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y
,
lattice
-
b
ased
cr
y
p
t
o
g
r
ap
h
y
,
an
d
c
o
d
e
-
b
ased
cr
y
p
to
g
r
ap
h
y
am
o
n
g
o
th
e
r
s
.
L
ea
d
i
n
g
PQC
ca
n
d
id
ates
m
ath
em
atica
lly
o
f
f
er
s
ec
u
r
ity
ev
en
ag
ain
s
t
ass
au
lt
b
y
a
f
u
ll
-
s
ca
le,
q
u
an
tu
m
co
m
p
u
ter
th
at
is
f
au
lt
-
to
ler
an
t
[
2
]
.
T
h
e
Natio
n
al
I
n
s
titu
te
o
f
Stan
d
ar
d
s
an
d
T
ec
h
n
o
lo
g
y
(
NI
ST)
o
f
th
e
Un
ited
States
lau
n
ch
e
d
a
m
u
lti
-
y
ea
r
g
lo
b
al
s
tan
d
ar
d
izatio
n
p
r
o
ce
s
s
in
2
0
1
7
to
th
o
r
o
u
g
h
ly
a
n
aly
s
e
p
o
s
t
-
q
u
an
tu
m
alg
o
r
ith
m
s
,
d
u
e
to
th
e
u
r
g
e
n
cy
b
y
th
e
q
u
an
tu
m
th
r
ea
t
an
d
s
elec
t
th
e
m
o
s
t
s
ec
u
r
e
an
d
ef
f
icien
t
d
esig
n
s
ac
r
o
s
s
en
cr
y
p
tio
n
,
s
i
g
n
atu
r
es,
an
d
k
ey
ex
ch
an
g
e
.
Ou
t
o
f
an
in
itial
f
ield
o
f
o
v
er
8
0
s
u
b
m
is
s
io
n
s
,
af
ter
th
r
ee
in
ten
s
iv
e
r
o
u
n
d
s
o
f
ass
e
s
s
m
en
t,
NI
S
T
an
n
o
u
n
ce
d
f
o
u
r
al
g
o
r
ith
m
s
in
J
u
ly
2
0
2
2
to
p
r
o
ce
ed
to
th
e
s
tan
d
ar
d
izatio
n
p
ip
elin
e
-
lattice
-
b
ased
cr
y
p
to
g
r
ap
h
i
c
s
u
ite
f
o
r
Alg
eb
r
aic
lattices
(
C
R
YSTA
L
S
)
-
Ky
b
er
,
N
-
th
d
eg
r
ee
tr
u
n
ca
te
d
p
o
ly
n
o
m
ial
r
i
n
g
u
n
it
(
NT
R
U
)
,
a
n
d
s
ec
u
r
ity
attr
ib
u
te
-
b
ased
s
ec
u
r
e
(
SAB
E
R
)
a
s
well
a
s
th
e
lattice
-
b
ased
s
ig
n
atu
r
e
s
ch
em
e
C
R
YSTA
L
S
-
Dilith
iu
m
.
Ad
d
itio
n
ally
,
f
o
u
r
o
th
er
ca
n
d
i
d
ates
in
clu
d
in
g
th
e
is
o
g
en
y
-
b
ased
s
u
p
e
r
s
in
g
u
lar
is
o
g
en
y
k
ey
en
ca
p
s
u
latio
n
(
SIK
E
)
wer
e
s
elec
ted
f
o
r
f
u
r
th
e
r
an
aly
s
is
in
th
e
f
o
u
r
t
h
r
o
u
n
d
.
As
PQC
co
n
tin
u
es
r
ap
id
m
at
u
r
atio
n
to
war
d
ev
en
t
u
al
r
ea
l
-
wo
r
ld
d
ep
lo
y
m
en
t
ac
r
o
s
s
th
e
in
ter
n
et'
s
tr
u
s
ted
p
u
b
lic
k
e
y
in
f
r
astru
ct
u
r
e,
in
s
p
ec
ialized
n
etwo
r
k
s
,
an
d
in
cr
itical
em
b
e
d
d
ed
d
e
v
ices,
ef
f
icien
t
a
n
d
v
er
if
iab
ly
s
ec
u
r
e
e
n
g
in
ee
r
i
n
g
is
cr
u
cial
alo
n
g
s
id
e
th
e
f
u
n
d
a
m
en
tal
r
esear
ch
.
W
h
ile
th
e
elab
o
r
ate
m
ath
em
atics
b
eh
in
d
s
ch
em
es
lik
e
Ky
b
e
r
an
d
SIK
E
m
ay
in
h
er
e
n
tly
p
r
o
v
i
d
e
q
u
a
n
tu
m
r
esil
ie
n
ce
,
s
id
e
-
ch
an
n
el
v
u
ln
er
ab
ilit
ies
in
tr
o
d
u
ce
d
in
im
p
lem
en
tatio
n
s
ca
n
s
till
en
ab
le
v
ar
io
u
s
p
r
ac
tical
attac
k
s
if
n
o
t
ad
d
r
ess
ed
.
Ph
y
s
ically
o
b
s
er
v
ab
le
ch
ar
ac
t
er
is
tics
d
u
r
in
g
an
o
p
er
atio
n
lik
e
tim
in
g
,
p
o
wer
c
o
n
s
u
m
p
tio
n
,
elec
tr
o
m
ag
n
etic
r
ad
iatio
n
,
an
d
m
o
r
e
ca
n
leak
s
ec
r
ets
th
at
b
y
p
ass
m
ath
em
atica
l
d
ef
en
ce
s
.
T
h
u
s
ex
te
n
s
iv
e
an
aly
s
is
o
f
a
s
id
e
-
ch
an
n
el
s
u
s
ce
p
tib
ilit
y
as
well
as
ef
f
ec
tiv
e
,
ef
f
icien
t
c
o
u
n
ter
m
ea
s
u
r
es
is
an
im
p
er
at
iv
e,
co
m
p
lem
en
tar
y
f
ac
et
o
f
f
u
n
d
am
e
n
tal
PQC
r
esear
ch
all
th
e
way
th
r
o
u
g
h
s
tan
d
ar
d
izatio
n
a
n
d
ad
o
p
tio
n
.
L
attice
-
b
ased
cr
y
p
to
g
r
ap
h
y
h
a
s
em
er
g
ed
as
a
lead
in
g
ap
p
r
o
a
ch
f
o
r
d
e
v
elo
p
in
g
PQC
s
ch
em
es
s
ec
u
r
e
ag
ain
s
t
q
u
an
tu
m
co
m
p
u
tin
g
a
ttack
s
[
3
]
.
T
h
e
C
R
YSTA
L
S
Ky
b
er
k
e
y
en
ca
p
s
u
latio
n
m
ec
h
an
is
m
(
KE
M)
is
a
p
r
o
m
in
e
n
t
lattice
-
b
ased
al
g
o
r
ith
m
cu
r
r
en
tly
u
n
d
e
r
g
o
i
n
g
e
v
alu
atio
n
f
o
r
p
o
s
t
-
q
u
an
tu
m
s
tan
d
ar
d
izatio
n
[
4
]
.
W
h
ile
th
e
u
n
d
er
ly
in
g
co
n
s
tr
u
ctio
n
p
r
o
m
is
es,
th
eo
r
etica
l
q
u
an
tu
m
r
esil
ien
ce
,
r
ea
l
-
wo
r
l
d
v
u
ln
er
ab
ilit
ies
s
till
n
ee
d
to
b
e
ass
ess
ed
b
ef
o
r
e
wi
d
esp
r
ea
d
im
p
lem
en
tatio
n
.
Sid
e
-
ch
an
n
el
attac
k
s
p
o
s
e
p
ar
ticu
lar
r
is
k
s
o
f
leak
in
g
s
ec
r
et
k
ey
in
f
o
r
m
atio
n
th
r
o
u
g
h
p
h
y
s
ical
em
an
atio
n
s
an
d
n
ee
d
co
u
n
ter
m
ea
s
u
r
es.
T
h
is
r
esear
ch
em
p
ir
ically
an
aly
s
es
th
e
s
id
e
-
ch
an
n
el
atta
ck
r
esil
ien
ce
o
f
h
ar
d
war
e
Ky
b
er
im
p
lem
en
tatio
n
s
to
ev
alu
ate
a
s
u
s
ce
p
tib
ilit
y
an
d
d
eter
m
in
e
ef
f
ec
tiv
e
d
ef
en
ce
s
.
Po
wer
an
aly
s
is
an
d
elec
tr
o
m
ag
n
etic
s
id
e
ch
an
n
els
ar
e
lev
er
ag
ed
to
ex
tr
ac
t
in
f
o
r
m
atio
n
.
A
d
u
al
r
ail
lo
g
ic
with
m
ask
in
g
is
an
aly
s
ed
as
a
co
u
n
ter
m
ea
s
u
r
e
s
tr
ateg
y
.
T
h
e
r
esu
lts
p
r
o
v
id
e
p
r
ac
tical
s
ec
u
r
ity
v
alid
atio
n
an
d
r
ec
o
m
m
e
n
d
atio
n
s
f
o
r
s
ec
u
r
in
g
n
ascen
t
p
o
s
t
-
q
u
a
n
tu
m
s
y
s
tem
s
as
th
ey
ar
e
in
teg
r
ated
in
to
c
o
m
m
u
n
icatio
n
in
f
r
astru
ctu
r
e
in
th
e
co
m
in
g
y
ea
r
s
.
Qu
an
tify
in
g
v
u
ln
er
ab
ilit
y
a
n
d
d
em
o
n
s
tr
atin
g
a
m
itig
atio
n
v
i
ab
ilit
y
ag
ain
s
t
co
n
tem
p
o
r
ar
y
attac
k
tech
n
iq
u
es
d
eliv
er
s
cr
u
cial
in
s
ig
h
t
b
ey
o
n
d
m
ath
em
atica
l p
r
o
o
f
s
alo
n
e
as
cr
y
p
to
g
r
ap
h
y
m
ig
r
ates in
to
th
e
q
u
an
tu
m
ag
e.
B
ased
o
n
t
h
e
f
i
n
d
i
n
g
s
o
f
t
h
i
s
s
t
u
d
y
,
th
e
s
u
b
s
e
q
u
e
n
t
s
i
g
n
if
i
ca
n
c
es
ar
e
c
o
n
s
id
er
e
d
p
a
r
a
m
o
u
n
t
i
n
co
n
t
r
i
b
u
ti
n
g
t
o
th
e
e
x
is
t
i
n
g
b
o
d
y
o
f
k
n
o
wl
ed
g
e
r
eg
ar
d
i
n
g
PQC
s
e
c
u
r
it
y
.
