Intern
ati
o
n
a
l
Journ
a
l of
Re
con
f
igur
able
and Embe
dded
Sys
t
ems
(I
JRES)
V
o
l.
2, N
o
. 3
,
N
o
v
e
m
b
er
2
013
, pp
. 99
~105
I
S
SN
: 208
9-4
8
6
4
99
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRES
FPGA Implementation of Park-Miller Algorithm to Generate
Sequence of 32-Bit Pseudo Ra
ndom Key for Encryption and
Decryption of Plain Text
B
h
ar
ates
h
N
,
Ro
hi
th S
Department o
f
Electronics
and C
o
mm
unication Engineer
ing, Nag
a
rjuna Coll
ege o
f
Engin
eering
an
d Technolog
y
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 21, 2013
Rev
i
sed
Sep
20
, 20
13
Accepted Oct 12, 2013
There are man
y
problems arises in
randomized
algorithms whose solutions
are fundamentally
based on
assumptions that pur
e random numbers exist, so
pseudo-random number generators can
imitate r
a
ndomness suffi
cien
tly
well
for most
applications. The prop
osed
scheme is
a FPGA imple
m
entation of
Park-Miller Alg
o
rithm
for gener
a
ting se
qu
ence o
f
Pseudo-Random
key
s
.
Th
e
properties like
High speed, lo
w power
and flexibility
of designed PRNG
(Pseudo Random Nu
mber Gen
e
rator) make
s an
y
digital
circu
i
t faster and
smaller. Th
e algorithm uses a PRNG
Module, it contains 3
2
-bit Booth
Multipli
er, 32-bi
t Float
i
ng po
int
divide
r
and
a FSM m
odule. Aft
e
r
gener
a
tin
g
a sequen
c
e of 3
2
-bit Pseudo-Ra
ndom numbers we have used
th
ese numbers
as a key
to
Encr
y
p
t 128-b
it
plain text to
becom
e
a cipher
text
and b
y
using
the sam
e
ke
y to
decr
ypt th
e en
cr
y
p
ted d
a
ta
to
get origin
al Pla
i
n text
. The
Programming i
s
done in Verilog-HDL
, successfully
s
y
n
t
h
e
sized
and
im
plem
ented
in
XILINX Spartan
3E FPGA kit
.
Keyword:
Decry
p
tion
En
cry
p
tio
n
Lo
gi
st
i
c
m
a
p
Pseud
o
-Ran
dom
B
it Gen
e
rato
r
Cryptogra
p
hic security
Copyright ©
201
3 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ro
h
ith S
Depa
rt
em
ent
of El
ect
r
oni
cs
a
n
d
C
o
m
m
uni
cat
i
on E
n
gi
nee
r
i
n
g
,
Naga
r
j
u
n
a C
o
l
l
e
ge
of
En
gi
ne
e
r
i
n
g a
n
d
Tech
n
o
l
o
gy
Ven
k
at
agi
r
i
K
o
t
e
,
Deva
na
hal
l
i
(T) B
a
ngal
o
r
e
, Ka
r
n
at
aka,
I
ndi
a
Em
a
il: ro
h
ithv
j
p
200
6@g
m
ai
l.co
m
1.
INTRODUCTION
En
cry
p
tio
n
is
u
s
ed
to
secu
rely tran
smit d
a
ta in
ope
n
net
w
o
r
k
s
. Eac
h
t
y
pe o
f
dat
a
h
a
s i
t
s
ow
n
feat
ure
s
, t
h
ere
f
ore
di
f
f
er
ent
t
e
chni
que
s s
h
o
u
l
d
be
use
d
t
o
protect confi
d
ent
i
al data
from
unaut
h
orized ac
cess.
The Pse
u
d
o
-
R
a
nd
om
num
bers are pl
ay
s ver
y
im
port
a
nt
ro
l
e
i
n
t
h
e com
m
uni
cat
i
on sy
st
em
for pr
ot
ect
i
on
o
f
inform
ation from
unauthoriz
e
d access.
