
em
e
u
s
ed
g
eo
m
etr
y
to
r
e
m
ed
y
s
ec
r
et
s
h
ar
in
g
tr
o
u
b
le
[
3
]
.
T
h
e
s
e
cr
e
t
m
ess
ag
e
is
a
f
ac
to
r
in
a
k
-
d
im
en
s
io
n
al
s
p
ac
e
an
d
n
s
to
c
k
s
ar
e
af
f
in
e
h
y
p
er
p
lan
es
th
at
in
ter
s
ec
t
o
n
th
is
p
o
in
t.
T
h
e
s
et
an
s
wer
=
(
1
,
2
,
3
,
…
,
)
to
an
eq
u
atio
n
1
1
+
2
2
+
3
3
+
⋯
+
=
f
o
r
m
s
an
af
f
in
e
h
y
p
er
p
la
n
e.
T
h
e
in
ter
s
ec
ti
o
n
p
o
in
t
is
o
b
tain
ed
b
y
f
in
d
in
g
th
e
in
ter
s
ec
tio
n
o
f
an
y
o
f
th
ese
p
l
an
es.
Asmu
th
-
B
lo
o
m
’
s
s
ec
r
et
s
h
ar
i
n
g
s
ch
em
e:
Asmu
th
-
b
l
o
o
m
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
em
e
[
2
]
s
h
a
r
es
a
s
ec
r
et
m
an
y
o
f
th
e
in
d
iv
id
u
al
ev
e
n
ts
u
s
in
g
m
o
d
u
lar
ar
ith
m
etic
an
d
r
ec
o
n
s
tr
u
ctio
n
it
with
th
e
aid
o
f
C
h
in
ese
r
em
ain
d
er
th
e
o
r
em
(
C
R
T
)
.
Ab
o
v
e
all
o
f
th
e
s
ec
r
et
s
h
ar
in
g
s
ch
em
es
ar
e
ap
p
ea
r
ed
as
a
g
r
ea
t
s
ec
r
et
s
h
ar
in
g
s
ch
em
e
b
ec
au
s
e
am
alg
am
atio
n
o
f
(
k
-
1
)
s
h
ar
es
d
o
esn
’
t
r
ev
ea
l
an
y
f
ac
ts
ap
p
r
o
x
im
ately
t
h
e
s
ec
r
et.
I
n
k
ey
b
ased
s
ec
u
r
e
th
r
esh
o
ld
cr
y
p
to
g
r
ap
h
y
,
in
itially
a
1
6
-
b
y
te
d
ig
est
s
t
r
in
g
is
g
en
er
ated
f
r
o
m
g
i
v
en
v
ar
iab
le
len
g
th
k
ey
u
s
in
g
MD
5
an
d
th
is
k
ey
is
s
h
a
r
ed
.
3.
O
UR
CO
NT
RI
B
U
T
I
O
N
I
n
th
is
ar
ticle
th
e
t
h
r
ee
n
o
v
el
asp
ec
ts
o
f
o
u
r
wo
r
k
ar
e
–
(
i)
t
h
e
u
s
e
o
f
r
ec
u
r
r
en
ce
r
elatio
n
i
n
r
an
d
o
m
n
u
m
b
er
g
e
n
er
atio
n
(
ii)
th
e
u
s
e
o
f
DNA
s
eq
u
en
ce
f
o
r
n
o
n
lin
ea
r
ity
(
iii)
th
e
u
s
e
o
f
u
n
it
m
atr
ix
in
m
ask
g
en
er
atio
n
alg
o
r
ith
m
.
T
h
is
m
ask
g
en
er
atio
n
p
r
o
ce
s
s
is
a
n
ew
ap
p
r
o
ac
h
in
c
r
y
p
t
o
g
r
ap
h
y
an
d
it
is
v
e
r
y
ea
s
y
th
an
Sh
am
ir
’
s
s
ec
r
et
s
h
ar
i
n
g
s
ch
em
e
o
r
B
lak
ey
’
s
s
ec
r
et
s
h
ar
in
g
s
ch
e
m
e
with
r
esp
ec
t
to
co
m
p
lex
ity
.
B
esid
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
R
ec
u
r
r
en
ce
r
ela
tio
n
a
n
d
DN
A
s
eq
u
en
ce
:
A
s
ta
te
-
of
-
a
r
t te
ch
n
iq
u
e
fo
r
s
ec
r
et
s
h
a
r
in
g
(
A
n
ir
b
a
n
B
h
o
w
mik
)
67
we
h
av
e
in
clu
d
ed
s
y
m
m
etr
ic
k
ey
a
n
d
h
ash
f
u
n
ctio
n
b
ase
d
m
ess
ag
e
au
th
en
ticatio
n
an
d
R
SA
b
ased
u
s
er
au
th
en
ticatio
n
.
Fo
r
s
ess
io
n
k
ey
g
en
e
r
atio
n
we
h
av
e
u
s
ed
th
e
co
n
ce
p
t
o
f
r
ec
u
r
r
e
n
ce
r
elatio
n
an
d
DNA
s
eq
u
en
ce
.
T
h
e
s
h
ar
e
g
en
e
r
atio
n
is
d
o
n
e
o
n
g
en
er
ate
d
m
as
k
.
All
th
e
s
tep
s
ar
e
d
escr
ib
e
d
b
elo
w
b
y
a
p
r
o
p
er
alg
o
r
ith
m
.
A
ca
s
e
s
tu
d
y
is
also
g
iv
en
f
o
r
clea
r
u
n
d
e
r
s
tan
d
in
g
o
f
p
r
o
p
o
s
ed
s
ch
em
e
.
4.
O
UR
P
RO
P
O
SE
D
T
E
CH
NI
Q
UE
T
h
e
s
u
m
m
ar
y
o
f
o
u
r
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
g
iv
en
th
r
o
u
g
h
an
alg
o
r
ith
m
wh
ich
co
n
tain
s
f
iv
e
m
o
d
u
les.
E
ac
h
m
o
d
u
le
is
d
escr
ib
ed
v
ia
an
alg
o
r
ith
m
.
Alg
o
r
ith
m
:
I
n
p
u
t: seed
v
alu
es,
p
lain
tex
t,
s
y
m
m
etr
ic
k
ey
.
Step
1
: c
all
m
ask
_
Gen
er
atio
n
(
)
.
// M
ask
g
en
er
atio
n
alg
o
r
ith
m
.
Step
2
: c
all
SKG
(
)
.
// Sess
io
n
k
ey
g
e
n
er
atio
n
.
Step
3
: c
all
en
c_
m
s
g
(
)
.
// p
lain
tex
t e
n
cr
y
p
tio
n
.
Step
4
: c
all
s
h
ar
e_
Gen
er
atio
n
(
)
// sh
ar
e
g
en
er
atio
n
&
tr
an
s
m
is
s
io
n
f
ile
cr
ea
tio
n
Step
5
:
ca
ll r
ec
o
n
s
t_
m
s
g
(
)
.
// d
ec
r
y
p
tio
n
an
d
r
ec
o
n
s
tr
u
ctio
n
o
f
m
ess
ag
e.
E
n
d
4
.
1
.