Fi
r
s
t
ly
,
it
p
r
o
p
o
s
es
a
n
ex
te
n
s
i
v
e
em
p
i
r
ic
al
ass
ess
m
e
n
t
o
f
s
id
e
-
c
h
a
n
n
el
v
u
l
n
er
a
b
ili
ty
o
n
a
p
i
ec
e
o
f
h
a
r
d
wa
r
e
t
h
a
t i
m
p
le
m
e
n
ts
C
R
YSTA
L
S
-
K
y
b
e
r
an
d
tak
es
ca
r
e
o
f
t
h
e
ab
s
en
ce
o
f
th
o
r
o
u
g
h
s
ec
u
r
ity
ass
ess
m
en
ts
o
f
th
is
p
r
o
m
is
in
g
p
o
s
t
-
q
u
an
tu
m
ca
n
d
id
ate.
T
h
e
s
tu
d
y
m
ea
s
u
r
es
th
e
ef
f
icien
cy
o
f
d
if
f
er
en
t
m
ask
in
g
s
tr
a
teg
ies
co
n
s
id
er
in
g
h
o
w
well
th
ey
p
r
o
tect
ag
ain
s
t
p
o
wer
an
al
y
s
is
attac
k
s
,
it
p
r
o
v
id
es
r
ea
l
n
u
m
b
er
s
o
n
th
e
im
p
r
o
v
em
en
t
in
s
ec
u
r
ity
th
at
is
o
b
t
ain
ab
le
ag
ain
s
t
th
e
co
s
t
o
f
im
p
lem
en
tatio
n
.
T
h
is
wo
r
k
an
aly
s
es
b
o
th
th
e
p
o
wer
an
d
elec
tr
o
m
ag
n
etic
s
id
e
-
ch
a
n
n
el,
an
d
th
e
r
ef
o
r
e
p
r
o
v
id
es
with
d
i
f
f
er
en
t
i
n
f
o
r
m
atio
n
ab
o
u
t
p
o
ten
tial
attac
k
s
c
o
m
p
ar
ed
to
th
e
wo
r
k
s
wh
ich
h
av
e
b
ee
n
f
o
c
u
s
in
g
o
n
ly
o
n
th
e
p
o
wer
an
aly
s
is
.
Fu
r
th
er
,
it
also
p
r
esen
ts
an
d
an
aly
ze
s
n
ew
b
len
d
ed
co
u
n
te
r
m
ea
s
u
r
es
b
ased
o
n
b
o
th
h
ig
h
e
r
-
lev
el
m
ask
in
g
an
d
co
n
tr
o
lled
tim
e
d
is
p
er
s
io
n
t
h
at
im
p
r
o
v
e
th
e
ex
is
tin
g
s
id
e
-
ch
an
n
el
p
r
o
tectio
n
m
eth
o
d
s
f
o
r
lattice
-
b
ased
cr
y
p
to
s
y
s
tem
s
.
T
h
ese
co
n
tr
ib
u
tio
n
s
f
ill
th
e
e
x
is
tin
g
k
n
o
wled
g
e
g
ap
s
in
th
e
ev
alu
atio
n
o
f
s
id
e
-
ch
a
n
n
el
attac
k
s
f
o
r
p
o
s
t
-
q
u
an
tu
m
alg
o
r
ith
m
s
an
d
p
r
o
v
i
d
e
b
o
t
h
n
ew
th
e
o
r
etica
l
f
r
am
ewo
r
k
s
an
d
p
r
ac
tical
r
e
co
m
m
en
d
atio
n
s
f
o
r
d
esig
n
in
g
s
id
e
-
ch
an
n
el
r
o
b
u
s
t
cr
y
p
to
g
r
ap
h
ic
alg
o
r
ith
m
s
.
T
h
is
wo
r
k
o
f
f
er
s
im
p
o
r
ta
n
t
g
u
id
an
ce
in
th
e
r
ea
l
-
wo
r
ld
co
s
t
o
f
s
ec
u
r
ity
,
p
er
f
o
r
m
an
ce
,
an
d
r
eso
u
r
ce
co
n
s
u
m
p
tio
n
b
ased
o
n
s
u
b
s
tan
tial
PQ
C
im
p
lem
en
tatio
n
s
an
d
co
m
p
ar
ativ
e
s
tu
d
ies
ca
r
r
ied
o
u
t
in
th
is
r
esear
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h
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ib
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tes
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e
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p
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t
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f
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tr
ateg
ies
f
o
r
co
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p
r
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e
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iv
e
r
is
k
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aly
s
is
a
n
d
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o
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ter
m
ea
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r
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ag
ain
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t
C
R
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L
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-
Ky
b
er
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s
u
r
e
th
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o
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tim
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m
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ec
u
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it
y
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c
r
y
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t
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ap
h
ic
s
y
s
tem
s
in
th
e
co
n
te
x
t
o
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n
ewly
d
is
co
v
e
r
ed
th
r
ea
t
s
ce
n
a
r
io
s
b
ased
o
n
q
u
an
t
u
m
co
m
p
u
tin
g
.
T
h
e
r
esu
lts
an
d
ap
p
r
o
ac
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escr
ib
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er
e
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o
t
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ly
s
tr
en
g
th
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th
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ec
u
r
ity
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Ar
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I
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tell
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SS
N:
2252
-
8
9
3
8
S
ec
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g
p
o
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t
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u
a
n
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m
cryp
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r
a
p
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y:
s
id
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n
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el
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C
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S
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5253
o
f
C
R
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L
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Ky
b
er
in
s
tan
tiatio
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s
b
u
t
also
o
f
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e
r
a
p
r
o
ce
d
u
r
e
to
e
v
alu
ate
a
n
d
im
p
r
o
v
e
th
e
s
id
e
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ch
an
n
el
s
id
e
o
f
o
t
h
er
PQC
co
n
te
n
d
er
s
.
Fig
u
r
e
1
illu
s
tr
ates
p
o
o
ls
f
o
r
m
a
n
ag
in
g
k
e
y
s
in
q
u
an
tu
m
cr
y
p
to
g
r
ap
h
y
co
m
m
u
n
icatio
n
n
etwo
r
k
s
.
I
n
th
is
in
s
tan
ce
,
th
e
q
u
a
n
tity
o
f
q
u
an
tu
m
k
ey
s
h
el
d
b
y
e
v
er
y
q
u
a
n
tu
m
k
ey
d
is
tr
ib
u
tio
n
(
QKD
)
d
o
m
ain
.
I
n
r
ec
e
n
t
y
ea
r
s
,
s
ig
n
if
ican
t
a
d
v
an
ce
s
h
av
e
b
ee
n
m
ad
e
in
t
h
e
s
tate
o
f
th
e
ar
t
in
s
id
e
ch
a
n
n
el
an
aly
s
is
o
f
PQC
,
with
f
o
cu
s
o
n
lattice
-
b
ased
s
ch
em
es
lik
e
C
R
YSTA
L
S
-
Ky
b
er
t
h
at
h
a
v
e
b
ee
n
d
is
cu
s
s
ed
o
v
er
liter
atu
r
e
r
ev
iew
s
ec
tio
n
o
f
th
is
p
ap
er
.
Desp
ite
p
r
o
v
id
in
g
p
r
o
m
is
e
ag
ain
s
t
s
im
p
le
p
o
wer
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aly
s
is
at
tack
s
,
th
eir
wo
r
k
o
n
f
ir
s
t
o
r
d
er
m
ask
in
g
f
o
r
Ky
b
er
leav
es
o
p
en
q
u
esti
o
n
s
ab
o
u
t
h
o
w
to
d
ef
en
d
ag
ai
n
s
t
h
ig
h
er
o
r
d
er
attac
k
s
.
Ou
r
wo
r
k
attem
p
ts
to
clo
s
e
th
e
g
a
p
b
etwe
en
th
eo
r
etica
l
s
ec
u
r
ity
g
u
ar
an
tees
an
d
p
r
ac
tical
im
p
le
m
en
tatio
n
is
s
u
es
in
Ky
b
er
h
ar
d
war
e
d
e
p
lo
y
m
e
n
ts
b
y
ad
d
r
ess
in
g
th
ese
asp
ec
ts
.
T
h
is
s
tu
d
y
b
u
ild
s
u
p
o
n
t
h
ese
f
o
u
n
d
atio
n
s
b
y
:
i)
A
co
m
p
r
eh
e
n
s
iv
e
s
id
e
ch
an
n
el
s
ec
u
r
ity
an
aly
s
is
f
o
r
all
Ky
b
e
r
p
ar
am
eter
s
ets o
n
FP
GA
p
lat
f
o
r
m
s
.
ii)
C
h
ao
tic
an
aly
s
is
o
f
h
ig
h
er
o
r
d
er
m
ask
in
g
(
u
p
to
8
b
its
)
v
s
.
a
d
v
an
ce
d
p
o
wer
a
n
aly
s
is
.
iii)
A
n
o
v
el
h
y
b
r
id
co
u
n
ter
m
ea
s
u
r
e
th
at
co
m
b
in
es m
ask
in
g
with
co
n
tr
o
lled
tim
e
r
an
d
o
m
izatio
n
.
iv
)
Dem
o
n
s
tr
ate
th
e
v
alid
atio
n
o
f
p
r
o
p
o
s
ed
c
o
u
n
te
r
m
ea
s
u
r
es
in
r
ea
l
I
o
T
,
f
in
a
n
cial
,
an
d
s
atellite
co
m
m
u
n
icatio
n
.
Fig
u
r
e
1
.
Stru
ctu
r
e
o
f
q
u
a
n
tu
m
k
ey
m
a
n
ag
em
e
n
t sy
s
tem
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
2
.
1
.
Q
ua
ntu
m
k
e
y
dis
t
ributi
o
n a
nd
po
s
t
-
qu
a
ntum
cr
y
pto
g
ra
ph
y
Qu
an
tu
m
co
m
p
u
tin
g
in
cr
y
p
t
o
g
r
ap
h
y
h
as
b
ee
n
a
f
o
c
u
s
o
f
r
esear
ch
in
ter
est
f
o
r
th
e
p
ast
co
u
p
le
o
f
d
ec
ad
es.
T
h
is
f
ield
o
f
s
tu
d
y
was
in
tr
o
d
u
ce
d
b
y
R
ich
ar
d
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n
m
an
i
n
1
9
8
2
a
n
d
is
b
ased
o
n
th
e
c
o
n
ce
p
t
o
f
q
u
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tu
m
co
m
p
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ter
s
th
at
ca
n
s
im
u
late
q
u
a
n
tu
m
s
y
s
tem
s
m
u
ch
m
o
r
e
ef
f
ec
tiv
ely
th
an
class
ical
co
m
p
u
ter
s
.
Sin
ce
th
en
,
s
cien
tis
ts
h
av
e
b
e
en
lo
o
k
in
g
at
h
o
w
th
e
ch
em
i
ca
l
an
d
p
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y
s
ical
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ts
th
at
co
n
s
titu
te
q
u
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ec
h
an
ics
co
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ld
b
e
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s
ed
t
o
s
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en
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en
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et
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o
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s
o
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cr
y
p
tio
n
,
a
n
d
p
o
s
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le
d
er
ailin
g
th
e
co
n
v
en
tio
n
al
cr
y
p
to
g
r
ap
h
ic
m
o
d
els.