T
h
e
efficiency of t
h
e PRNG base
d
crypt
o
system is
mainly based on
t
h
e ra
n
dom
ke
y
gene
rat
e
d
by
i
t
s
PR
NG
[
1
]
-
[
5
]
.
Dep
e
nd
ing
on th
e ap
p
licatio
n, th
ree typ
e
s o
f
num
b
er sequences m
i
ght prove as the “rando
m
num
bers”.
A n
u
m
b
ers gene
ra
t
e
d by
a t
r
ul
y
rand
om
process
i
s
m
o
st desi
rabl
e. Thi
s
t
y
pe of se
que
nce i
s
cal
l
e
d
a rand
om
-num
ber se
que
nce,
and t
h
e key
pr
o
b
l
e
m
i
s
deci
di
ng
whet
he
r or
not
t
h
e g
e
nerat
i
n
g p
r
oc
ess i
s
r
a
ndo
m
.
A
mo
r
e
p
r
actical seq
u
e
n
ce is th
e p
s
eudo
-r
a
ndom seq
u
e
n
c
e, a ser
i
es o
f
num
b
e
r
s
g
e
n
e
rated
b
y
a
d
e
term
in
istic p
r
o
cess th
at is i
n
tend
ed m
e
rel
y
to
i
m
itate a
rando
m
seq
u
e
n
ce
b
u
t
wh
ich
,
o
f
cou
r
se,
d
o
es no
t
correctly obey
suc
h
thi
n
gs
as
the laws
of la
rge
num
bers
.
A quasi-rando
m
sequence
is a
s
e
ries
of
num
b
ers tha
t
m
a
kes n
o
gu
a
r
ant
y
at
bei
n
g
ran
d
o
m
but
t
h
at
has
i
m
port
a
nt
pre
d
efi
n
e
st
at
i
s
t
i
cal
prope
rt
i
e
s o
f
ra
nd
o
m
sequences
.
PRNGs are
e
f
ficient
,
m
ean
i
n
g
th
at in
a sh
ort ti
m
e
,
t
h
ey
can pr
o
duce m
a
ny
num
bers
an
d d
e
term
in
is
tic
,
m
ean
s th
at if th
e starting
p
o
i
n
t
in
th
e
seq
u
e
nce is
known a
gi
ven s
e
quence
of num
b
ers ca
n
be re
ge
nerate
at a later tim
e
[1]. E
fficiency
is a ni
ce cha
r
acteristic, if our appli
cat
i
on
n
eeds m
a
ny
nu
m
b
ers,
an
d
d
e
term
in
is
m
is h
a
n
d
y
i
f
we
n
e
ed
to replay th
e sa
m
e
seque
nce
of
num
bers again at a later
stage.
PRNGs
are typ
i
cally p
e
riod
ic
,
wh
ich
m
ean
s th
at the sequ
en
ce
wi
ll seq
u
e
n
tially
rep
eat itself.
Wh
ile
p
e
riod
icity is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S
V
o
l
.
2,
No
. 3,
N
o
vem
b
er
2
0
1
3
:
99
– 10
5
10
0
hardly ever a
desirable cha
r
ac
teristic,
m
odern PRNGs
have
a
p
e
r
i
o
d
t
h
a
t
i
s
s
o
l
o
n
g
th
at it can
b
e
igno
red
fo
r
m
o
st
pract
i
cal
pu
r
poses
.
Pseu
do
ra
nd
om
sequ
ences
[
1
]
have b
een
wi
del
y
use
d
i
n
va
ri
o
u
s fi
el
ds,
navi
gat
i
o
n
,
i
n
cl
u
d
i
n
g
com
m
uni
cat
i
ons, ra
dar t
ech
nol
ogy
, ci
p
h
er
t
echnol
ogi
es
,
rem
o
t
e
cont
r
o
l
,
m
easurem
ent
s
, an
d i
n
d
u
st
ri
al
au
to
m
a
tio
n
[2
]. Fo
r
ex
am
p
l
e, p
s
eu
dor
andom
seq
u
e
n
ces
hav
e
b
een u
s
ed
in
err
o
r
-
c
o
r
r
ect
in
g
cod
e
s
[
3
],
sp
r
e
ad
spect
r
u
m
co
m
m
uni
cat
i
on [4]
,
[
5
]
,
an
d sy
st
em
i
d
ent
i
f
i
cat
i
on a
n
d pa
ram
e
t
e
r m
easurem
ent
s
[
6
]
,
[
7
]
.