M
a
s
k
g
ener
a
t
io
n mo
du
le
Ou
r
p
r
o
p
o
s
ed
wo
r
k
is
lar
g
ely
a
d
ep
en
d
in
g
o
n
p
r
o
tectin
g
th
e
p
r
e
-
d
e
f
in
ed
k
n
u
m
b
er
o
f
s
h
a
r
es
o
n
th
e
m
ess
ag
e
o
r
s
ec
r
et
d
ata
an
d
th
e
n
to
ca
r
r
y
o
u
t
OR
o
p
er
ati
o
n
o
n
th
e
p
r
e
-
d
ef
in
ed
k
v
ar
iety
o
f
s
h
ar
es
to
r
eg
e
n
er
ate
th
e
u
n
i
q
u
e
tr
an
s
m
itted
m
ess
ag
e
o
r
s
ec
r
et
in
f
o
r
m
atio
n
.
T
h
e
s
ec
r
et
d
ata
m
ay
b
e
co
n
s
id
er
e
d
as
an
im
a
g
e,
a
u
d
io
,
v
id
eo
o
r
a
n
y
tex
t
f
ile.
Ou
r
in
i
tial
task
is
to
d
ec
o
m
p
o
s
e
th
e
f
ile
o
f
an
y
s
ize
in
to
k
n
u
m
b
e
r
o
f
s
h
ar
es.
On
th
e
r
ec
eiv
er
en
d
,
if
we
p
er
f
o
r
m
b
i
twis
e
O
R
o
p
er
atio
n
u
p
o
n
n
u
m
b
er
o
f
s
h
a
r
es
th
en
o
n
l
y
th
e
o
r
ig
in
a
l
d
ata
will
b
e
r
ec
o
n
s
tr
u
cted
,
n
o
t
e
v
en
u
p
o
n
(
−
1
)
s
h
ar
es.
E
v
e
r
y
s
h
ar
e
m
u
s
t
h
av
e
s
o
m
e
m
is
s
in
g
b
its
an
d
h
en
ce
th
o
s
e
m
is
s
in
g
b
its
ca
n
b
e
r
ep
lace
d
b
y
k
s
h
ar
es e
x
ac
tly
.
Step
1
: Fr
o
m
n
u
m
b
er
o
f
to
tal
r
ec
ep
ien
ts
we
ca
n
ch
o
o
s
e
an
y
n
u
m
b
er
o
f
r
ec
ip
ien
ts
to
s
en
d
m
ess
ag
e
(
<
)
.
Step
2
: A
u
n
it m
atr
ix
o
f
o
r
d
er
is
tak
en
.
Step
3
: T
h
e
m
ask
m
atr
ix
is
g
en
er
ated
b
y
s
h
u
f
f
lin
g
all
th
e
r
o
w
s
o
f
u
n
it m
atr
ix
.
Step
4
: T
h
e
m
ask
m
atr
ix
is
u
s
ed
f
o
r
s
h
a
r
e
g
en
e
r
atio
n
.
4
.
2
.
Ses
s
io
n k
ey
g
ener
a
t
io
n m
o
d
ule
I
n
th
is
m
o
d
u
le
we
h
av
e
g
e
n
er
ated
s
ess
io
n
k
ey
f
o
r
d
at
a
en
cr
y
p
tio
n
.
Her
e
No
n
-
Ho
m
o
g
en
e
o
u
s
R
ec
u
r
r
en
ce
R
elatio
n
f
o
r
m
u
la
is
u
s
ed
f
o
r
th
e
s
ess
io
n
k
e
y
g
en
er
atio
n
.
At
f
ir
at
s
ess
io
n
k
ey
is
XORed
with
s
y
m
m
etr
ic
k
ey
an
d
th
en
d
iv
id
e
in
to
n
u
m
b
er
o
f
s
h
ar
es
u
s
in
g
m
ask
m
atr
ix
an
d
th
en
ea
ch
s
h
ar
e
o
f
s
ess
io
n
k
ey
is
tr
an
s
m
itted
to
r
ec
eiv
er
en
d
as
an
attac
h
m
e
n
t
o
f
ea
c
h
s
h
ar
e
o
f
m
ess
ag
e.
T
h
e
s
ize
o
f
s
es
s
io
n
k
ey
is
s
am
e
as
th
e
s
ize
o
f
s
y
m
m
etr
ic
k
e
y
.
Alg
o
r
ith
m
:
I
n
p
u
ts
:
-
s
ee
d
v
al
u
es,
co
ef
f
icie
n
t v
alu
e
an
d
n
o
n
h
o
m
o
g
en
eo
u
s
r
ec
u
r
r
en
ce
e
q
u
atio
n
.
Ou
tp
u
ts
:
-
s
ess
io
n
k
ey
Me
th
o
d
:
1.
Set i, j, m, n, f, lr as integer and
[
]
,
[
]
,
[
]
as integer array.
2.
<
−
total random number.
3.
<
−
total no.of
coefficient in non
-
homogeneous recurrence relation.
4. For
=
0
5.
[
]
<
−
get_coeff () and
[
]
<
−
get_seedVal ()
end for
6
.
<
−
get_largestPrimeFact (
[
2
]
[
3
]
). {/* a[2] and c [3] are chosenby the user.*/}
7
.
[
0
]
<
−
[
0
]
.
8
. for
=
1
9
.
[
]
=
(
[
]
[
−
1
]
)
end for
1
0
. for
=
3
1
1
.
[
]
<
−
_
(
_
(
)
)
1
2
. if (
[
]
<
0
)
1
3
.
[
]
<
−
[
]
end if
1
4
.
[
]
<
−
[
]
1
5
. f<
-
((((
[
]
[
1
]
)
[
3
]
)
[
5
]
)
.
.
.
[
]
)
1
6
.
[
]
<
−
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
65
–
76
68
end for
1
7
. if (
>
=
3
)
1
8
.
[
]
<
−
get_shuffle
(
[
]
)
//
[
]
represent the session key.
19
.
[
]
← get_DNAsequen (
[
]
)
end if
20. End
D
NA
Seq
u
en
ce
Mo
d
u
le
(
g
et_
DNAseq
u
en
ce
(
)
)
:
I
t
tak
es
r
a
n
d
o
m
s
eq
u
en
ce
g
en
e
r
ated
f
r
o
m
R
C
as
p
ar
am
eter
v
x
x
alu
es.
1.
E
ac
h
in
teg
er
is
d
iv
i
d
ed
in
t
o
f
o
u
r
b
its
.
2.
DNA
s
eq
u
en
ce
is
g
en
er
ated
b
y
tak
in
g
two
b
its
to
g
eth
er
a
n
d
v
alu
es o
f
T
ab
le
1.
3.
T
h
u
s
,
we
g
et
a
s
eq
u
e
n
ce
o
f
,
,
,
in
an
y
o
r
d
er
wh
ic
h
is
tr
ea
ted
as
Ses
s
io
n
k
ey
.
4
.
3
.
E
ncry
ptio
n
a
nd
s
ha
re
g
ener
a
t
io
n m
o
du
le
Alg
o
r
ith
m
:
I
n
p
u
ts
:
-
s
ess
io
n
k
ey
,
s
y
m
m
etr
ic
k
ey
,
p
lain
tex
t a
n
d
to
tal
n
u
m
b
er
o
f
r
ec
ip
ien
t.
Ou
tp
u
ts
:
-
s
h
ar
e
g
en
e
r
atio
n
a
n
d
tr
an
s
m
is
s
io
n
f
ile.