Path
ar
e
an
d
Desh
m
u
k
h
[
5
]
h
av
e
b
ee
n
s
tu
d
y
in
g
th
e
p
o
s
s
ib
ilit
ies
o
f
q
u
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tu
m
co
m
p
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tin
g
f
o
r
c
r
y
p
to
g
r
ap
h
y
f
o
r
s
ev
er
al
d
ec
ad
es.
Stu
d
ies
s
h
o
w
th
at
t
h
e
s
tr
en
g
th
o
f
s
o
m
e
m
ath
em
atica
l
p
r
o
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lem
s
,
s
u
ch
as
f
ac
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in
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b
ig
p
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im
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n
u
m
b
er
s
an
d
co
m
p
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tin
g
d
is
cr
ete
lo
g
ar
i
th
m
s
,
is
es
s
en
tial
to
k
ey
cr
y
p
to
g
r
ap
h
y
.
Ho
wev
er
,
q
u
an
tu
m
c
o
m
p
u
ter
s
m
ay
b
e
a
b
le
to
s
o
lv
e
th
ese
p
r
o
b
lem
s
m
u
ch
f
aster
u
s
in
g
al
g
o
r
ith
m
s
li
k
e
Sh
o
r
'
s
alg
o
r
ith
m
.
T
h
is
co
u
ld
b
r
ea
k
wid
ely
u
s
ed
s
ch
em
es
lik
e
R
SA
en
cr
y
p
tio
n
.
R
esear
ch
er
s
h
av
e
th
u
s
in
v
esti
g
ated
q
u
a
n
tu
m
k
ey
d
is
tr
ib
u
tio
n
an
d
o
th
er
q
u
a
n
tu
m
cr
y
p
to
g
r
ap
h
ic
m
eth
o
d
s
th
a
t
co
u
ld
b
e
r
esis
tan
t
ev
en
to
q
u
an
tu
m
c
o
m
p
u
ter
s
.
QKD
p
r
o
to
co
ls
lik
e
B
en
n
ett
an
d
B
r
ass
ar
d
1
9
8
4
(
B
B
8
4
)
e
n
co
d
e
in
f
o
r
m
atio
n
in
q
u
an
tu
m
s
tates
o
f
p
h
o
to
n
s
.
T
h
e
B
B
8
4
p
r
o
to
co
l
tr
an
s
m
its
p
h
o
to
n
s
p
o
lar
ized
v
e
r
tically
,
h
o
r
izo
n
tally
,
4
5
°
d
iag
o
n
al
o
r
1
3
5
°
d
iag
o
n
al,
r
ep
r
esen
tin
g
b
it
v
alu
es
o
f
0
an
d
1
.
An
ea
v
esd
r
o
p
p
er
d
is
tu
r
b
i
n
g
th
ese
q
u
an
tu
m
s
tates
will
b
e
d
etec
ted
th
r
o
u
g
h
er
r
o
r
s
.
T
h
is
allo
ws
two
p
ar
ti
es
to
s
ec
u
r
ely
s
h
ar
e
r
an
d
o
m
b
it
k
ey
s
.
T
h
e
s
ec
u
r
ity
o
f
B
B
8
4
ca
n
b
e
p
r
o
v
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
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tif
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tell
,
Vo
l.
1
4
,
No
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6
,
Dec
em
b
er
2
0
2
5
:
5
2
5
1
-
5
2
6
7
5254
in
f
o
r
m
atio
n
-
th
eo
r
etica
lly
u
s
in
g
en
tr
o
p
y
ca
lcu
latio
n
s
.
I
f
th
e
b
it
e
r
r
o
r
r
ate
is
lo
w
e
n
o
u
g
h
,
E
v
e'
s
in
f
o
r
m
atio
n
I
(
A;E
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ab
o
u
t th
e
k
e
y
is
less
th
an
Alice
an
d
B
o
b
'
s
s
h
ar
ed
in
f
o
r
m
atio
n
I
(
A;B
)
.
T
h
is
g
u
ar
an
te
es secu
r
e
k
ey
s
.
(
;
)
<
(
;
)
(
1
)
Oth
er
QKD
p
r
o
to
c
o
ls
lik
e
co
h
er
en
t
o
n
e
-
wa
y
(
C
OW
)
s
ch
em
e
en
c
o
d
e
in
f
o
r
m
atio
n
i
n
p
h
o
to
n
tr
an
s
m
is
s
io
n
tim
e.
Secu
r
ity
p
r
o
o
f
s
r
ely
o
n
en
t
r
o
p
y
an
d
a
u
t
h
en
ticated
ch
an
n
el
ass
u
m
p
tio
n
s
[
6
]
.
Ni
et
a
l
.
[
7
]
h
ig
h
lig
h
ted
n
o
v
el
cr
y
p
to
g
r
ap
h
y
tech
n
iq
u
es
th
at
with
s
tan
d
attac
k
s
f
r
o
m
q
u
a
n
tu
m
an
d
tr
a
d
itio
n
al
co
m
p
u
ter
s
alik
e.
T
h
is
n
ew
f
ield
is
ca
lled
PQC
.
On
e
alg
o
r
ith
m
ca
lled
SIK
E
u
s
es
s
u
p
er
s
in
g
u
lar
is
o
g
en
ies
to
g
e
n
er
ate
en
cr
y
p
tio
n
k
e
y
s
.
T
h
e
y
h
av
e
s
tu
d
ied
way
s
t
o
o
p
tim
ize
h
ar
d
war
e
im
p
lem
en
tatio
n
s
o
f
SIK
E
.
T
h
e
y
h
av
e
d
esig
n
ed
im
p
r
o
v
e
d
m
u
ltip
lie
r
cir
cu
its
th
at
ca
n
p
er
f
o
r
m
m
ath
em
atica
l
o
p
er
atio
n
s
f
aster
.
Oth
er
wo
r
k
h
as
f
o
cu
s
ed
o
n
ar
r
an
g
in
g
th
e
co
m
p
u
tatio
n
s
in
an
ef
f
icien
t
p
ip
elin
ed
m
an
n
e
r
to
in
cr
ea
s
e
s
p
ee
d
s
.
An
o
th
er
alg
o
r
ith
m
ca
lled
K
y
b
er
t
h
at
is
b
ased
o
n
lattices
h
as
also
b
ee
n
o
p
tim
ized
.
Ky
b
e
r
u
s
es
a
tech
n
iq
u
e
c
alled
n
u
m
b
er
th
e
o
r
etic
tr
an
s
f
o
r
m
s
to
p
er
f
o
r
m
th
e
m
u
ltip
licatio
n
o
f
lar
g
e
n
u
m
b
e
r
s
m
o
r
e
ef
f
i
cien
tly
.
Har
d
war
e
ac
ce
ler
ato
r
s
h
av
e
b
e
en
d
e
v
elo
p
ed
to
im
p
lem
en
t th
e
tr
a
n
s
f
o
r
m
atio
n
s
an
d
o
t
h
er
o
p
er
atio
n
s
i
n
Ky
b
er
[
8
]
.
Ug
wu
is
h
iwu
et
a
l
.
[
9
]
f
o
cu
s
ed
o
n
e
x
p
lo
r
i
n
g
h
o
w
q
u
an
t
u
m
co
m
p
u
ter
s
co
u
ld
b
r
ea
k
tr
ad
itio
n
al
en
cr
y
p
tio
n
.
On
e
im
p
o
r
tan
t
f
i
n
d
in
g
was
Sh
o
r
'
s
alg
o
r
ith
m
,
wh
ich
s
h
o
ws
h
o
w
a
q
u
an
t
u
m
co
m
p
u
ter
m
ay
ef
f
ec
tiv
ely
d
eter
m
in
e
a
v
er
y
b
ig
n
u
m
b
e
r
'
s
p
r
im
e
f
ac
to
r
s
.
T
h
is
wo
u
ld
r
en
d
er
m
a
n
y
c
o
m
m
o
n
p
u
b
lic
-
k
ey
en
cr
y
p
tio
n
m
eth
o
d
s
in
s
ec
u
r
e.
Su
b
s
eq
u
en
t
wo
r
k
s
tu
d
ied
h
o
w
to
im
p
lem
en
t
Sh
o
r
'
s
al
g
o
r
ith
m
o
n
ac
tu
al
q
u
an
tu
m
co
m
p
u
ter
s
as
th
ey
w
er
e
b
u
ilt.
T
h
e
y
h
a
v
e
s
tu
d
ied
t
h
e
s
ec
u
r
ity
o
f
d
if
f
e
r
en
t
q
u
an
t
u
m
k
ey
d
is
tr
ib
u
tio
n
p
r
o
to
co
ls
an
d
th
eir
r
esil
ien
ce
ag
ain
s
t
attac
k
s
w
ith
f
u
tu
r
e
q
u
an
tu
m
co
m
p
u
ter
s
.
W
o
r
k
h
as
also
f
o
cu
s
ed
o
n
d
ev
elo
p
in
g
"
p
o
s
t
-
q
u
a
n
tu
m
"
c
r
y
p
to
g
r
ap
h
y
s
tan
d
a
r
d
s
th
at
c
o
u
ld
b
e
s
ec
u
r
e
e
v
en
ag
ain
s
t
q
u
a
n
tu
m
attac
k
s
u
tili
zin
g
Sh
o
r
'
s
alg
o
r
ith
m
[
1
0
]
.
Nir
au
la
et
a
l
.
[
1
1
]
h
av
e
p
r
o
m
p
ted
r
esear
ch
in
to
q
u
an
tu
m
-
r
esis
tan
t
cr
y
p
to
g
r
a
p
h
ic
s
y
s
tem
s
th
at
co
u
ld
with
s
tan
d
a
n
attac
k
f
r
o
m
a
q
u
a
n
tu
m
c
o
m
p
u
ter
.
PQC
is
o
n
e
ap
p
r
o
ac
h
b
ein
g
d
e
v
el
o
p
ed
to
cr
ea
te
n
ew
p
u
b
lic
-
k
e
y
en
c
r
y
p
tio
n
s
tan
d
a
r
d
s
.
Oth
er
s
tu
d
ies
h
av
e
f
o
c
u
s
ed
o
n
s
tu
d
y
in
g
th
e
p
er
f
o
r
m
an
ce
d
if
f
er
en
ce
s
b
etwe
en
q
u
an
t
u
m
an
d
class
i
ca
l
alg
o
r
ith
m
s
f
o
r
s
im
ilar
p
r
o
b
lem
s
.
R
esear
ch
er
s
h
av
e
f
o
u
n
d
th
at
q
u
an
tu
m
alg
o
r
ith
m
s
lik
e
f
o
r
d
atab
as
e
s
ea
r
ch
is
s
u
es,
Gr
o
v
er
'
s
ap
p
r
o
ac
h
en
a
b
les
q
u
ad
r
atic
i
m
p
r
o
v
e
m
en
ts
o
v
e
r
co
n
v
en
tio
n
al
alg
o
r
ith
m
s
.