Ot
he
r
exam
ple applications are found in
s
u
rface
characterization a
nd
3D sc
en
e m
odel
i
ng
[8]
.
T
h
e desi
g
n
o
f
a
gene
ral
p
u
r
p
os
e pseu
d
o
ra
n
d
o
m
sequence
ge
nerat
o
r
ha
s m
a
ture
d and has
already bee
n
c
o
mmercialized [9]-
[1
1]
.
Pseu
do
ra
nd
om
seque
nces are
seri
es of
1’s an
d 0’
s t
h
at
lack
an
y d
e
fi
n
ite p
a
ttern
and
lo
ok
statistical
ly
i
nde
pen
d
e
n
t
and
uni
fo
rm
l
y
di
st
ri
b
u
t
e
d. T
h
e seque
nces ar
e det
e
rm
i
n
i
s
t
i
c
, but
e
x
i
s
t
e
nce
of n
o
i
s
e p
r
o
p
e
rt
i
e
s
sim
i
l
a
r t
o
ran
dom
ness [
1
2]
. In
ge
neral
,
a
pse
u
d
o
ra
n
d
o
m
seque
nce g
e
nerat
o
r i
s
us
ual
l
y
m
a
de up
of s
h
i
f
t
reg
i
sters with
feed
b
a
ck
. By lin
early
com
b
ini
n
g elem
ents from
the shift re
gi
ster a
nd
fee
d
ing t
h
em
back
to the
i
n
p
u
t
o
f
t
h
e
g
e
nerat
o
r,
we c
a
n
obt
ai
n a
se
que
nce
o
f
m
u
ch l
o
n
g
er
re
pea
t
l
e
ngt
h
usi
n
g
t
h
e sam
e
num
ber
o
f
d
e
lay ele
m
en
ts in
th
e sh
ift reg
i
ster.
T
h
e
r
efore, these
bl
ocks are also
refe
rre
d to as a li
near
fee
dbac
k
shift
regi
st
er
(LFSR
) [
13]
, [
1
4]
. Th
e l
e
ngt
h
of t
h
e shi
f
t
re
gi
st
er, t
h
e n
u
m
b
er of t
a
ps an
d t
h
ei
r
p
o
si
t
i
ons i
n
t
h
e
LFSR
are i
m
port
a
nt
t
o
gene
rat
e
pse
u
d
o
r
an
d
o
m
sequence
s
with
d
e
sirab
l
e au
to-correlatio
n pro
p
e
rties [1
5
]
.
The
out
put
s
fr
om
above sai
d
PR
NG
s su
ffe
r
fr
om
so
m
e
probl
em
s t
h
ey
i
n
cl
ude;
Pe
ri
o
d
s
are sh
ort
e
r
than e
x
pected
for
som
e
seed s
t
ates. Ge
nerate
d
num
bers
ha
ve lack
o
f
un
ifor
m
i
ty o
f
d
i
str
i
bu
tio
n, C
o
rr
elatio
n of
su
ccessi
v
e
v
a
l
u
es,
O
u
t
p
u
t
seq
u
e
n
ce is poor
d
i
m
e
n
s
io
n
a
l
d
i
str
i
bu
tio
n, Th
e d
i
stan
ces betw
een
w
h
er
e
so
m
e
val
u
es
occ
u
r
ar
e di
st
ri
b
u
t
e
d
di
ffe
rent
l
y
f
r
om
t
hose
i
n
a
ra
nd
om
seque
nce
d
i
st
ri
but
i
o
n.