Me
th
o
d
:
1.
s
et
p
lain
tex
t[
]
,
cip
h
e
r
tx
t[
]
,
s
h
ar
e_
m
s
g
[
]
[
]
,
s
h
ar
e
_
s
ess
io
n
k
ey
[
]
[
]
,
an
d
s
h
a
r
e_
h
ash
[
]
[
]
as
C
h
ar
ac
ter
ar
r
a
y
an
d
as in
teg
er
.
2.
cip
h
er
tx
t [
k
]
←
ca
ll Xo
R
_
OP (
p
lain
tex
t[
k
]
,
s
ess
io
n
k
ey
)
a
n
d
k
←
n
o
.
o
f
s
h
ar
e
.
3.
s
h
ar
e_
s
ess
io
n
k
ey
[
k
]
[
k
]
←ca
ll sh
ar
e_
Gen
er
atio
n
(
m
ask
m
at
r
ix
[
k
]
[
k
]
,
s
ess
io
n
k
ey
)
.
4.
s
h
ar
e_
m
s
g
[
k
]
[
k
]
←ca
ll sh
ar
e_
Gen
er
atio
n
(
m
ask
m
atr
ix
[
k
]
[
k
]
,
cip
h
e
r
tx
t [
k
]
[
k
]
)
.
5.
s
h
ar
e_
h
ash
[
k
]
[
k
]
←ca
ll sh
ar
e_
Gen
er
atio
n
(
m
ask
m
atr
ix
[
k
]
[
k
]
,
h
ash
(
s
y
m
m
etr
ic
k
ey
)
)
.
6.
C
r
ea
te
tr
an
s
m
is
s
io
n
f
ile
f
o
r
ea
ch
r
ec
ip
ien
t.
7.
T
h
e
tr
an
s
m
is
s
io
n
f
ile
is
s
en
t to
th
e
r
ec
ip
ien
t e
n
d
u
s
in
g
p
u
b
lic
k
ey
o
f
ea
ch
r
ec
ip
ien
t.
8.
E
n
d
.
T
h
e
tr
an
s
m
is
s
io
n
f
ile
[
16
]
is
cr
ea
ted
u
s
in
g
m
ess
ag
e
s
h
ar
e,
s
ess
io
n
k
ey
s
h
ar
e
an
d
h
ash
v
alu
e
s
h
ar
e.
T
h
e
Stru
ctu
r
e
is
g
iv
e
n
b
elo
w.
T
h
is
tr
an
s
m
is
s
io
n
f
ile
is
ter
m
ed
as
m
ess
ag
e.
S
H
A
R
E
O
F
C
I
P
H
ER
T
EX
T
S
H
A
R
E
O
F
S
ESS
I
O
N
K
EY
H
A
S
H
V
A
LU
E
S
H
A
R
E(
P
A
D
D
I
N
G
)
T
h
is
tr
an
s
m
is
s
io
n
f
ile
is
g
en
er
ated
f
o
r
ea
c
h
s
h
ar
e.
Fo
r
h
ash
v
alu
e
g
en
e
r
atio
n
,
MD
5
h
ash
f
u
n
ctio
n
o
n
s
y
m
m
etr
ic
k
ey
is
u
s
ed
as
h
as
h
v
alu
e.
E
ac
h
s
h
ar
e
o
f
m
ess
ag
e
is
g
en
er
ated
b
y
u
s
in
g
AND
o
p
er
atio
n
b
etwe
en
ea
ch
r
o
w
o
f
m
ask
m
atr
i
x
an
d
m
ess
ag
e.
E
ac
h
s
h
ar
e
is
tr
an
s
m
itted
to
r
ec
ip
ien
t e
n
d
th
r
o
u
g
h
R
SA.
4
.
4
.
Rec
o
ns
t
ruct
io
n o
f
encr
y
pte
d m
ess
a
g
e
(
decr
y
ptio
n mo
du
le)
Alg
o
r
ith
m
:
I
n
p
u
t:
-
p
u
b
lic
k
ey
s
o
f
n
n
u
m
b
er
o
f
r
ec
i
p
ien
ts
an
d
th
e
ir
s
h
ar
e
s
.
Ou
tp
u
t:
-
Or
ig
in
al
s
ec
r
et
m
ess
ag
e
Me
th
o
d
:
-
1.
n
u
m
b
e
r
o
f
r
ec
ip
ien
ts
s
h
o
u
ld
jo
in
in
k
e
y
r
ec
o
n
s
tr
u
ctio
n
u
s
in
g
th
eir
in
d
i
v
id
u
al
s
h
ar
es.
2.
T
h
e
r
ec
ip
ien
ts
will
d
ec
r
y
p
t
th
eir
in
d
i
v
id
u
al
s
h
ar
e
b
y
th
eir
p
r
iv
ate
k
ey
s
.
T
h
is
p
r
o
v
id
es
th
e
u
s
e
r
Au
th
en
ticatio
n
.
3.
At
f
ir
s
t
h
ash
v
lau
e
o
f
s
y
m
m
et
r
ic
k
ey
is
g
en
e
r
ated
f
o
r
m
ess
ag
e
au
th
en
ticatio
n
an
d
t
o
g
et
t
h
e
h
ash
v
alu
e
b
ac
k
,
it is
n
ec
ess
ar
y
to
b
it
b
y
b
it ORed
o
f
ea
ch
k
n
u
m
b
er
o
f
s
h
ar
es o
f
r
ec
ip
ien
ts
.
4.
Af
ter
ch
ec
k
i
n
g
th
e
a
u
th
en
tica
tio
n
b
o
th
u
s
er
an
d
m
ess
ag
e,
th
e
s
ess
io
n
k
ey
is
g
en
e
r
ated
b
y
u
s
in
g
OR
o
p
er
atio
n
o
n
b
it b
y
b
it o
f
ea
c
h
k
n
u
m
b
er
o
f
s
h
ar
es
.
5.
Nu
m
b
er
s
o
f
r
ec
ip
ien
t
g
en
er
at
e
m
ess
ag
e
o
r
d
ata
b
y
u
s
in
g
b
it
b
y
b
it OR o
p
er
ati
o
n
o
n
th
e
s
h
ar
es.
6.
T
h
e
d
ec
r
y
p
tio
n
is
d
o
n
e
o
n
cip
h
er
tex
t to
g
et
th
e
p
lain
tex
t b
y
u
s
in
g
s
ess
io
n
k
ey
.
5.
A
CASE
ST
UD
Y
A
s
n
ap
s
h
o
t
wh
ich
co
n
tain
s
a
s
et
o
f
s
ev
en
r
ec
ep
ien
ts
an
d
o
u
t
o
f
s
ev
en
f
iv
e
r
ec
ip
ien
ts
ar
e
ch
o
s
en
to
s
en
d
m
ess
ag
e.
T
h
u
s
,
th
e
th
r
es
h
o
ld
v
alu
e
is
f
iv
e
a
n
d
it is
g
iv
en
in
th
e
f
o
llo
win
g
tab
u
lar
f
o
r
m
at.
No
w
ac
co
r
d
in
g
to
m
ask
g
en
er
atio
n
alg
o
r
ith
m
f
ir
s
t
a
u
n
it
m
atr
i
x
o
f
o
r
d
e
r
5
x
5
is
ch
o
s
en
a
n
d
th
en
s
h
u
f
f
le
o
p
er
atio
n
is
d
o
n
e
5
tim
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
R
ec
u
r
r
en
ce
r
ela
tio
n
a
n
d
DN
A
s
eq
u
en
ce
:
A
s
ta
te
-
of
-
a
r
t te
ch
n
iq
u
e
fo
r
s
ec
r
et
s
h
a
r
in
g
(
A
n
ir
b
a
n
B
h
o
w
mik
)
69
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
Un
it m
atr
ix
o
f
5
x
5
Af
ter
s
h
u
f
f
le
o
p
er
atio
n
we
g
et
th
e
f
o
llo
win
g
m
atr
i
x
.