T
h
is
h
as
im
p
licatio
n
s
in
ter
m
s
o
f
h
o
w
q
u
ick
ly
a
q
u
an
t
u
m
co
m
p
u
ter
m
ay
b
e
ab
le
to
s
ea
r
ch
th
r
o
u
g
h
e
n
cr
y
p
ted
d
ata
[
1
2
]
.
Ng
u
y
en
et
a
l
.
[
1
3
]
f
o
cu
s
ed
o
n
h
o
w
to
im
p
lem
e
n
t
q
u
a
n
tu
m
k
ey
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
to
s
ec
u
r
ely
tr
an
s
m
it
en
cr
y
p
ti
o
n
k
ey
s
b
etw
ee
n
d
if
f
e
r
en
t
lo
ca
tio
n
s
.
T
h
e
y
h
av
e
p
r
o
p
o
s
ed
tech
n
i
q
u
es
f
o
r
s
ep
ar
atin
g
q
u
an
tu
m
s
ig
n
als
f
r
o
m
class
ical
d
ata
s
ig
n
als
s
in
ce
th
ey
o
f
ten
n
ee
d
to
b
e
tr
an
s
m
itted
to
g
eth
er
o
n
th
e
s
am
e
o
p
tical
f
ib
e
r
s
.
Pro
p
er
ly
r
o
u
tin
g
th
e
q
u
a
n
tu
m
s
ig
n
als
ca
n
h
elp
r
ed
u
ce
is
s
u
es
ca
u
s
ed
b
y
th
e
class
ical
s
ig
n
als.
Oth
er
wo
r
k
h
as
f
o
cu
s
ed
o
n
h
o
w
to
d
esig
n
n
etwo
r
k
ar
ch
itectu
r
e
an
d
r
o
u
tin
g
alg
o
r
ith
m
s
th
at
o
p
tim
ize
k
ey
g
e
n
er
atio
n
a
n
d
d
is
tr
ib
u
tio
n
.
T
h
is
in
clu
d
es
d
e
ter
m
in
in
g
th
e
b
est
p
ath
s
ac
r
o
s
s
th
e
n
etwo
r
k
to
d
eliv
er
k
e
y
s
wh
er
e
th
ey
ar
e
n
ee
d
ed
.
Ad
d
itio
n
al
r
esear
ch
aim
ed
to
in
teg
r
ate
q
u
a
n
tu
m
k
ey
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
with
ap
p
licatio
n
s
th
at
r
eq
u
ir
e
s
ec
r
et
k
e
y
s
[
1
4
]
.
2
.
2
.
H
a
rdwa
re
im
plem
ent
a
t
io
ns
a
nd
ef
f
iciency
o
ptim
iza
t
io
n
W
u
et
a
l
.
[
1
5
]
h
a
v
e
ex
p
l
o
r
e
d
m
an
y
d
if
f
er
en
t
a
p
p
r
o
ac
h
es
f
o
r
p
er
f
o
r
m
i
n
g
m
o
d
u
lar
m
u
ltip
licatio
n
ef
f
icien
tly
.
On
e
ea
r
ly
m
et
h
o
d
was
Mo
n
tg
o
m
er
y
r
ed
u
ctio
n
,
wh
ich
was
in
tr
o
d
u
ce
d
in
1
9
8
5
.
T
h
is
m
eth
o
d
av
o
id
s
tr
ial
d
iv
is
io
n
an
d
allo
ws
m
o
d
u
lar
m
u
ltip
licatio
n
t
o
b
e
p
er
f
o
r
m
e
d
with
o
n
ly
ad
d
itio
n
s
an
d
s
h
if
ts
.
Ho
wev
er
,
it
d
o
es
r
e
q
u
ir
e
p
r
ec
o
m
p
u
tin
g
v
alu
es.
L
ater
w
o
r
k
f
o
cu
s
ed
o
n
o
p
tim
izin
g
a
m
o
d
u
lar
m
u
ltip
licatio
n
f
o
r
u
s
e
in
p
o
s
t
-
q
u
a
n
tu
m
c
r
y
p
t
o
s
y
s
tem
s
estab
lis
h
ed
o
n
is
o
g
en
ies,
as
th
e
s
u
p
er
s
in
g
u
lar
is
o
g
en
y
Dif
f
ie
–
Hellm
a
n
k
ey
e
x
ch
an
g
e
(
SID
H)
.
Dif
f
er
en
t
alg
o
r
ith
m
s
wer
e
p
r
o
p
o
s
ed
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
f
i
eld
m
u
ltip
licatio
n
s
n
ee
d
ed
,
in
clu
d
i
n
g
f
ast
f
in
ite
f
ield
m
u
ltip
lier
1
(
FF
M1
)
,
F
FM2
,
an
d
im
p
r
o
v
ed
f
ast
f
in
i
te
f
ield
m
u
ltip
lier
(
I
FF
M
)
.
Har
d
war
e
ar
ch
itect
u
r
e
wer
e
also
d
esig
n
ed
to
im
p
lem
en
t
th
ese
alg
o
r
ith
m
s
ef
f
icien
tly
u
s
in
g
tech
n
iq
u
es lik
e
p
a
r
alleliza
tio
n
ac
r
o
s
s
m
u
ltip
le
m
u
ltip
lier
s
[
1
6
]
.
C
h
en
g
et
a
l
.
[
1
7
]
d
is
cu
s
s
es
h
o
w
q
u
an
tu
m
c
r
y
p
t
o
g
r
ap
h
y
c
o
m
m
u
n
icatio
n
h
as
s
ev
er
al
ad
v
an
t
ag
es
o
v
er
tr
ad
itio
n
al
cr
y
p
t
o
g
r
a
p
h
y
m
et
h
o
d
s
.
I
t
h
as
b
ee
n
u
s
ed
t
o
s
ec
u
r
ely
co
n
n
ec
t
n
etwo
r
k
s
f
o
r
g
o
v
er
n
m
en
t
a
g
en
cies,
b
an
k
s
,
an
d
f
in
an
cial
in
s
titu
tio
n
s
d
u
e
to
th
e
n
ee
d
to
p
r
o
tect
s
en
s
itiv
e
d
ata.
I
t
is
also
b
ei
n
g
im
p
lem
en
ted
in
p
o
wer
g
r
id
s
an
d
u
tili
ty
n
etwo
r
k
s
to
en
cr
y
p
t
co
m
m
u
n
icatio
n
s
as
th
ese
s
y
s
tem
s
b
ec
o
m
e
m
o
r
e
au
to
m
ated
a
n
d
in
ter
co
n
n
ec
ted
.
Satellite
-
b
ased
q
u
a
n
tu
m
cr
y
p
to
g
r
a
p
h
y
n
et
wo
r
k
s
ar
e
b
ein
g
ex
p
lo
r
ed
f
o
r
ap
p
licatio
n
s
th
at
r
eq
u
ir
e
lo
n
g
d
is
tan
ce
s
ec
u
r
e
tr
an
s
m
is
s
io
n
.
T
h
e
p
ap
er
o
u
tlin
e
s
s
o
m
e
ch
allen
g
es
th
at
s
till
n
e
ed
to
b
e
ad
d
r
ess
ed
f
o
r
wid
er
ad
o
p
tio
n
o
f
t
h
is
tech
n
o
lo
g
y
.
T
h
e
m
a
x
im
u
m
t
r
an
s
m
is
s
io
n
d
is
tan
ce
s
o
v
er
o
p
tical
f
ib
er
a
r
e
cu
r
r
en
tl
y
lim
ited
to
ar
o
u
n
d
5
0
-
1
0
0
k
m
[
1
8
]
.
Pas
tu
s
h
en
k
o
an
d
Kr
o
n
b
er
g
[
1
9
]
d
is
cu
s
s
es
r
esear
ch
o
n
im
p
r
o
v
in
g
th
e
s
ec
u
r
ity
o
f
p
r
o
to
co
ls
f
o
r
th
e
QKD.
W
ith
QKD,
two
p
eo
p
l
e
ca
n
cr
ea
te
a
s
h
ar
e
d
r
a
n
d
o
m
k
ey
th
at
is
o
n
ly
k
n
o
wn
to
th
em
.
b
y
e
n
co
d
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
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tell
I
SS
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-
8
9
3
8
S
ec
u
r
in
g
p
o
s
t
-
q
u
a
n
tu
m
cryp
to
g
r
a
p
h
y:
s
id
e
-
c
h
a
n
n
el
r
esil
ien
ce
in
C
R
YS
TALS
-
K
yb
er
…
(
S
h
r
ey
a
s
K
a
s
tu
r
e)
5255
in
f
o
r
m
atio
n
in
th
e
p
o
la
r
izatio
n
o
f
p
h
o
to
n
s
.
Ho
wev
e
r
,
a
n
ea
v
esd
r
o
p
p
e
r
c
o
u
ld
tr
y
to
in
ter
c
ep
t
th
e
p
h
o
to
n
s
a
n
d
o
b
tain
s
o
m
e
in
f
o
r
m
atio
n
ab
o
u
t
th
e
k
ey
.
T
h
e
au
th
o
r
s
s
u
g
g
est
a
way
t
o
r
aise
t
h
e
s
ec
r
et
k
ey
r
ate
with
o
u
t
ch
an
g
in
g
th
e
QKD
h
ar
d
wa
r
e
o
r
p
r
o
to
co
ls
t
h
at
ar
e
cu
r
r
e
n
tly
in
u
s
e.
T
h
ey
s
u
g
g
est
e
n
cr
y
p
tin
g
er
r
o
r
co
r
r
ec
tio
n
co
m
m
u
n
icatio
n
s
u
s
in
g
o
n
e
o
f
th
e
k
e
y
s
th
at
was
p
r
e
-
d
is
tr
ib
u
ted
,
r
ath
e
r
th
a
n
tr
an
s
m
itti
n
g
th
is
in
f
o
r
m
atio
n
in
th
e
clea
r
.
T
h
is
d
en
ies
an
ea
v
esd
r
o
p
p
er
ac
ce
s
s
to
th
e
er
r
o
r
co
r
r
ec
tio
n
d
ata
.
B
y
en
cr
y
p
ti
n
g
er
r
o
r
co
r
r
ec
tio
n
,
leg
itima
te
u
s
er
s
ca
n
g
en
er
ate
m
o
r
e
s
ec
u
r
e
k
ey
b
its
co
m
p
ar
e
d
to
th
e
ac
ce
s
s
ib
le
in
f
o
r
m
atio
n
b
o
u
n
d
[
2
0
]
.
Fo
u
r
n
ar
is
et
a
l
.
[
2
1
]
h
av
e
s
tu
d
ied
h
o
w
to
im
p
lem
en
t
PQC
s
ch
em
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em
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.
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Dilith
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n
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SP
HI
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a
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ly
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th
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m
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in
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h
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ll
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s
ag
e.
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attice
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b
ased
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ch
em
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lik
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Ky
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er
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d
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iu
m
th
at
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s
e
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in
g
lear
n
in
g
with
t
h
e
e
r
r
o
r
s
p
r
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lem
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e
also
b
ee
n
im
p
lem
en
ted
o
n
c
o
n
s
tr
ain
ed
d
ev
ices.