Park
-Miller alg
o
rith
m
is u
s
ed
to
g
e
n
e
rate 3
2
-b
it seq
u
e
n
c
es o
f
k
e
y [16
]
. Th
e Park-Miller alg
o
rith
m
satisfies th
e fo
llo
wi
n
g
three criteria to
g
e
n
e
rate goo
d
pseud
o
rand
o
m
n
u
m
b
e
rs: sequ
en
ce is suffi
cien
tly
Ran
d
o
m
,
Sequen
ce fu
ll p
e
ri
od
, Efficien
t
Im
p
l
em
en
tatio
n
with
3
2
-b
it
arith
m
e
t
i
c.
The ge
ner
a
t
e
d
seque
nce o
f
3
2
-
b
i
t
seque
nce
key
s
are pl
ay
s a im
port
a
nt
rol
e
i
n
t
h
e cas
e of st
ream
ci
phe
r t
o
e
n
cr
y
p
t
and
dec
r
y
p
t
pl
ai
n t
e
xt
. I
n
c
r
y
p
t
o
gra
p
hy, a
stream
cipher
is asymme
tric key
cipher
whe
r
e
pl
ai
nt
ext
di
gi
t
s
are c
o
m
b
i
n
ed
wi
t
h
a
pse
u
do
ra
nd
om
ci
ph
er
di
gi
t
st
rea
m
(key
st
ream).
In a stream
ciphe
r
each plaintext digit
is
encrypt
e
d
one
at
a
time with the corresponding
digi
t
of t
h
e key strea
m
, to gi
ve a
digit
of t
h
e ci
p
h
e
r
t
e
xt
st
ream
. Fi
na
l
l
y
t
h
e gene
rat
e
d se
que
nce
o
f
3
2
-
b
i
t
pse
u
do
ran
d
o
m
key
s
and
by
sam
e
seq
u
ence
of
key
s
use
d
t
o
enc
r
y
p
t
an
d decry
p
t
pl
ai
n t
e
xt
of
12
8-
bi
t
.
sim
u
l
a
t
i
on of
pr
o
pose
d
sc
he
m
e
i
s
by
usi
ng veri
l
o
g-
HDL an
d MATLAB.Th
e im
p
l
em
en
tatio
n
with
th
e
h
e
lp
of
XI
LI
NX
Sp
artan
3E FPGA
kit.
The o
r
gani
zat
i
on
of t
h
i
s
pa
pe
r i
s
as fol
l
o
ws.
Sect
i
on I
I
des
c
ri
bes
Al
g
o
ri
t
h
m
desi
gn a
nd
archi
t
ect
u
r
e
of t
h
e
pr
op
os
ed PR
NG
, S
ect
i
on I
I
I
des
c
ri
be t
h
e
desi
gn
o
f
E
n
cry
p
t
i
on a
nd
Dec
r
y
p
t
i
o
n bl
ock
Th
e
im
pl
em
ent
a
t
i
o
n res
u
l
t
s
and s
y
nt
hesi
s re
po
rt
di
scusse
d i
n
s
ect
i
on I
V
. Fi
n
a
l
l
y
, t
h
e concl
u
si
o
n
i
s
pre
s
e
n
t
e
d i
n
th
e last section.
2.
PAR
K
-
M
ILL
E
R AL
GO
RI
THM
Park
-Miller al
g
o
rith
m
[16
]
is b
a
sed
on
t
h
e li
n
ear cong
ru
en
tial form
: X+1
= A X m
o
d
(2
31
-
1
)
. W
h
er
e
the consta
nt va
lue “A”
chose
n
as
16,807.