Sh
u
f
f
le
o
p
er
atio
n
m
a
y
b
e
n
tim
es
,
wh
er
e
n
less
th
an
n
u
m
b
er
o
f
r
o
ws o
f
m
atr
i
x
.
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
No
w
th
e
s
h
ar
es a
r
e
s
h
o
wn
i
n
T
ab
le
2
.
T
ab
le
2
.
Sn
ap
s
h
o
ts
o
f
s
h
ar
es
0
1
0
0
0
S
h
a
r
e
N
o
.
1
1
0
0
0
0
S
h
a
r
e
N
o
.
2
0
0
0
0
1
S
h
a
r
e
N
o
.
3
0
0
0
1
0
S
h
a
r
e
N
o
.
4
0
0
1
0
0
S
h
a
r
e
N
o
.
5
L
et
th
e
m
ess
ag
e
o
r
p
lain
tex
t
b
e
A
7
B
C
1
DE
3
F
H2
G
,
th
e
s
ess
io
n
k
ey
AC
3
GE
8
R
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u
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u
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s
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ith
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itted
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s
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g
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e
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ticatio
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6.
RE
SU
L
T
S
A
ND
ANA
L
Y
SI
S
O
F
O
UR
P
RO
T
O
CO
L
I
n
th
is
s
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tio
n
,
s
im
u
latio
n
r
e
s
u
lts
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
ar
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p
r
esen
ted
.
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th
e
p
r
o
g
r
am
s
an
d
ca
lcu
latio
n
s
ar
e
d
o
n
e
in
a
m
ac
h
in
e
with
f
o
llo
win
g
co
n
f
ig
u
r
a
tio
n
s
.
T
ab
le
3
s
h
o
ws
th
e
co
n
f
i
g
u
r
atio
n
d
etails.
I
n
o
u
r
ex
p
e
r
im
en
ts
,
d
if
f
er
e
n
t
ty
p
es
o
f
f
iles
ar
e
u
s
ed
as
p
lain
tex
t.
Ou
r
r
esu
lt
s
ec
tio
n
is
d
iv
id
ed
in
to
f
o
u
r
p
ar
ts
:
(
i)
An
aly
s
is
o
f
m
ask
g
en
er
atio
n
(
i
i)
An
aly
s
is
o
f
k
ey
s
tr
en
g
th
(
iii
)
An
aly
s
is
o
f
en
cr
y
p
tio
n
tec
h
n
iq
u
e
[
1
7
,
1
8
]
.
T
ab
le
3
.
Ma
ch
i
n
e
d
escr
ip
tio
n
C
o
m
p
u
t
e
r
Le
n
o
v
o
G
8
0
.
P
r
o
c
e
ss
o
r
I
n
t
e
l
®
P
e
n
t
i
u
m
®
C
P
U
B
9
5
0
@
2
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0
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H
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m
W
i
n
d
o
w
s 7
U
l
t
i
m
a
t
e
(
3
2
B
i
t
s)
6
.
1
.
Co
m
pa
ra
t
iv
e
a
na
ly
s
is
o
f
t
he
m
a
s
k
g
ener
a
t
io
n a
lg
o
rit
hm
Her
e
we'
v
e
g
o
t
u
s
ed
a
tex
t
m
ess
ag
e
as
s
ec
r
et.
B
u
t
o
u
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
lik
ewise
s
im
ilar
ly
ap
p
licab
le
f
o
r
an
y
b
in
ar
y
r
ec
o
r
d
co
n
s
is
tin
g
o
f
I
m
ag
e
(
.
B
m
p
)
,
au
d
io
an
d
m
an
y
o
th
er
s
.
I
n
s
ec
r
et
s
h
ar
in
g
[
4
]
f
o
r
n
s
to
ck
s
with
th
r
esh
o
ld
v
alu
e
k
d
u
r
atio
n
o
f
ea
ch
m
ask
is
−
1
wh
er
e
we
h
av
e
−
2
−
1
ze
r
o
s
an
d
−
−
1
o
n
es.
T
h
en
ea
ch
s
h
ar
e
c
o
n
tain
s
−
−
1
n
u
m
b
er
o
f
b
y
tes
f
o
r
−
1
n
u
m
b
e
r
o
f
b
y
tes
o
f
s
ec
r
et
m
ess
ag
e.
T
h
e
o
r
ig
in
al
s
ec
r
et
m
ess
ag
e
ca
n
b
e
r
ec
o
n
s
tr
u
cted
b
y
o
n
ly
k
n
u
m
b
er
o
f
co
llatin
g
s
h
ar
es
:
o
th
er
wis
e
m
ess
a
g
e
ca
n
n
o
t
b
e
r
ec
o
n
s
tr
u
cted
.
B
ec
au
s
e
f
ewe
r
s
h
ar
es
ca
n
n
o
t
r
ec
o
n
s
tr
u
ct
th
e
o
r
ig
in
al
h
ea
d
er
,
th
u
s
we
ca
n
n
o
t
h
av
e
eith
er
r
ig
h
t
k
ey
(
K)
o
r
th
e
i
n
f
o
r
m
atio
n
to
co
n
s
tr
u
ct
th
e
co
r
r
ec
t m
ask
in
g
p
atter
n
.
Ou
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
h
as
u
s
ed
b
est
u
n
it
m
atr
ix
o
f
o
r
d
er
k
in
ar
ea
o
f
p
er
m
u
tatio
n
a
n
d
a
g
g
r
eg
ate
o
f
p
r
ec
ed
in
g
a
p
p
r
o
ac
h
.
I
t
ca
n
d
e
clar
e
to
b
e
a
Per
f
ec
t
Secr
et
S
h
ar
in
g
(
PS
S)
m
eth
o
d
[
19
]
as
well
as
c
lean
with
r
ec
o
g
n
ize
to
o
th
er
.
Her
e
all
g
en
er
ated
s
h
ar
es
ar
e
c
o
m
p
r
e
s
s
ed
an
d
co
m
p
r
is
e
p
ar
tial
s
e
cr
et
in
f
o
r
m
atio
n
in
en
cr
y
p
ted
s
h
ap
e
th
at
p
r
o
v
id
es
ex
tr
a
s
af
ety
to
th
e
n
am
e
o
f
t
h
e
s
ec
r
et
m
ess
ag
e.
On
ly
wh
e
n
allo
wab
le
s
et
o
f
s
h
ar
es
co
m
es
co
llectiv
ely
,
th
en
s
im
p
lest
th
e
au
th
en
tic
s
ec
r
e
t
m
ess
ag
e
i
s
r
ec
o
n
s
tr
u
cted
.
No
w
in
ca
s
e
o
f
b
ig
v
alu
es
o
f
an
d
,
p
r
ev
io
u
s
s
ec
r
et
s
h
ar
in
g
m
eth
o
d
s
u
g
g
ests
g
r
ea
ter
co
m
p
lex
it
y
th
an
o
u
r
tech
n
iq
u
e.