NT
R
U
lattice
s
ch
em
es r
ely
in
g
o
n
th
e
s
h
o
r
t in
teg
er
s
o
l
u
tio
n
p
r
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lem
h
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v
e
b
ee
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ad
ap
te
d
as we
ll.
Po
s
t
-
q
u
an
tu
m
s
ch
em
es
lik
e
SIK
E
a
r
e
b
ased
o
n
s
u
p
e
r
s
in
g
u
lar
is
o
g
en
y
g
r
ap
h
s
a
n
d
h
ar
d
ass
u
m
p
tio
n
s
r
elate
d
to
f
in
d
in
g
s
m
o
o
th
is
o
g
en
ies b
etwe
en
elli
p
tic
cu
r
v
es.
Key
e
x
ch
an
g
e
r
eli
es o
n
th
e
co
m
m
u
tativ
e
p
r
o
p
er
t
y
as in
(
2
)
.
∘
=
∘
(
2
)
SIK
E
's
s
ec
u
r
ity
d
ep
en
d
s
o
n
d
if
f
icu
lty
o
f
s
o
lv
in
g
th
e
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u
p
e
r
s
in
g
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lar
is
o
g
en
y
p
r
o
b
lem
t
o
f
in
d
cu
r
v
e
r
elatio
n
s
h
ip
s
.
Ky
b
er
an
d
o
th
e
r
lattice
-
b
ased
s
ch
em
es
co
n
s
t
r
u
ct
p
u
b
lic
k
ey
s
as
lattice
p
o
i
n
ts
with
s
ec
r
et
s
a
s
s
h
o
r
t
v
ec
to
r
s
.
Secu
r
ity
r
elies
o
n
th
e
lear
n
in
g
with
er
r
o
r
s
(
L
W
E
)
ass
u
m
p
tio
n
th
at
n
o
is
y
lin
ea
r
eq
u
atio
n
s
h
id
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s
ec
r
et
v
ec
to
r
s
as in
(
3
)
a
n
d
(
4
)
.
=
(
)
(
3
)
=
+
(
4
)
C
r
y
p
tan
aly
s
is
in
v
o
lv
es
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o
lv
in
g
L
W
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ap
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x
im
ate
s
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r
test
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ec
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r
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d
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tim
izatio
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s
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n
u
m
b
er
th
e
o
r
etic
tr
an
s
f
o
r
m
s
[
2
2
]
.
2
.
3
.
Secure
da
t
a
s
t
o
ra
g
e
a
nd
net
wo
rk
s
ec
urit
y
Sh
im
et
a
l
.
[
2
3
]
d
is
cu
s
s
es
th
e
d
esig
n
o
f
a
q
u
a
n
tu
m
k
ey
m
an
ag
e
m
en
t
s
y
s
tem
(
QKM
S)
to
h
elp
in
teg
r
ate
QKD
in
to
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ea
l
n
etwo
r
k
s
.
I
t
p
r
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p
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a
m
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lti
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lay
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ch
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r
e,
in
clu
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a
q
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an
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m
d
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er
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ag
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lay
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to
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a
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d
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ib
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tr
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s
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is
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ay
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to
s
u
p
p
ly
k
ey
s
to
n
etwo
r
k
eq
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ip
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en
t.
T
h
e
s
y
s
tem
was
te
s
ted
in
m
u
ltip
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tag
es
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tin
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lab
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n
d
d
is
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ib
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tio
n
.
T
h
ey
f
o
cu
s
ed
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d
e
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in
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ew
n
etwo
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k
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ch
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d
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g
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s
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tem
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to
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elp
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ak
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p
r
ac
tical
s
o
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tio
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f
o
r
s
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r
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m
m
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n
icatio
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n
etwo
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k
s
o
f
t
h
e
f
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tu
r
e.
Mo
d
u
lar
m
u
ltip
licatio
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is
ess
en
tial
in
p
u
b
lic
-
k
ey
cr
y
p
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g
r
a
p
h
y
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Mo
n
tg
o
m
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p
er
f
o
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m
s
f
ast
m
o
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lar
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ltip
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s
u
s
in
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s
h
if
ted
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d
d
itio
n
s
in
s
tead
o
f
t
r
ial
d
iv
is
io
n
.
=
−
1
(
)
(
5
)
=
2
(
6
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Par
alleliza
tio
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an
d
s
p
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m
o
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u
lar
al
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ith
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s
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p
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ch
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FP
GA
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d
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p
latf
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r
m
s
p
r
o
v
id
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f
f
icien
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g
ain
s
[
2
4
]
.
U
k
w
u
o
m
a
e
t
a
l
.
[
2
5
]
h
a
v
e
l
o
o
k
e
d
a
t
w
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y
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t
o
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c
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c
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li
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to
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M
c
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ce
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t
i
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f
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c
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w
h
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s
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n
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a
p
p
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O
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f
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A
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c
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o
n
,
m
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s
s
a
g
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d
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s
t
5
(
MD
5
)
in
t
e
g
r
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t
y
c
h
e
c
k
s
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a
n
d
e
l
l
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p
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c
u
r
v
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c
r
y
p
t
o
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r
a
p
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en
a
b
l
i
n
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n
c
r
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p
t
i
o
n
.
O
t
h
e
r
i
d
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n
t
i
t
y
b
as
e
d
e
n
c
r
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p
t
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o
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s
i
n
g
l
a
t
ti
c
e
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w
as
o
n
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t
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c
h
n
i
q
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e
p
r
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p
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s
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d
t
o
m
a
k
e
k
e
y
m
a
n
a
g
e
m
e
n
t
e
a
s
i
e
r
[
2
6
]
.
A
k
t
e
r
e
t
a
l
.
[
2
7
]
h
a
v
e
b
e
e
n
e
x
p
l
o
r
i
n
g
d
i
f
f
e
r
e
n
t
a
p
p
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h
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t
w
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8
4
,
w
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m
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w
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[
2
8
]
.
W
an
g
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l
.
[
2
9
]
a
n
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th
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s
id
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GA’
s
ar
ch
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r
e
to
ex
tr
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m
o
r
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in
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o
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m
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Po
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r
e
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ce
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t
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e
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ican
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tr
ad
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l CP
A
[
3
0
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.
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.
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3
1
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p
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lem
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lac
k
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h
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eliab
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f
cu
r
r
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n
ter
m
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3.
M
E
T
H
O
DO
L
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G
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A
m
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d
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m
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d
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d
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r
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q
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v
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tis
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l
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lu
ati
o
n
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I
m
p
le
m
e
n
ta
ti
o
n
:
t
h
e
r
ef
e
r
e
n
c
e
C
i
m
p
le
m
e
n
t
ati
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n
o
f
t
h
e
Ky
b
e
r
KE
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f
r
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m
t
h
e
C
R
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AL
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p
r
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ec
t
v
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1
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p
p
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n
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id
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n
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is
:
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f
f
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p
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is
(
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et
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g
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m
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p
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g
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s
p
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d
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co
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P
o
w
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am
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l
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at
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0
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it
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r
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p
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ete
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T
e
m
p
lat
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c
o
n
s
tr
u
c
ti
o
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:
Ga
u
s
s
ia
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t
em
p
l
ates
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d
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t
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s
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h
e
H
am
m
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d
is
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h
t st
r
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r
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r
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co
r
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al
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n
d
p
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p
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r
co
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m
p
t
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n
.
C
o
u
n
t
e
r
m
ea
s
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r
e
a
p
p
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ca
ti
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n
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ca
l
ar
m
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l
ti
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t B
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m
as
k
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Fig
u
r
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illu
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ates
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e
h
a
r
d
wa
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im
p
lem
en
tatio
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o
f
th
e
C
R
YSTA
L
S
-
Ky
b
er
KE
M,
a
PQC
alg
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m
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d
esig
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m
p
r
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Me
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f
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Fu
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.
.
.
,
)
=
∗
]
(
8
)
W
h
er
e
g
is
th
e
k
ey
r
ec
o
v
e
r
y
f
u
n
ctio
n
,
T
i a
r
e
th
e
o
b
s
er
v
ed
tr
ac
es,
an
d
k
*
is
th
e
co
r
r
ec
t
k
ey
.
B
ey
o
n
d
B
o
o
lean
m
ask
in
g
,
t
h
e
s
tu
d
y
ev
alu
ated
th
e
ef
f
e
ctiv
en
ess
o
f
s
h
u
f
f
lin
g
tech
n
i
q
u
es,
tim
e
r
an
d
o
m
izatio
n
,
a
n
d
h
id
in
g
co
u
n
ter
m
ea
s
u
r
es.
A
n
o
v
el
h
y
b
r
id
co
u
n
ter
m
ea
s
u
r
e
co
m
b
in
in
g
h
ig
h
e
r
-
o
r
d
er
m
ask
in
g
with
co
n
tr
o
lled
ti
m
e
r
an
d
o
m
izatio
n
was
p
r
o
p
o
s
ed
an
d
an
al
y
ze
d
.
T
h
e
d
-
th
o
r
d
er
m
ask
ed
r
ep
r
esen
tatio
n
o
f
a
v
al
u
e
x
wa
s
d
ef
in
ed
as
in
(
9
)
.
=
1
⊕
2
⊕
.
.
.
⊕
+
1
(
9
)
W
h
er
e
⊕
d
en
o
tes b
itwis
e
XOR an
d
x
i a
r
e
r
a
n
d
o
m
s
h
ar
es.
T
-
test
b
ased
leak
ag
e
ass
ess
m
en
t
was
co
n
d
u
cted
u
s
in
g
t
h
e
test
v
ec
to
r
leak
ag
e
ass
ess
m
en
t
(
T
VL
A)
m
eth
o
d
o
l
o
g
y
.
T
h
e
t
-
s
tatis
tic
was c
alcu
lated
as
in
(
1
0
)
.
=
(
0
−
1
)
/
√
(
0²
/
0
+
1²
/
1
)
(
1
0
)
W
h
er
e
μ
i,
s
1
²,
an
d
Ni
ar
e
th
e
m
ea
n
,
v
ar
ian
ce
,
an
d
n
u
m
b
er
o
f
tr
ac
es
f
o
r
f
ix
ed
(
i=0
)
an
d
r
an
d
o
m
(
i=1
)
in
p
u
ts
r
esp
ec
tiv
ely
.
T
h
e
s
id
e
-
ch
an
n
el
r
esil
ien
ce
o
f
Ky
b
er
was
c
o
m
p
ar
ed
a
g
ain
s
t
o
th
er
lattice
-
b
ased
ca
n
d
id
ates.
T
h
e
r
elativ
e
s
id
e
-
ch
a
n
n
el
attac
k
co
m
p
le
x
ity
C
was d
ef
in
ed
a
s
in
(
1
1
)
.
=
2
(
)
/
2
(
)
(
1
1
)
W
h
er
e
N
is
th
e
lattice
d
im
en
s
io
n
an
d
q
is
th
e
m
o
d
u
lu
s
.