C
onst
A=168007;
(
2
<
A
< M
-
1)
M=2
147
483
647
;
(2
31
-1
)
q=127773;
(M di
v
A)
r=2836;
(M m
od A
)
Var
hi
:
=i
n_
seed
di
v
q;
lo
: =in
_
seed mo
d q
;
test: =a*
l
o
–
r
*h
i;
if test > 0 th
en
Ou
t
_
seed
:= test;
r
a
ndo
m
:
=o
u
t
_seed
/ m
;
else
Ou
t
_
seed
:= test +
m
;
r
a
ndo
m
:
=o
u
t
_seed
/ m
;
end;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
9-4
8
6
4
FPGA Imp
l
emen
ta
tion
o
f
Pa
rk-Miller Algo
rith
m t
o
Gen
e
ra
t
e
S
e
q
u
e
n
ce
o
f
3
2
-Bit Pseu
do… (Bh
a
r
a
t
esh
N
)
10
1
Steps
of the al
gorithm
are as
follows:
In
itialize th
e inp
u
t
i
n
_seed and
p
a
ram
e
ters,
1.
a = 168
07
m
=
2
,
1
4
7
,
48
3,647
, q
= 127
773
,
r
= 28
36
.
2.
Co
m
p
u
t
e th
e
valu
e of
h
i
= i
n
_seed
d
i
v q and
lo
= in_
s
eed
m
o
d q.
3.
The
n
c
o
m
put
e t
h
e co
rre
sp
o
n
d
i
ng t
e
st
val
u
e
.
4.
If test >
0, sa
ve test as ne
w
out_see
d
, ot
herwise sa
ve test
+ m
.
5.
Out
put
t
h
e ne
w out
_see
d.
6.
Iterate, a
n
d let
the out_seed be the
new in_s
eed.
As th
is algorith
m
is d
e
sig
n
e
d
fo
r co
m
p
u
t
er syste
m
, th
e li
mita
tio
n
of th
e p
r
ecision
o
f
t
h
e op
eratio
n
sy
st
em
i
s
cons
i
d
ere
d
. It
i
s
desi
gne
d f
o
r any
sy
st
em
whose
preci
si
o
n
i
s
32 bi
t
s
or l
a
r
g
e
r
. I
n
or
de
r t
o
avoi
d
ove
rfl
ow e
r
r
o
r,
t
h
e seed a
d
ds
a
m
a
xim
u
m
al
lowa
bl
e n
u
m
b
er m
i
n
t
h
e 32
bi
t
s
sy
st
em
at
bef
o
re t
h
e
out
put
i
n
th
e ev
en
t t
h
at th
e
v
a
lu
e
of th
e seed is no
t
p
o
s
itiv
e, as is illu
strated
in abov
e alg
o
rith
m
[16
]
.
Th
e
b
e
low Fi
gu
re
1
sho
w
s the flow ch
art
o
f
Park
Miller alg
o
rith
m
.
Here
first in
itialize ‘m
’ (2
31
-1
),
‘a’
(168
07
), ‘q’ (1
277
73
), ‘r’
(283
6), En
=0
an
d
In_
s
ee
d
is a u
s
er cho
i
ce 32
-b
it v
a
lu
e. After in
itializin
g
th
ese
val
u
es f
o
r
fi
rst
ran
d
o
m
genera
t
i
on En = 0 at
that
t
i
m
e
,
t
h
e
vari
abl
e
s hi
an
d l
o
have t
o
be c
a
l
c
ul
at
ed as In
_se
e
d
di
v
q
an
d
In
_s
eed m
od
q
res
p
ect
i
v
el
y
.
T
h
e
n
a
not
her
va
ri
a
b
l
e
Test
as
a*l
o
–
r*
hi
, i
f
t
h
i
s
val
u
e
i
s
great
er t
h
a
n
zero
t
h
en
ou
t_seed
b
eco
m
e
s Test, else ou
t_seed
b
eco
m
e
s Test + m
.
fin
a
lly ran
d
o
m
o
u
t
p
u
t
will calcu
lated
as
out
_see
d di
vi
d
e
d
by
m
.
at
t
h
i
s
st
age fi
r
s
t
r
a
nd
om
out
p
u
t
i
s
gene
rat
e
d
.