T
h
u
s
with
r
ec
o
g
n
ize
t
o
tim
e
co
m
p
lex
ity
an
d
c
o
m
p
u
tatio
n
al
co
m
p
lex
i
ty
o
u
r
m
ask
g
e
n
er
atio
n
m
eth
o
d
is
h
ig
h
e
r
th
a
n
p
r
ev
io
u
s
tec
h
n
iq
u
es.
Her
e
two
alg
o
r
ith
m
s
ar
e
u
s
ed
o
n
e
f
o
r
u
n
it
m
atr
ix
e
r
a
a
n
d
d
if
f
er
e
n
t
f
o
r
s
u
f
f
llin
g
th
e
r
o
ws
o
f
u
n
it m
at
r
ix
.
6
.
2
.
Ana
ly
s
is
o
f
k
ey
s
t
re
ng
t
h
I
n
o
u
r
p
r
o
to
co
l
s
h
ar
ed
d
ata
is
v
er
y
s
en
s
itiv
e
with
r
esp
ec
t
to
th
e
s
ec
r
et
k
e
y
v
alu
e.
T
h
e
s
ess
io
n
k
e
y
is
u
s
ed
as
en
c
r
y
p
tio
n
k
e
y
a
n
d
it
is
g
en
er
ate
d
u
s
in
g
r
ec
u
r
r
e
n
ce
f
o
r
m
u
la.
Dif
f
er
en
t
ty
p
es
o
f
e
x
p
er
im
en
ta
l
r
esu
lts
p
r
o
v
e
t
h
e
s
tr
en
g
th
o
f
o
u
r
s
ess
io
n
k
ey
.
R
an
d
o
m
n
ess
test
&
en
tr
o
p
y
test
o
n
s
e
s
s
io
n
k
ey
:
-
Her
e
th
e
s
es
s
io
n
s
ec
r
et
i
s
g
en
er
ated
f
r
o
m
r
ec
u
r
r
en
ce
r
elatio
n
an
d
DNA
co
llectio
n
.
No
w
to
ch
ec
k
th
e
r
an
d
o
m
n
ess
o
f
s
ess
io
n
k
ey
w
e
u
s
e
s
o
m
e
s
ty
li
s
h
tech
n
iq
u
es w
h
ich
in
cl
u
d
e
f
r
eq
u
en
cy
test
[
10
]
,
en
t
r
o
p
y
[
2
0
,
2
1
]
.
Fre
q
u
en
cy
test
:
-
T
h
e
f
r
eq
u
e
n
c
y
ch
ec
k
is
th
e
m
ax
im
u
m
s
im
p
le
ch
ec
k
f
o
r
r
an
d
o
m
n
ess
ch
ec
k
in
g
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
s
ch
em
e
is
t
o
d
eter
m
in
e
wh
eth
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o
r
n
o
t
o
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n
o
t
t
h
e
r
an
g
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f
1
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s
an
d
0
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s
in
a
s
er
ies
is
ap
p
r
o
x
im
ately
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im
ilar
to
m
ig
h
t
b
e
ex
p
ec
ted
f
o
r
a
g
en
u
in
ely
r
an
d
o
m
s
eq
u
en
ce
.
Ma
th
em
ati
ca
l
Stru
ctu
r
e
o
f
th
e
T
est:
F
r
eq
u
en
cy
(
n
)
,
wh
er
e
n
is
th
e
len
g
th
o
f
b
it st
r
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
R
ec
u
r
r
en
ce
r
ela
tio
n
a
n
d
DN
A
s
eq
u
en
ce
:
A
s
ta
te
-
of
-
a
r
t te
ch
n
iq
u
e
fo
r
s
ec
r
et
s
h
a
r
in
g
(
A
n
ir
b
a
n
B
h
o
w
mik
)
71
ℰ
: th
e
s
eq
u
en
ce
o
f
b
its
wh
ich
ar
e
g
en
er
ate
d
b
y
R
NG
o
r
PR
N
G.
S
obs
:
th
e
ab
s
o
lu
te
v
alu
e
o
f
th
e
s
u
m
o
f
th
e
(
wh
er
e
=
2ℰ
−
1
)
is
th
e
s
eq
u
en
ce
d
iv
id
ed
b
y
th
e
s
q
u
a
r
e
r
o
o
t
o
f
th
e
len
g
th
o
f
th
e
s
eq
u
e
n
ce
.
1)
C
o
n
v
er
s
io
n
to
±
1
:
T
h
e
ze
r
o
s
an
d
o
n
es
o
f
th
e
in
p
u
t
s
eq
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en
ce
s
(
ℰ
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ar
e
co
n
v
er
ted
to
v
al
u
es
o
f
-
1
an
d
+1
an
d
ar
e
a
d
d
ed
t
o
g
e
th
er
to
p
r
o
d
u
ce
=
1
+
2
+
⋯
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e
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e
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ℰ
−
1
.
2)
C
o
m
p
u
te
th
e
test
s
tatic
=
(
)
/
√
.
3)
C
o
m
p
u
te
−
=
e
r
fc
(
/
√
2)
.
4)
If
−
≥
0
.
01
th
en
th
e
c
o
n
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s
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th
at
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o
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d
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m
.
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h
e
f
o
llo
win
g
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ab
le
4
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d
Fig
u
r
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1
s
h
o
w
t
h
e
d
etails
o
f
f
r
eq
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en
cy
test
r
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lt
.
T
ab
le
4
.
Fre
q
u
en
cy
test
r
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lt
S
e
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o
n
k
e
y
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z
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(
b
i
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s)
F
r
e
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e
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y
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l
t
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r
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h
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e
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r
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e
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e
s
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l
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P
R
N
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656
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422
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300
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356
Fig
u
r
e
1.
Gr
a
p
h
o
f
f
r
e
q
u
en
c
y
t
est o
f
T
ab
le
4
Ob
s
er
v
atio
n
s
:
NI
ST
SP
8
0
0
-
2
2
s
p
ec
if
ies
th
at
t
h
e
r
a
n
d
o
m
n
ess
tak
e
a
lo
o
k
at
o
u
g
h
t
to
f
o
llo
w
th
e
3
tr
aits
in
clu
s
iv
e
o
f
Un
if
o
r
m
ity
,
Scalab
ilit
y
an
d
C
o
n
s
is
ten
cy
.
I
n
ca
s
e
o
f
u
n
if
o
r
m
ity
a
n
d
s
ca
lab
ilit
y
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th
e
p
r
ev
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ce
o
f
a
0
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r
1
is
eq
u
ally
in
all
lik
elih
o
o
d
th
is
is
th
e
p
o
s
s
ib
ilit
y
o
f
o
cc
u
r
r
en
ce
o
f
0
o
r
o
n
e
is
h
alf
.
T
h
e
T
ab
le
4
o
f
f
r
e
q
u
en
c
y
ch
ec
k
r
e
s
u
lt in
d
icate
s
u
n
if
o
r
m
ity
a
n
d
s
ca
lab
ilit
y
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f
o
u
r
m
eth
o
d
.
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n
ca
s
e
o
f
co
n
s
is
ten
cy
,
we
ca
n
s
ay
th
at
th
e
s
ee
d
d
ata
f
r
o
m
wh
ich
we
will
g
en
er
ate
th
e
s
ess
io
n
s
ec
r
e
t
is
s
y
m
m
etr
ic
k
ey
.
Fo
r
cr
y
p
to
g
r
ap
h
ic
a
p
p
licatio
n
s
,
th
e
s
y
m
m
etr
ic
k
ey
n
ee
d
s
to
b
e
r
elax
e
d
.