T
o
im
p
r
o
v
e
th
e
ex
ter
n
al
v
ali
d
ity
an
d
o
b
tain
h
ig
h
r
o
b
u
s
tn
ess
ac
r
o
s
s
d
if
f
er
en
t
ca
s
es,
we
h
ea
v
ily
en
r
ich
ed
th
e
d
ataset
b
y
th
e
v
o
lu
m
e
an
d
v
a
r
iab
ilit
y
.
T
o
h
av
e
a
m
o
r
e
ex
ten
s
iv
e
d
ataset,
th
e
in
itial
b
en
ch
m
ar
k
was
s
u
p
p
lem
en
ted
with
m
o
r
e
p
o
wer
tr
ac
es
o
b
tain
ed
f
r
o
m
th
r
ee
d
if
f
er
en
t
p
latf
o
r
m
s
b
ased
o
n
FP
GA
d
ev
ices:
Xilin
x
Ar
tix
-
7
a
n
d
Vir
tex
-
7
,
a
n
d
I
n
tel
C
y
clo
n
e
V.
T
h
is
ex
p
a
n
s
io
n
au
g
m
en
ted
o
u
r
s
am
p
le
s
ize
f
r
o
m
1
0
,
0
0
0
t
o
5
0
,
0
0
0
tr
ac
es
p
er
Ky
b
er
p
ar
a
m
eter
s
et
ac
r
o
s
s
a
b
r
o
a
d
er
r
a
n
g
e
o
f
o
p
er
atin
g
co
n
d
itio
n
s
,
clo
ck
s
p
ee
d
s
,
an
d
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
M
o
r
eo
v
er
,
we
ex
ten
d
ed
t
h
e
d
atas
et
b
y
a
d
d
in
g
im
p
lem
en
tatio
n
tr
ac
es,
in
clu
d
in
g
a
h
ig
h
ly
o
p
tim
ized
ass
em
b
ly
co
d
e
f
o
r
AR
M
C
o
r
tex
-
M4
m
icr
o
co
n
tr
o
ller
a
n
d
x
8
6
-
6
4
d
esk
to
p
p
r
o
ce
s
s
o
r
as
well
as
th
e
r
ef
er
en
ce
C
co
d
e.
T
h
u
s
,
we
u
s
ed
r
ea
l
-
wo
r
ld
ex
p
er
i
m
en
ts
th
at
allo
wed
u
s
to
illu
s
tr
ate
th
e
p
r
ac
tical
ap
p
licab
ilit
y
o
f
o
u
r
ap
p
r
o
ac
h
in
r
ea
lis
tic
d
ep
lo
y
m
en
t
s
ce
n
a
r
io
s
.
T
h
ese
ex
p
er
im
e
n
ts
co
n
s
is
ted
o
f
in
teg
r
atin
g
o
u
r
s
ec
u
r
ed
K
y
b
er
d
esig
n
s
in
t
o
a
s
am
p
le
I
o
T
,
a
f
in
an
cial
t
r
an
s
ac
tio
n
s
y
s
tem
,
an
d
a
s
atellite
co
m
m
u
n
icatio
n
s
ce
n
ar
io
.
Sev
er
al
p
er
f
o
r
m
a
n
ce
p
ar
am
ete
r
s
s
u
ch
as
k
e
y
g
e
n
er
atio
n
tim
e,
en
ca
p
s
u
latio
n
/
d
ec
a
p
s
u
latio
n
tim
e,
an
d
o
v
er
all
s
y
s
tem
th
r
o
u
g
h
p
u
t
wer
e
ev
alu
ated
with
d
if
f
er
e
n
t
n
etwo
r
k
ch
a
r
ac
ter
is
tics
a
n
d
co
m
p
u
tatio
n
a
l
wo
r
k
lo
ad
s
.
Fu
r
th
er
m
o
r
e,
we
co
n
d
u
cted
ex
p
er
im
en
ts
with
v
ar
io
u
s
p
o
s
t
-
q
u
a
n
tu
m
im
p
lem
en
tatio
n
s
ag
ain
s
t
s
im
u
lated
s
id
e
-
ch
an
n
el
attac
k
s
to
ass
ess
ap
p
licab
ilit
y
an
d
r
o
b
u
s
tn
ess
o
f
t
h
e
co
u
n
ter
m
ea
s
u
r
es
p
r
o
p
o
s
ed
in
th
is
p
ap
er
[
3
2
]
.
I
n
a
d
d
itio
n
to
af
f
i
r
m
in
g
th
e
th
eo
r
etica
l
s
ec
u
r
ity
ass
u
r
an
ce
s
,
th
ese
ex
ten
s
iv
e
e
x
p
er
im
en
ts
en
a
b
led
r
ea
lis
tic
in
v
esti
g
atio
n
o
f
o
u
r
p
r
o
p
o
s
ed
s
ec
u
r
e
Ky
b
er
d
ep
lo
y
s
in
ter
m
s
o
f
b
o
th
f
ea
s
ib
ilit
y
an
d
co
s
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
4
,
No
.
6
,
Dec
em
b
er
2
0
2
5
:
5
2
5
1
-
5
2
6
7
5258
4.
P
RO
P
O
SE
D
M
O
D
E
L
I
n
itial
s
id
e
-
ch
an
n
el
an
al
y
s
is
ex
p
er
im
en
ts
h
av
e
ch
ar
ac
ter
ize
d
th
e
an
alo
g
em
is
s
io
n
s
f
r
o
m
a
b
aselin
e
h
ar
d
war
e
im
p
lem
en
tatio
n
o
f
th
e
C
R
YSTA
L
S
-
Ky
b
er
KE
M
with
th
e
Ky
b
e
r
5
1
2
p
a
r
am
eter
s
et.
An
a
g
ilen
t
MSOX3
0
2
4
A
o
s
cillo
s
co
p
e
was
u
tili
ze
d
to
ca
p
tu
r
e
tim
e
-
s
er
ies
p
o
wer
tr
ac
es
d
u
r
in
g
th
e
ex
ec
u
tio
n
o
f
th
e
Ky
b
er
5
1
2
_
g
e
n
er
ate_
k
ey
p
air
(
)
f
u
n
ctio
n
,
wh
ich
c
o
m
p
u
tes
th
e
p
u
b
lic
an
d
p
r
iv
ate
k
ey
.
T
h
e
o
s
cillo
s
co
p
e
s
am
p
lin
g
r
ate
was
co
n
f
i
g
u
r
ed
to
a
p
r
ec
is
io
n
o
f
1
2
-
b
it
a
n
alo
g
-
to
-
d
i
g
ital
co
n
v
er
s
io
n
at
5
0
0
m
eg
a
-
s
am
p
les
p
er
s
ec
o
n
d
(
MSPS).
Fig
u
r
e
3
d
e
m
o
n
s
tr
ates
lo
n
g
-
ter
m
s
ec
u
r
ity
o
f
clo
u
d
d
ata
an
d
in
f
r
astru
ct
u
r
e
ag
ain
s
t
q
u
an
tu
m
th
r
ea
ts
wh
ile
m
in
im
izin
g
d
is
r
u
p
tio
n
to
ex
is
tin
g
s
y
s
tem
s
an
d
wo
r
k
f
lo
ws
d
u
r
in
g
th
e
tr
an
s
itio
n
.
As
a
p
r
o
ac
tiv
e
ap
p
r
o
ac
h
is
ess
en
tial to
g
et
ah
ea
d
o
f
th
e
q
u
a
n
tu
m
co
m
p
u
tin
g
cu
r
v
e
.
Fig
u
r
e
3
.
B
asic secu
r
ity
ar
ch
it
ec
tu
r
e
f
o
r
clo
u
d
co
m
p
u
tin
g
th
at
u
s
es PQC
Vis
u
al
in
s
p
ec
tio
n
o
f
th
e
ac
q
u
i
r
ed
p
o
wer
tr
ac
es
s
h
o
ws
d
ata
-
d
ep
en
d
e
n
t
am
p
litu
d
e
f
lu
ctu
ati
o
n
s
d
u
r
in
g
m
ath
em
atica
l
o
p
er
atio
n
s
o
n
t
h
e
2
5
6
-
b
it
p
r
iv
ate
k
ey
v
alu
e
.
Po
wer
an
aly
s
is
attac
k
s
lik
e
C
PA
ex
p
lo
it
th
is
leak
ag
e
to
r
ec
o
v
er
s
ec
r
et
in
f
o
r
m
atio
n
.
On
th
e
b
asis
o
f
th
e
k
ey
b
y
te
v
alu
es'
Ham
m
in
g
w
eig
h
t
an
d
d
is
tan
ce
,
h
y
p
o
th
etica
l
p
o
wer
m
o
d
els
wer
e
b
u
ilt
[
3
3
]
.
Pear
s
o
n
'
s
co
r
r
elatio
n
co
e
f
f
icien
t
was
ca
lc
u
lated
b
etwe
en
th
e
m
o
d
elled
a
n
d
m
ea
s
u
r
ed
p
o
wer
tr
ac
es,
y
ield
in
g
v
alu
es
e
x
ce
ed
in
g
0
.
9
f
o
r
6
3
%
o
f
th
e
p
r
iv
ate
k
ey
b
y
tes.
T
h
is
h
ig
h
co
r
r
elatio
n
co
n
f
ir
m
s
th
e
f
ea
s
ib
ilit
y
o
f
s
u
cc
ess
f
u
l
C
PA
attac
k
s
o
n
u
n
p
r
o
tec
ted
h
ar
d
war
e
K
y
b
er
im
p
lem
en
tatio
n
s
.
T
h
ese
in
iti
al
r
esu
lts
m
o
tiv
ate
ad
d
itio
n
al
r
esear
ch
in
to
co
u
n
ter
m
ea
s
u
r
es
to
s
af
eg
u
ar
d
h
ar
d
war
e
Ky
b
er
ag
ai
n
s
t
p
o
wer
an
aly
s
is
s
id
e
-
ch
a
n
n
el
at
tack
s
.
R
an
d
o
m
ized
B
o
o
lean
m
ask
in
g
p
r
esen
ts
a
p
r
o
m
is
in
g
d
ef
en
s
e
ap
p
r
o
ac
h
.
4
.
1
.
P
o
wer
a
na
ly
s
is
v
uln
er
a
bil
it
y
o
f
ha
rdwa
re
K
y
ber
imp
lem
ent
a
t
io
ns
DPA
an
d
C
P
A
co
n
s
titu
te
th
e
p
r
in
cip
al
s
id
e
-
ch
an
n
el
ass
au
lt m
eth
o
d
s
th
at
will b
e
u
s
ed
to
c
o
m
p
r
o
m
is
e
th
e
p
r
iv
ac
y
o
f
co
n
te
n
t
th
at
is
co
n
s
id
er
ed
s
ec
r
et.
C
PA
lev
er
ag
es
s
tatis
tica
l
d
ep
en
d
en
ce
b
e
twee
n
in
ter
m
ed
iate
co
m
p
u
tatio
n
al
v
alu
es
an
d
th
e
r
esu
ltin
g
p
o
wer
co
n
s
u
m
p
ti
o
n
em
an
ati
o
n
s
to
ca
r
r
y
o
u
t
an
ex
h
a
u
s
tiv
e
k
ey
h
y
p
o
th
esis
s
ea
r
ch
.