F
o
r t
h
e
next
ps
eud
o
r
an
d
o
m
num
ber
g
e
n
e
ration
,
En
= 1
no
w
ou
t_
seed
b
e
co
m
e
s In
_
s
eed
o
r
h
i
and
lo
will calcu
lated
as ou
t_
seed
d
i
v
q
an
d
ou
t_
seed
m
o
d
q
th
ere aft
e
r sam
e
step
s
will co
n
tinu
e
to
g
e
n
e
rate sequ
en
ce of
p
s
eu
do
rand
o
m
n
u
m
b
e
r
g
e
n
e
ration
.
Fi
gu
re
1.
Fl
o
w
C
h
art
The ent
i
r
e
ge
n
e
ral
bl
oc
k di
a
g
ram
i
s
show
n
i
n
Fi
gu
re
2. I
t
consi
s
t
s
o
f
P
R
NG m
odul
e,
Encry
p
t
i
o
n
B
l
ock,
Decry
p
t
i
on B
l
oc
k an
d sl
ave r
e
gi
st
e
r
. T
h
ese i
n
t
e
r
n
al
m
odul
es d
e
scri
be
d i
n
Fi
gu
re 3 a
n
d Fi
gu
re 5
.
PR
NG
bl
ock g
e
nerat
e
s
se
q
u
e
n
ce of 32
bi
t
p
s
eu
do ran
d
o
m
key
s
wi
t
h
t
h
e hel
p
of st
at
e
m
achi
n
e, di
vi
d
e
r
a
n
d
m
u
lt
i
p
l
i
e
r. He
r
e
we
use
d
a
n
A
H
B
b
u
s
p
r
ot
oc
ol
f
o
r
FP
G
A
I
m
pl
em
ent
a
t
i
on o
f
pr
op
ose
d
P
R
NG.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S
V
o
l
.
2,
No
. 3,
N
o
vem
b
er
2
0
1
3
:
99
– 10
5
10
2
Fi
gu
re
2.
Ge
ne
ral
B
l
ock
Di
a
g
ram
Fi
gu
re
3.
PR
N
G
B
l
oc
k
Th
e PR
NG m
o
du
le will u
s
e th
is 32
-b
it inp
u
t
in_
s
eed
nu
m
b
er to
g
e
n
e
rate its first 32
-b
it ou
tpu
t
out
_see
d w
h
e
n
‘R
eset
’ i
s
act
i
v
at
ed.
T
h
e sec
o
n
d
ran
d
o
m
num
ber ge
nerat
i
on
i
s
di
f
f
e
r
ent
fr
om
t
h
e fi
rst
i
n
t
h
e
i
n
p
u
t
dat
a
. The
secon
d
o
u
t
p
ut
out
_see
d i
s
generat
e
d usi
n
g t
h
e fi
rst
o
u
t
p
ut
out
_see
d as i
t
s
i
n_see
d n
u
m
b
er an
d
t
h
e s
ubse
q
uent
o
u
t
p
ut
s are
ge
nerat
e
d
usi
n
g t
h
ei
r i
m
m
e
di
at
e p
r
evi
ous
o
u
t
p
ut
s as i
n
_
s
eed
num
ber.
The PR
N
G
m
o
d
u
l
e
s
h
o
w
n i
n
Fi
gu
re
3 i
s
com
pose
d
m
a
i
n
l
y
of a
st
a
t
e
m
achi
n
e,
3
2
bi
t
b
oot
h
m
u
lt
i
p
l
i
e
r and
32
bi
t
fl
oat
i
n
g
poi
nt
di
vi
de
r.
The st
at
e
di
ag
r
a
m
of t
h
e PR
N
G
i
s
pres
ent
e
d
i
n
Fi
g
u
r
e
4.
Figure 4.
State Diagram
Th
e d
e
fau
lt state is 1
1
and
th
e PRNG will b
e
ac
tiv
ated
wh
en
th
e ‘Reset’ sig
n
a
l is hig
h
,
wh
i
c
h
changes the st
ate to 0. From
state
0
,
th
e in
pu
t in_
s
eed
i
s
co
m
p
ared
again
s
t q
u
o
tien
t
1
277
73
.