T
h
e
co
n
s
u
ltatio
n
k
ey
is
g
en
er
ated
b
y
way
o
f
th
e
u
s
ag
e
o
f
t
h
e
id
ea
o
f
r
e
cu
r
r
en
ce
r
elatio
n
an
d
DNA
s
er
ies.
No
w
if
t
h
e
co
ef
f
icien
t
o
f
r
ec
u
r
r
en
c
e
r
elatio
n
is
u
n
k
n
o
wn
o
r
m
a
y
ex
ch
an
g
e
tim
e
to
tim
e
a
n
d
if
t
h
e
s
y
m
m
etr
ic
s
ec
r
et'
s
s
ec
u
r
ed
th
en
th
e
f
o
llo
win
g
o
u
tp
u
t
b
it
with
in
th
e
s
eq
u
en
c
e
h
av
e
to
b
e
u
n
p
r
ed
ictab
le
n
o
twith
s
tan
d
in
g
an
y
u
n
d
er
s
tan
d
i
n
g
o
f
p
r
ec
e
d
in
g
b
its
in
s
id
e
th
e
co
llectio
n
.
I
t
s
h
o
u
ld
n
o
lo
n
g
er
b
e
v
ia
b
le
to
d
eter
m
in
e
th
e
s
y
m
m
et
r
ic
k
ey
f
r
o
m
th
e
ex
p
e
r
tis
e
o
f
an
y
g
en
er
ated
v
alu
es.
T
h
er
e
is
n
'
t
an
y
co
r
r
ela
tio
n
am
o
n
g
s
y
m
m
etr
ic
k
e
y
an
d
g
en
er
ate
d
v
alu
es.
T
h
u
s
o
u
r
m
eth
o
d
p
r
o
v
es
th
e
ah
ea
d
an
d
b
ac
k
war
d
u
n
p
r
e
d
ictab
ilit
y
.
Fu
r
th
er
m
o
r
e
,
f
r
o
m
t
h
e
ab
o
v
e
d
esk
a
n
d
g
r
a
p
h
it'
s
f
ar
v
is
ib
le
th
at
o
u
r
p
r
o
p
o
s
ed
tech
n
iq
u
e
o
f
f
er
s
ex
tr
a
r
an
d
o
m
n
ess
th
an
PR
NG
(
)
th
at
is
wellk
n
o
wn
tech
n
iq
u
e.
E
n
tr
o
p
y
test
:
Her
e
we
d
escr
ib
e
a
c
o
m
p
ar
ativ
e
s
tu
d
y
b
etwe
e
n
o
u
r
tech
n
iq
u
e
a
n
d
s
tan
d
ar
d
t
ec
h
n
iq
u
e,
PR
NG
(
)
with
s
ess
io
n
k
ey
an
d
s
y
m
m
etr
ic
k
ey
.
T
h
e
f
o
llo
win
g
T
ab
le
5
an
d
Fig
u
r
e
2
s
h
o
w
th
e
d
etails
o
f
e
n
tr
o
p
y
v
alu
e
.
T
ab
le
5
.
E
n
tr
o
p
y
v
alu
e
S
e
ssi
o
n
k
e
y
si
z
e
(
b
i
t
s)
En
t
r
o
p
y
v
a
l
u
e
o
f
o
u
r
t
e
c
h
n
i
q
u
e
.
En
t
r
o
p
y
v
a
l
u
e
o
f
P
R
N
G
(
)
56
6
.
8
8
7
.
0
0
64
6
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8
1
7
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6
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6
6
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9
0
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0
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
65
–
76
72
Fig
u
r
e
2
.
2
D
g
r
ap
h
o
f
en
tr
o
p
y
v
alu
e
o
f
T
ab
le
5
Ob
s
er
v
atio
n
s
:
I
n
cr
y
p
to
g
r
ap
h
y
,
a
cr
y
p
to
s
y
s
tem
is
s
tated
to
b
e
s
em
an
tically
c
o
m
f
o
r
tab
le
i
f
it
is
v
er
y
d
if
f
icu
lt
to
an
attac
k
er
to
e
x
tr
ac
t
an
y
in
f
o
r
m
atio
n
ab
o
u
t
t
h
e
p
lain
tex
t
f
r
o
m
cip
h
er
tex
t
an
d
its
d
u
r
atio
n
.
E
n
tr
o
p
y
ca
n
b
e
d
escr
ib
ed
as
r
an
d
o
m
n
ess
o
r
u
n
p
r
ed
ictab
ilit
y
o
f
in
f
o
r
m
atio
n
co
n
tain
e
d
i
n
a
m
ess
ag
e.
T
h
is
r
an
d
o
m
n
ess
b
r
ea
k
s
th
e
s
h
ap
e
o
f
u
n
d
e
n
iab
le
tex
t
u
al
co
n
t
en
t.
E
n
tr
o
p
ic
s
ec
u
r
ity
in
en
c
r
y
p
tio
n
is
ju
s
t
lik
e
s
em
an
tic
p
r
o
tectio
n
wh
ils
t
r
ec
o
r
d
s
h
a
v
e
p
r
etty
e
n
tr
o
p
ic
d
is
tr
ib
u
tio
n
.
Plain
tex
tu
al
c
o
n
ten
t
en
tr
o
p
y
f
ee
is
ze
r
o
.
No
w
f
r
o
m
th
e
c
o
m
p
ar
ativ
e
h
a
s
a
lo
o
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o
f
en
tr
o
p
y
p
r
ice
b
e
twee
n
o
u
r
ap
p
r
o
ac
h
an
d
PR
NG
(
)
,
it'
s
f
ar
v
is
ib
le
th
at
th
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en
tr
o
p
y
f
ee
o
f
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r
ap
p
r
o
ac
h
is
clo
s
e
to
to
th
e
en
d
r
es
u
lt o
f
PR
NG
(
)
.
T
h
e
x
-
ax
is
s
h
o
ws th
e
k
ey
p
er
io
d
.
T
h
u
s
,
f
r
o
m
th
e
d
ef
in
itio
n
o
f
en
tr
o
p
ic
p
r
o
tectio
n
we
s
ay
th
at
it's
m
iles
im
p
o
s
s
ib
le
to
ar
e
ex
p
ec
tin
g
s
im
p
le
tex
tu
al
co
n
ten
t
f
r
o
m
ci
p
h
er
te
x
t
if
o
u
r
a
p
p
r
o
a
ch
is
u
s
ed
to
g
en
er
ate
s
ess
io
n
k
ey
a
n
d
t
h
e
u
s
ag
e
o
f
th
is
s
ess
io
n
k
ey
an
d
s
y
m
m
etr
ic
k
e
y
in
e
n
c
r
y
p
tio
n
g
iv
es r
o
b
u
s
tn
ess
.
6
.
3
.
Ana
ls
is
o
f
encr
y
ptio
n t
ec
hn
i
qu
e
I
n
s
ec
tio
n
we
h
a
v
e
an
al
y
s
ed
th
e
en
c
r
y
p
tio
n
tech
n
i
q
u
e
th
r
o
u
g
h
f
lo
atin
g
p
o
in
t
f
r
e
q
u
en
cy
an
d
h
is
to
g
r
am
o
f
ea
ch
s
h
ar
e
[
3
,
22
].