DPA
s
u
b
tr
ac
ts
o
u
t
d
ata
-
in
d
ep
en
d
en
t
p
o
wer
d
r
aws
to
is
o
late
th
e
m
in
u
te
d
ata
-
d
ep
e
n
d
en
t
co
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ctu
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attr
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lectr
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m
an
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s
a
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ca
p
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if
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er
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tial
p
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e
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ased
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m
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io
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th
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h
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en
s
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r
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cr
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p
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am
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les
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ea
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in
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lar
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ize
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p
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r
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wit
h
cr
y
p
to
g
r
ap
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ic
ex
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tio
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R
an
d
o
m
ized
b
lin
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tech
n
iq
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es
s
u
p
p
lem
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th
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B
o
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ask
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g
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o
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n
ter
m
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r
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A
r
an
d
o
m
l
y
g
en
e
r
ated
b
lin
d
f
ac
to
r
th
at
is
c
o
n
tin
u
o
u
s
ly
r
ef
r
esh
e
d
f
r
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m
a
cr
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g
r
ap
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s
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war
e
r
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d
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m
n
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m
b
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r
is
ad
d
ed
to
ea
ch
in
ter
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to
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id
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it.
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h
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h
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ce
s
o
b
f
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s
ca
tio
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k
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s
ig
n
atu
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Mu
tu
al
in
f
o
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m
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an
al
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s
is
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ased
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n
a
k
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n
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est
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will
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u
p
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Pear
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co
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to
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tify
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esid
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tatis
t
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d
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d
en
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t
to
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n
tio
n
al
co
u
n
ter
m
ea
s
u
r
es.
Ad
ap
tiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
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2252
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8
9
3
8
S
ec
u
r
in
g
p
o
s
t
-
q
u
a
n
tu
m
cryp
to
g
r
a
p
h
y:
s
id
e
-
c
h
a
n
n
el
r
esil
ien
ce
in
C
R
YS
TALS
-
K
yb
er
…
(
S
h
r
ey
a
s
K
a
s
tu
r
e)
5259
s
am
p
lin
g
tech
n
iq
u
es
s
elec
tiv
ely
an
aly
s
e
th
e
m
o
s
t
in
f
o
r
m
ativ
e
tr
ac
e
s
u
b
s
ets
to
ac
ce
le
r
ate
k
ey
r
ec
o
v
er
y
.
Prin
cip
al
co
m
p
o
n
en
t a
n
al
y
s
is
p
r
o
jects tr
ac
es in
to
an
o
r
th
o
g
o
n
al
b
asis
to
co
n
ce
n
tr
ate
in
f
o
r
m
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n
leak
ag
e.
A
ze
r
o
-
m
ea
n
u
n
it
-
v
ar
ian
ce
n
o
r
m
aliza
tio
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p
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p
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ce
s
s
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tr
ac
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m
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ate
g
lo
b
al
o
f
f
s
et
d
i
m
in
is
h
in
g
co
r
r
elatio
n
o
b
s
er
v
ab
ilit
y
.
L
e
ak
ag
e
ass
ess
m
en
t
in
co
r
p
o
r
ates
n
o
n
-
s
p
ec
if
ic
t
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test
s
ev
alu
atin
g
th
e
f
u
ll
tr
ac
e
d
is
tr
ib
u
tio
n
in
ad
d
itio
n
to
l
o
c
alize
d
attac
k
s
.
Ky
b
er
'
s
p
o
ly
n
o
m
ial
ar
ith
m
etic
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elies
o
n
th
e
n
u
m
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er
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e
o
r
etic
tr
an
s
f
o
r
m
(
NT
T
)
,
an
d
p
o
te
n
tial
f
laws
in
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ar
e
ass
ess
ed
b
y
co
n
tr
asti
n
g
d
if
f
er
en
t
f
ast
Fo
u
r
ier
tr
an
s
f
o
r
m
(
FFT
)
im
p
lem
en
tatio
n
s
o
n
is
o
m
o
r
p
h
i
c
r
in
g
s
.
T
h
e
Ham
m
in
g
d
is
tan
ce
an
d
weig
h
t p
o
wer
f
r
am
ewo
r
k
s
will ser
v
e
as th
e
p
r
im
ar
y
s
tatis
tical
est
im
ato
r
s
t
o
co
r
r
elate
h
y
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o
th
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ter
m
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r
d
ed
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wav
ef
o
r
m
s
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h
e
Ham
m
in
g
weig
h
t
m
o
d
el
lin
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ly
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ciate
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o
n
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m
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with
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r
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lity
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to
r
s
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h
e
Ham
m
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g
d
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tan
ce
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etr
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c
co
m
p
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tes
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e
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clu
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e
d
is
ju
n
ctio
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b
etwe
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cc
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A
co
r
p
u
s
o
f
1
0
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0
0
0
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tr
o
m
ag
n
etic
p
o
we
r
tr
ac
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e
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m
p
iled
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er
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er
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ar
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eter
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et
ex
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n
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th
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k
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en
er
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n
r
o
u
tin
e.
At
a
s
ig
n
if
ican
ce
th
r
esh
o
l
d
o
f
α
=
0
.
0
5
,
th
e
W
elch
'
s
t
-
test
ca
n
b
e
u
s
ed
to
i
d
en
tify
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y
p
o
ten
tially
ex
p
l
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itab
le
in
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o
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ag
e
b
etwe
en
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h
y
p
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th
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m
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d
el
an
d
r
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l
p
o
wer
tr
ac
es
with
a
Pear
s
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ef
f
icien
t
ex
ce
e
d
in
g
0
.
8
.
A
d
iv
id
e
-
an
d
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co
n
q
u
er
a
p
p
r
o
ac
h
r
ec
o
n
s
titu
tes
2
5
6
-
b
it
p
r
iv
ate
k
ey
8
b
its
at
a
tim
e
b
y
ex
p
lo
itin
g
th
e
m
a
x
im
al
co
r
r
elatio
n
s
.
C
o
m
p
a
r
at
iv
e
an
aly
s
is
b
etwe
en
Ky
b
er
5
1
2
an
d
Ky
b
er
1
0
2
4
elu
cid
ates th
e
p
r
o
p
o
r
tio
n
al
in
c
r
ea
s
e
in
m
ea
s
u
r
em
en
ts
r
eq
u
ir
e
d
to
co
m
p
r
o
m
is
e
lar
g
e
r
k
e
y
s
izes.
Fig
u
r
e
4
d
em
o
n
s
tr
ates
th
e
s
ec
u
r
ity
im
p
ac
t
o
f
d
if
f
er
e
n
t
m
a
s
k
in
g
lev
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ag
ain
s
t
a
p
o
wer
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es
s
m
en
t
s
id
e
-
ch
an
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el
ass
au
lt.
I
t
d
is
p
l
ay
s
a
p
er
ce
n
tag
e
o
f
b
y
tes
with
th
e
r
ig
h
t
cr
y
p
to
g
r
ap
h
ic
k
ey
r
ec
o
v
er
e
d
as
an
in
cr
ea
s
in
g
n
u
m
b
e
r
o
f
p
o
wer
tr
ac
es
ar
e
s
tu
d
ied
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r
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m
ea
ch
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n
.
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ith
n
o
m
ask
in
g
,
th
e
u
n
p
r
o
tecte
d
im
p
lem
en
tatio
n
s
ee
s
r
ap
id
k
e
y
r
ec
o
v
e
r
y
.
Af
te
r
an
aly
zin
g
ju
s
t
1
0
0
tr
ac
es,
th
e
attac
k
e
r
ca
n
r
ec
o
v
er
1
0
%
o
f
th
e
co
r
r
ec
t
k
ey
.
B
y
1
,
0
0
0
tr
ac
es,
7
0
%
o
f
th
e
k
ey
is
k
n
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wn
.
T
h
e
f
u
ll
k
ey
g
ets
leak
ed
af
te
r
5
,
0
0
0
tr
ac
es
ar
e
an
aly
ze
d
.
Ad
d
in
g
m
ask
in
g
s
u
b
s
tan
tially
h
in
d
er
s
th
is
k
ey
r
e
co
v
er
y
.
W
ith
1
-
b
it
m
ask
in
g
,
o
n
ly
2
%
o
f
th
e
k
ey
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ed
af
ter
1
0
0
tr
ac
es.
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v
e
n
af
ter
1
0
,
0
0
0
tr
ac
es,
1
0
%
o
f
th
e
k
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r
em
ain
s
p
r
o
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d
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n
cr
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s
in
g
to
2
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b
it
m
ask
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g
f
u
r
t
h
er
en
h
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ce
s
s
ec
u
r
ity
,
with
o
n
l
y
1
%
o
f
th
e
k
ey
co
m
p
r
o
m
is
ed
af
te
r
1
0
0
t
r
ac
es.
T
h
e
b
en
e
f
its
co
n
tin
u
e
i
m
p
r
o
v
in
g
with
4
-
b
it
an
d
8
-
b
it
m
ask
in
g
,
n
eith
er
o
f
wh
ich
leak
an
y
k
e
y
b
y
tes
af
t
er
ju
s
t
1
0
0
tr
ac
es.
E
v
en
with
1
0
,
0
0
0
t
r
ac
es
an
al
y
ze
d
,
th
e
4
-
b
it
m
ask
ed
im
p
le
m
en
tatio
n
o
n
ly
lo
s
es
4
0
%
o
f
th
e
k
ey
,
wh
ile
8
-
b
it
m
ask
in
g
lim
its
th
is
to
1
5
%.
T
h
is
d
em
o
n
s
tr
ates
th
e
"d
iv
id
e
-
a
n
d
-
co
n
q
u
er
"
attac
k
p
r
o
ce
s
s
g
ettin
g
ex
p
o
n
en
tially
m
o
r
e
d
if
f
icu
lt a
s
g
r
ea
ter
m
ask
i
n
g
is
ad
d
ed
.
Fig
u
r
e
4
.
I
n
cr
em
e
n
tal
k
ey
r
ec
o
v
er
y
r
ate
ch
ar
t
4
.
2
.
E
v
a
lua
t
ing
B
o
o
lea
n m
a
s
k
ing
co
un
t
er
m
ea
s
ures f
o
r
ha
rdwa
re
K
y
ber
Ad
d
itiv
e
B
o
o
lean
m
ask
in
g
will
b
e
im
p
lem
en
ted
,
wh
e
r
e
an
in
ter
m
ed
iate
v
alu
e
x
is
s
p
lit
in
to
x
=x
1
⊕
x
2
.
Fre
s
h
r
an
d
o
m
m
ask
s
ar
e
g
en
er
ated
u
s
in
g
a
c
r
y
p
to
g
r
a
p
h
ically
s
ec
u
r
e
h
ar
d
w
ar
e
r
an
d
o
m
n
u
m
b
er
g
en
er
ato
r
(
R
NG
)
.