If th
e in
pu
t
in
_
s
eed
is less th
an
1
277
73
,
hi =in
_
seed
d
i
v q
will b
e
0
and
lo
= in_
s
eed
m
o
d
q
will b
e
th
e inp
u
t
in_
seed
. So
fro
m
Fig
u
r
e 2
,
o
n
l
y a
m
u
ltip
li
catio
n
ou
t_
seed
= a *
lo
i
s
needed a
nd a s
h
o
r
t
e
r pe
ri
o
d
of
p
r
o
d
u
ci
n
g
t
h
e ra
nd
om
n
u
m
b
e
r can
be ach
iev
e
d
.
Th
e PRNG th
en
go
es to
state 1
an
d
t
h
e m
u
ltip
li
catio
n
is tak
e
n fro
m
state 3
t
o
state
4.
On t
h
e ot
her
han
d
, i
f
t
h
e i
n
put
i
n
_s
eed i
s
g
r
eat
er
t
h
an
12
7
7
7
3
,
one
di
vi
si
o
n
i
n_see
d/
q
and
two
m
u
l
tip
licatio
n
s
a*
lo
and
r*h
i
are n
e
ed
ed. So it
g
o
e
s to
state 2 and follows the state
path. From
state 5
to state
9, the
s
e com
p
utations are ta
ke
n.
As s
o
on as t
h
e ope
r
ati
o
n
co
m
p
letes, th
e statu
s
reg
i
ster is u
p
d
a
ted.
Wh
en
th
ey
co
nv
er
g
e
at state 1
0
,
a
r
a
ndom n
u
m
b
e
r
is gen
e
r
a
ted
and
this n
u
m
b
e
r
is tak
e
n
as t
h
e inp
u
t to
r
e
star
t th
e
f
l
ow
at
either state 1
or 2. As
pa
rt of
the PRNG m
odule, th
e
booth
m
u
ltiplier is im
plem
ented us
ing
repeate
d
s
h
ift and
ad
d
ition
al
g
o
ri
th
m
.
Th
at is, sh
ift th
e seco
nd m
u
ltip
lica
n
d
to
co
rresp
ond
with
each
1
i
n
th
e fi
rst m
u
ltip
lican
d
and add t
o
the
result.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
9-4
8
6
4
FPGA Imp
l
emen
ta
tion
o
f
Pa
rk-Miller Algo
rith
m t
o
Gen
e
ra
t
e
S
e
q
u
e
n
ce
o
f
3
2
-Bit Pseu
do… (Bh
a
r
a
t
esh
N
)
10
3
Th
e flo
a
ting
po
in
t d
i
v
i
d
e
r is d
e
sign
ed
u
s
ing th
e rep
eated
sh
ift and
sub
t
ractio
n
alg
o
rithm wh
ich
is th
e
rev
e
rse of th
e
m
u
ltip
licat
io
n b
y
sh
iftin
g
an
d
ad
d
i
n
g
. Basically, d
i
v
i
sio
n
p
r
o
cess can b
e
su
mmarized
as
follows: s
h
ift t
h
e
divis
o
r t
o
c
o
rres
pond
wit
h
each
portion
of the
di
vide
nd,
s
ubt
ract di
visor from
that port
ion
of
t
h
e di
vi
de
n
d
a
n
d
co
ncat
en
at
e 0
o
r
1 t
o
t
h
e
re
sul
t
base
d
o
n
t
h
e
resul
t
of
t
h
e
su
bt
ract
i
o
n.
On
e
go
od
feat
u
r
e
o
f
t
h
e Park
-Miller algo
ri
th
m
is th
at “
m
”
is m
o
re th
an 2
b
illio
n
and
is th
erefo
r
e
bene
fi
ci
al
for s
e
ri
es sim
u
l
a
t
i
ons. T
h
i
s
al
go
ri
t
h
m
t
h
i
s
al
gori
t
hm
has passed
a wi
de ra
nge
o
f
st
at
i
s
t
i
cal t
e
sts and
is kn
ow
n as
one of
th
e b
e
st
[16
]
.