T
h
e
f
o
llo
win
g
T
a
b
le
6
s
h
o
w
s
th
e
f
lo
atin
g
p
o
in
t a
n
aly
s
is
.
T
ab
le
6
.
Flo
atin
g
p
o
in
t a
n
aly
s
is
S
h
a
r
e
P
l
a
i
n
t
e
x
t
C
i
p
h
e
r
t
e
x
t
b
y
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
h
m
ℎ
1
ℎ
2
ℎ
3
ℎ
4
ℎ
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
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Sy
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t
I
SS
N:
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4
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4
R
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u
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tio
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DN
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eq
u
en
ce
:
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of
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a
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t te
ch
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iq
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ec
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ir
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a
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o
w
mik
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73
Ob
s
er
v
atio
n
:
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h
e
f
lo
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f
a
cto
r
f
r
eq
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e
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cy
an
aly
s
is
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escr
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o
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b
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alu
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x
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d
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a
x
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t
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a
g
r
ap
h
ical1
r
ep
r
es
en
tatio
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o
f
a
f
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eq
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d
is
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i
b
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n
.
Her
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we'
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e
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e
d
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atio
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,
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u
c
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th
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d
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y
o
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cip
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t.
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h
e
p
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k
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ep
r
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th
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m
o
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t
n
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t
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n
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s
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al
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f
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r
ep
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esen
ts
h
o
w
a
g
o
o
d
d
ea
l
o
u
r
d
ata
v
ar
ies.
Fro
m
th
e
ab
o
v
e
T
ab
le
7
,
it
h
as
b
ee
n
d
is
co
v
er
ed
th
at
th
e
s
tatis
tics
ar
en
'
t
s
k
ewe
d
.
His
to
g
r
am
an
aly
s
is
:
T
ab
le7
.
His
to
g
r
am
a
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aly
s
is
S
h
a
r
e
P
l
a
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Te
x
t
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p
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r
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d
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t
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m
S
h
1
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h
2
S
h
3
S
h
4
S
h
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
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4
8
6
4
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t J Reco
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&
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m
b
ed
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Sy
s
t,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
65
–
76
74
Ob
s
er
v
atio
n
:
T
h
e
b
in
a
r
y
h
is
to
g
r
am
d
escr
ib
es
in
T
a
b
le
8
,
h
o
w
b
in
ar
y
v
alu
es
o
f
a
f
ile
ar
e
d
is
tr
ib
u
ted
alo
n
g
x
-
a
x
is
an
d
y
-
ax
is
.
T
h
e
h
is
to
g
r
am
an
aly
s
is
o
f
th
e
r
esu
lts
s
h
o
ws
th
at
d
i
s
tr
ib
u
tio
n
is
n
o
r
m
al
an
d
n
o
r
m
al
in
s
h
ap
e.
T
h
e
h
is
to
g
r
am
o
f
s
h
ar
es
g
en
er
ated
th
r
o
u
g
h
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
s
h
o
ws
th
e
d
ata
d
is
tr
ib
u
tio
n
in
s
h
ar
ed
f
ile
a
r
e
eq
u
al
wh
ich
p
r
o
v
es
th
e
e
n
cr
y
p
tio
n
u
s
in
g
s
ess
io
n
k
ey
is
g
o
o
d
.
Usi
n
g
an
y
n
u
m
b
er
o
f
s
h
ar
es
we
g
et
b
ac
k
th
e
e
n
cr
y
p
ted
f
il
e
an
d
f
r
o
m
en
c
r
y
p
te
d
f
ile
it
is
in
f
ea
s
ib
le
to
g
et
an
i
d
ea
ab
o
u
t
s
ess
io
n
k
ey
.
T
h
is
p
r
o
v
es st
r
en
g
th
o
f
o
u
r
s
ch
e
m
e
.
6
.
4
.
Co
m
pa
ra
t
iv
e
a
na
ly
s
is
T
h
e
f
o
llo
win
g
T
ab
le
8
s
h
o
ws
th
e
c
o
m
p
ar
ativ
e
an
aly
s
is
am
o
n
g
s
ec
r
et
s
h
ar
in
g
tech
n
iq
u
es
an
d
also
p
r
o
v
es th
e
n
o
v
elty
o
f
o
u
r
s
ch
e
m
e.
T
ab
le
8
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
S
c
h
e
mes
S
e
c
u
r
i
t
y
P
r
o
p
e
r
t
i
e
s
R
e
f
[
16
]
R
e
f
[
1
]
R
e
f
[
22
]
R
e
f
[
3
]
R
e
f
[
4
]
P
r
o
p
o
se
d
t
e
c
h
n
i
q
u
e
C
o
n
f
i
d
e
n
t
i
a
l
i
t
y
Y
e
s
No
No
No
Y
e
s
Y
e
s
I
n
t
e
g
r
i
t
y
No
No
No
No
Y
e
s
Y
e
s
A
u
t
h
e
n
t
i
c
i
t
y
(
mess
a
g
e
a
u
t
h
e
n
t
i
c
a
t
i
o
n
a
n
d
u
ser
a
u
t
h
e
n
t
i
c
a
t
i
o
n
)
Y
e
s
No
No
Y
e
s
No
Y
e
s
P
r
i
v
a
c
y
P
r
o
t
e
c
t
i
o
n
No
Y
e
s
No
Y
e
s
Y
e
s
Y
e
s
D
e
f
e
n
d
a
g
a
i
n
st
M
a
n
-
i
n
–
m
i
d
d
l
e
a
t
t
a
c
k
No
No
No
No
No
Y
e
s
V
u
l
n
e
r
a
b
i
l
i
t
y
No
No
No
Y
e
s
Y
e
s
Y
e
s
C
r
y
p
t
a
n
a
l
y
si
s
(
l
i
n
e
a
r
a
n
d
d
i
f
f
e
r
e
n
t
i
a
l
)
No
No
No
Y
e
s
Y
e
s
Y
e
s
S
e
ssi
o
n
k
e
y
e
s
t
a
b
l
i
sh
m
e
n
t
No
No
No
No
Y
e
s
Y
e
s
6
.
5
.
Aut
hentic
a
t
io
n
Fo
r
an
y
cr
y
p
o
s
y
s
tem
au
th
en
ti
ca
tio
n
is
an
im
p
o
r
tan
t
is
s
u
e.
I
n
th
is
ar
ticle
we
h
av
e
u
s
ed
tw
o
ty
p
es
o
f
au
th
en
ticatio
n
s
o
n
e
u
s
er
a
u
th
e
n
ticatio
n
an
d
o
th
er
m
ess
ag
e
a
u
th
en
ticatio
n
f
o
r
o
u
r
s
ec
r
et
s
h
ar
in
g
.
T
wo
t
y
p
es
o
f
au
th
en
ticatio
n
s
ar
e
d
escr
ib
ed
b
elo
w.
User
au
th
en
ticatio
n
[
1
,
6
]
e
n
s
u
r
es
th
at
o
n
ly
au
th
o
r
ized
u
s
er
s
ar
e
g
ain
in
g
ac
ce
s
s
to
s
ec
r
et
in
f
o
r
m
atio
n
o
r
d
ata.
W
ith
o
u
t
a
s
ec
u
r
e
a
u
th
en
ticatio
n
p
r
o
ce
s
s
,
an
y
tr
a
n
s
m
is
s
io
n
th
r
o
u
g
h
n
etwo
r
k
co
u
ld
b
e
at
r
is
k
.