Ma
s
k
in
g
is
ap
p
lied
at
b
o
th
th
e
lo
g
ic
an
d
ar
ith
m
etic
lev
els
u
s
in
g
d
ed
icate
d
m
ask
ed
lo
g
ic
g
ates
an
d
m
ask
ed
m
u
ltip
licatio
n
cir
cu
its
.
Fre
s
h
r
e
-
m
ask
in
g
o
cc
u
r
s
b
ef
o
r
e
ea
c
h
cr
y
p
t
o
o
p
er
atio
n
u
s
in
g
n
ew
r
an
d
o
m
m
ask
s
.
Glitch
p
r
ev
e
n
tio
n
tech
n
iq
u
es
i
n
clu
d
e
ca
s
ca
d
ed
r
e
m
ask
in
g
an
d
b
alan
c
ed
r
o
u
tin
g
o
f
m
ask
s
ig
n
als.
Hig
h
er
o
r
d
er
4
-
b
it
m
ask
in
g
p
r
o
v
i
d
es
in
cr
ea
s
ed
s
ec
u
r
ity
b
y
d
is
tr
ib
u
tin
g
x
ac
r
o
s
s
4
s
h
ar
es
u
s
in
g
m
o
r
e
m
ask
b
its
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ates.
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s
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ates.
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e
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ity
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eq
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ir
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ce
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h
ar
m
in
g
f
r
e
q
u
en
c
y
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d
th
r
o
u
g
h
p
u
t.
Ar
o
u
n
d
1
0
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r
esh
m
ask
s
ar
e
g
en
er
ate
d
p
er
o
p
er
atio
n
to
lim
it
s
ec
u
r
ity
l
o
s
s
f
r
o
m
g
litch
es.
Ma
s
k
ed
d
esig
n
s
ar
e
s
y
n
th
esized
u
s
in
g
I
SE
Desig
n
Su
ite
f
o
r
d
ef
e
n
s
e
Sp
ar
tan
-
6
FP
GA.
T
im
in
g
co
n
s
tr
ain
ts
g
u
id
e
p
lace
a
n
d
r
o
u
te
to
h
it
1
0
0
MH
z
w
h
ile
m
in
im
izin
g
E
M
leak
ag
e
r
is
k
s
.
DPA
co
n
test
v
4
.
2
tech
n
iq
u
es
will
b
e
ad
ap
ted
to
an
aly
s
e
m
ask
e
d
p
o
wer
tr
ac
es b
y
tar
g
etin
g
s
h
ar
ed
in
ter
m
ed
iate
c
o
m
p
u
tatio
n
s
.
Fig
u
r
e
5
s
h
o
ws
th
e
FP
GA
r
eso
u
r
ce
u
tili
za
tio
n
o
f
th
e
u
n
m
as
k
ed
cr
y
p
to
g
r
a
p
h
ic
co
r
e
d
esig
n
co
m
p
ar
e
d
to
th
e
v
ar
i
o
u
s
m
ask
ed
v
er
s
io
n
s
.
Sp
ec
if
ically
,
it
tr
ac
k
s
s
lice
u
s
ag
e,
lo
o
k
u
p
ta
b
les
(
L
UT
s
)
,
f
lip
f
lo
p
s
,
a
n
d
b
lo
ck
R
AM
s
(
B
R
AM
s
)
.
T
h
e
u
n
m
ask
ed
im
p
lem
e
n
tatio
n
u
s
es
a
b
aselin
e
o
f
1
,
2
0
0
s
lices.
T
h
e
s
lice
co
u
n
t
r
is
es
b
y
2
5
%
to
1
,
5
0
0
s
lices
wh
en
1
-
b
it
m
ask
in
g
is
in
tr
o
d
u
ce
d
,
illu
s
tr
atin
g
th
e
ar
ea
b
u
r
d
e
n
ass
o
ciate
d
with
im
p
lem
en
tin
g
th
is
d
eg
r
ee
o
f
p
r
o
tectio
n
.
T
h
e
o
v
er
h
ea
d
g
e
ts
wo
r
s
e
as
m
o
r
e
m
ask
in
g
is
ad
d
ed
-
th
e
2
-
b
it
m
ask
ed
v
er
s
io
n
u
s
es 5
0
% m
o
r
e
s
lices a
t 1
8
0
0
,
wh
ile
4
-
b
it a
n
d
8
-
b
it m
ask
ed
d
esig
n
s
r
eq
u
ir
e
2
x
an
d
3
.
5
x
m
o
r
e
s
lices
r
e
s
p
ec
tiv
ely
.
T
h
e
o
th
e
r
r
eso
u
r
ce
s
o
f
L
UT
s
,
f
lip
f
lo
p
s
,
an
d
B
R
AM
s
s
im
ilar
ly
i
n
cr
ea
s
e
with
m
o
r
e
m
ask
in
g
.
T
h
e
8
-
b
it
m
ask
ed
d
e
s
ig
n
u
s
es
o
v
er
3
x
as
m
an
y
L
U
T
s
an
d
f
lip
f
lo
p
s
v
er
s
u
s
th
e
u
n
m
ask
ed
co
r
e
.
T
h
is
h
ig
h
lig
h
ts
th
e
s
u
b
s
tan
tial
co
s
ts
o
f
h
ig
h
er
s
ec
u
r
ity
in
ter
m
s
o
f
th
e
ad
d
itio
n
al
FP
GA
ar
ea
an
d
r
eso
u
r
ce
s
r
eq
u
ir
ed
.
E
v
en
th
e
2
-
b
it m
ask
ed
v
er
s
io
n
u
tili
ze
s
o
v
er
2
x
th
e
B
R
AM
s
o
f
th
e
u
n
p
r
o
tecte
d
d
e
s
ig
n
.
Fig
u
r
e
5
.
FP
GA
s
lice
u
tili
za
ti
o
n
f
o
r
u
n
m
ask
ed
v
s
m
ask
e
d
v
er
s
io
n
s
T
h
r
esh
o
ld
-
b
ased
ad
d
itiv
e
B
o
o
lean
m
ask
in
g
will
b
e
d
ep
l
o
y
ed
to
p
ar
titi
o
n
in
ter
m
e
d
iate
v
alu
es
in
to
r
an
d
o
m
ize
d
s
h
ar
es.
A
(
t+1
)
-
o
u
t
-
of
-
n
s
ch
em
e
with
t=3
will
b
e
im
p
lem
e
n
ted
to
r
esis
t
f
ir
s
t
-
o
r
d
er
s
id
e
-
ch
a
n
n
el
attac
k
s
.
Fre
s
h
m
ask
s
wi
ll
b
e
g
en
er
ated
u
s
in
g
a
s
u
ite
o
f
r
in
g
o
s
cillato
r
-
b
ased
t
r
u
e
r
an
d
o
m
n
u
m
b
er
g
en
er
ato
r
s
(
T
R
NGs
)
wi
th
n
ested
co
m
b
in
ato
r
ial
h
ash
in
g
ex
tr
ac
ted
f
r
o
m
th
e
r
aw
en
tr
o
p
y
.
Glitch
m
itig
atio
n
tech
n
iq
u
es
in
clu
d
in
g
ca
s
ca
d
ed
r
em
ask
in
g
an
d
d
y
n
am
ically
o
b
f
u
s
ca
ted
ce
ll
s
(
DOC)
,
will
h
elp
s
af
eg
u
ar
d
a
g
ain
s
t
tr
an
s
ien
t
in
f
o
r
m
atio
n
leak
ag
e.
Place
an
d
r
o
u
te
co
n
s
tr
ain
ts
will
en
f
o
r
ce
Ma
n
h
attan
r
o
u
tin
g
s
y
m
m
e
tr
y
to
b
alan
ce
E
M
em
an
atio
n
s
.
Hig
h
e
r
-
o
r
d
er
4
-
b
it
m
ask
in
g
u
tili
ze
s
co
m
p
o
s
ab
le
s
h
ar
in
g
cir
cu
its
s
y
n
th
esize
d
f
r
o
m
t
h
e
s
er
v
e
r
n
am
e
in
d
icatio
n
(
SNI
)
b
in
a
r
y
g
ate
lib
r
ar
y
t
o
m
in
im
ize
leak
a
g
e
.
Fig
u
r
e
6
d
en
o
tes
wh
en
u
n
m
ask
ed
im
p
lem
en
tatio
n
r
ea
c
h
e
s
th
e
h
ig
h
est
f
r
eq
u
en
cy
-
1
2
7
MH
z,
th
e
f
r
eq
u
e
n
cy
o
f
1
-
b
it
m
ask
in
g
d
r
o
p
s
to
1
1
8
MH
z,
ab
o
u
t
a
7
%
p
er
f
o
r
m
an
ce
im
p
ac
t.
Ho
wev
e
r
,
af
ter
o
p
tim
izin
g
th
e
1
-
b
it
m
ask
ed
d
esig
n
,
it
ca
n
ac
h
iev
e
alm
o
s
t
th
e
s
am
e
f
r
e
q
u
en
cy
o
f
1
2
5
MH
z.
As
m
o
r
e
m
ask
in
g
is
ad
d
ed
,
th
e
d
r
o
p
in
m
a
x
im
u
m
f
r
e
q
u
e
n
cy
g
ets
p
r
o
g
r
ess
iv
ely
wo
r
s
e
with
o
u
t
o
p
tim
izatio
n
.
T
h
e
2
-
b
it
m
ask
ed
v
er
s
io
n
r
ea
ch
es
1
1
2
MH
z,
wh
ile
4
-
b
it
an
d
8
-
b
it
m
ask
ed
d
esig
n
s
h
av
e
s
ig
n
if
ican
tly
lo
wer
f
r
e
q
u
en
c
ies
o
f
9
2
MH
z
an
d
7
1
MH
z
r
esp
ec
tiv
ely
.
T
h
is
s
h
o
ws
th
e
s
u
b
s
tan
tial
p
er
f
o
r
m
an
ce
co
s
ts
o
f
h
ea
v
ier
m
ask
in
g
.
Ho
wev
er
,
af
ter
o
p
tim
izatio
n
th
e
h
ig
h
er
m
ask
e
d
d
esig
n
s
r
eg
ain
s
o
m
e
lo
s
t
p
e
r
f
o
r
m
a
n
ce
.
T
h
e
o
p
tim
ized
2
-
b
it
m
ask
in
g
r
ea
ch
es
1
2
2
MH
z,
v
er
y
clo
s
e
to
t
h
e
u
n
m
ask
ed
f
r
eq
u
e
n
cy
.
O
p
tim
ized
4
-
b
it
an
d
8
-
b
it
m
ask
in
g
s
im
p
r
o
v
e
to
1
0
7
MH
z
an
d
9
6
MH
z,
th
o
u
g
h
s
till
lag
g
in
g
th
e
u
n
m
ask
ed
p
er
f
o
r
m
an
ce
.
Up
to
1
0
0
f
r
esh
r
an
d
o
m
m
ask
s
p
er
Evaluation Warning : The document was created with Spire.PDF for Python.