C
er
t
ain
lo
g
in
in
f
o
r
m
atio
n
ar
e
r
eq
u
ir
ed
f
o
r
u
s
er
au
th
e
n
ticatio
n
.
Her
e
we
h
av
e
u
s
e
d
s
in
g
le
f
ac
to
r
a
u
th
en
ticatio
n
w
h
er
e
ev
er
y
s
h
ar
e
is
tr
an
s
m
itted
to
th
e
r
ec
eiv
er
en
d
th
r
o
u
g
h
its
p
u
b
lic
k
e
y
an
d
ea
ch
u
s
er
tak
es
its
s
h
ar
e
u
s
in
g
in
d
iv
i
d
u
al
p
r
i
v
ate
k
ey
.
T
h
ese
two
k
ey
s
ar
e
en
o
u
g
h
to
co
m
f
ir
m
th
e
u
s
er
’
s
id
en
tity
an
d
t
h
is
will a
llo
w
th
e
s
y
s
tem
t
o
au
th
o
r
ize
th
e
u
s
er
.
W
e
h
av
e
u
s
ed
MA
C
r
u
les
f
o
r
m
ess
ag
e
au
th
en
ticatio
n
,
p
r
im
a
r
ily
b
ased
o
n
s
y
m
m
etr
ic
k
ey
[
1
,
2
3
, 2
4
]
.
Her
e
MD
5
h
ash
alg
o
r
ith
m
is
u
s
ed
as
MA
C
f
ea
t
u
r
e
w
h
ich
co
m
p
r
ess
es
an
ar
b
itra
r
y
in
p
u
t
p
er
io
d
i
n
to
a
s
et
d
u
r
atio
n
o
u
tp
u
t
(
1
2
8
-
b
its
)
.
Sen
d
er
t
r
an
s
m
its
th
e
m
ess
ag
e
in
co
n
ju
n
ctio
n
with
th
e
MA
C
.
Af
ter
r
ec
eiv
in
g
th
e
m
ess
ag
e
an
d
th
e
MA
C
,
th
e
r
ec
eiv
er
r
ec
o
m
p
u
tes
th
e
MA
C
v
alu
e
b
y
u
s
in
g
th
e
s
y
m
m
etr
ic
k
ey
.
I
f
th
e
co
m
p
u
ted
MA
C
v
alu
e
d
o
es
n
o
w
n
o
t
f
it
with
th
e
MA
C
wh
ich
is
d
esp
atch
ed
f
r
o
m
th
e
s
en
d
er
,
r
ec
ei
v
er
s
af
ely
ass
u
m
es
th
at
th
e
m
ess
ag
e
is
n
'
t th
e
r
ea
l.
6
.
6
.
P
er
f
o
rma
nce
ev
a
lua
t
io
n
I
n
ev
e
r
y
test
in
r
esu
lt
s
ec
tio
n
,
th
er
e
is
an
o
b
s
er
v
atio
n
p
ar
t
wh
ich
p
r
o
v
id
es
t
h
e
p
e
r
f
o
r
m
a
n
ce
o
f
o
u
r
s
ch
em
e
o
n
t
h
e
b
asis
o
f
r
esu
lt
an
aly
s
is
o
f
th
e
test
.
Fro
m
th
e
an
aly
s
is
o
f
th
e
o
b
s
er
v
atio
n
s
,
we
s
ay
th
at
o
u
r
tech
n
iq
u
e
f
o
r
s
ec
r
et
s
h
a
r
in
g
is
b
etter
th
an
p
r
e
v
io
u
s
tech
n
iq
u
es
with
r
esp
ec
t
t
o
tim
e
co
m
p
le
x
ity
,
im
p
lem
en
tatio
n
a
n
d
r
o
b
u
s
tn
ess
.
I
n
o
u
r
p
ap
e
r
we
h
av
e
in
tr
o
d
u
ce
d
a
n
ew
m
ask
g
en
er
atio
n
alg
o
r
ith
m
wh
ich
is
ea
s
y
to
im
p
lem
en
t
an
d
u
n
d
er
s
tan
d
.
T
h
is
n
ew
m
ask
g
en
er
atio
n
p
r
o
ce
s
s
r
ed
u
ce
s
th
e
tim
e
co
m
p
lex
ity
.
So
th
is
is
th
e
b
etter
o
n
e
th
an
p
r
ev
io
u
s
m
ask
g
en
er
atio
n
alg
o
r
ith
m
also
T
h
e
DNA
s
eq
u
en
ce
p
r
o
v
id
e
s
th
e
n
o
n
lin
ea
r
ity
in
k
ey
g
en
er
atio
n
.
R
an
d
o
m
n
u
m
b
er
g
en
e
r
atio
n
f
r
o
m
r
ec
u
r
r
en
ce
r
elatio
n
is
also
an
im
p
o
r
ta
n
t
s
tep
i
n
cr
y
p
to
g
r
ap
h
y
an
d
d
if
f
er
en
t
ty
p
es
o
f
test
an
d
its
r
esu
lts
b
o
o
s
ts
th
e
claim
.
Secr
et
s
h
ar
in
g
is
v
er
y
r
elev
a
n
t
in
b
i
g
d
ata
an
d
cl
o
u
d
co
m
p
u
tin
g
e
n
v
ir
o
n
m
en
t.
Ou
r
tech
n
i
q
u
e
will
b
e
wid
ely
u
s
ed
i
n
th
is
en
v
ir
o
n
m
en
t
f
o
r
its
s
im
p
licity
,
n
o
v
elty
an
d
ea
s
y
i
m
p
lem
en
tatio
n
.
7.
CO
NCLU
SI
O
N
Her
e
we
h
av
e
p
r
esen
te
d
a
s
ec
u
r
ed
s
ess
io
n
k
e
y
b
ased
s
ec
r
et
s
h
ar
in
g
ap
p
r
o
ac
h
with
m
in
im
u
m
co
m
p
u
tatio
n
o
v
er
h
ea
d
.
Her
e
a
n
ew
m
ask
g
en
er
atio
n
al
g
o
r
it
h
m
is
in
tr
o
d
u
ce
d
f
o
r
s
ec
r
et
s
h
ar
e
g
en
er
atio
n
with
lo
w
co
m
p
lex
ity
.
I
n
th
is
alg
o
r
i
th
m
a
u
n
it
m
atr
ix
o
f
s
p
ec
if
ic
o
r
d
er
is
tak
en
.
T
h
e
n
u
m
b
er
o
f
p
ar
ticip
an
t
is
eq
u
al
t
o
o
r
d
e
r
o
f
m
atr
ix
.
T
h
e
Ses
s
io
n
k
ey
is
g
en
er
ate
d
u
s
in
g
th
e
c
o
n
ce
p
t
o
f
r
ec
u
r
r
e
n
ce
r
elatio
n
an
d
DNA
s
eq
u
en
ce
.
Ses
s
io
n
k
ey
as
well
as
s
ec
r
et
d
ata
is
s
h
ar
ed
am
o
n
g
s
et
o
f
s
p
ec
if
ic
n
u
m
b
er
o
f
p
a
r
ticip
an
ts
an
d
th
ese
p
ar
ticip
an
ts
ar
e
ab
le
to
r
ec
o
n
s
tr
u
ct
th
e
o
r
ig
in
al
m
ess
ag
e.
T
o
th
e
b
est
o
f
o
u
r
k
n
o
wled
g
e
th
is
is
th
e
b
est
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