3.
ENC
R
Y
P
TIO
N
AN
D DEC
RYPTI
ON
B
L
OCK
The ge
ner
a
t
e
d
seque
nce o
f
3
2
-
b
i
t
seque
nce
key
s
are pl
ay
s a im
port
a
nt
rol
e
i
n
t
h
e cas
e of st
ream
ci
phe
r t
o
e
n
cr
y
p
t
and
dec
r
y
p
t
pl
ai
n t
e
xt
. I
n
c
r
y
p
t
o
gra
p
hy, a
stream
cipher
is asymme
tric key
cipher
whe
r
e
pl
ai
nt
ext
di
gi
t
s
are com
b
i
n
e
d
wi
t
h
a
pse
u
do
ra
nd
om
ci
ph
er di
gi
t
st
rea
m
(key
st
rea
m
). In ast
r
ea
m
ci
pher
each plaintext digit
is
encrypt
e
d
one
at
a
time with the corresponding
digi
t
of t
h
e key strea
m
, to gi
ve a
digit
of the ciphe
r
text stream
. An alternative nam
e
is a stat
e ci
pher, as t
h
e enc
r
y
p
t
i
on
of eac
h d
i
gi
t
i
s
depen
d
e
n
t
on
the curre
nt stat
e
Fi
gu
re 5.
Enc
r
y
p
t
i
on
a
n
d Dec
r
y
p
t
i
o
n of Pl
ai
n
Te
xt
The
desi
gn
B
l
ock
di
a
g
ram
o
f
E
n
cry
p
t
i
o
n
a
n
d
De
cry
p
t
i
o
n
i
s
sh
ow
n
i
n
Fi
gu
re
5.
He
re
w
e
use
d
a
xo
r
gat
e
s t
o
en
cry
p
t
an
d dec
r
y
p
t
t
h
e pl
ai
n
dat
a
.
W
h
at
e
v
er t
h
e
pse
u
d
o
ra
n
d
o
m
key
s
gene
ra
t
e
d fr
om
t
h
e desi
gne
d
PR
NG
we m
a
de t
h
at
3
2
-
b
i
t
seque
nce i
n
t
o
se
que
nce
of
1
28
bi
t
and
aft
e
r t
h
at
we di
d
bi
t
w
i
s
e x
o
r
ope
rat
i
o
n wi
t
h
a Pl
ai
n dat
a
t
h
e resul
t
obt
ai
n
e
d i
s
a ci
pher t
e
xt
i
e
, encry
p
t
e
d dat
a
of
12
8 bi
t
whi
c
h ca
nn
ot
be reada
b
l
e
so t
h
at
we can tra
n
sfer inform
ation. The
n
at the receiver si
de by using sa
m
e
128 bit of PRNG key to
Decry
p
t
En
cry
p
ted
d
a
ta b
y
th
e sam
e
b
itwise xo
r op
eratio
n
.
4.
IMPLEME
N
TATION AND
RESULT
The P
r
o
g
r
am
m
i
ng i
s
d
one
i
n
Ve
ri
l
o
g
-
Ha
r
d
wa
re
descri
pt
i
on l
a
n
g
u
ag
e
wi
t
h
be
ha
vi
o
r
al
l
e
vel
.
To
validate random
ness of the PRNG seque
nce MATLAB Software
used. The pr
oposed m
o
dule is successfully
sy
nt
hesi
zed
an
d i
m
pl
em
ent
e
d o
n
XIL
I
N
X
S
p
art
a
n
3E F
P
G
A
ki
t
.
Fi
gu
re
6.
Pl
ot
of
fi
rst
5
0
PR
N
seq
u
e
n
ce
wi
t
h
seed
in
pu
t 140
000
Fig
u
re 7
.
Mat
lab
first 2
000
0 PRN’s
with
inp
u
t
seed
1
400
00
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
64
IJR
E
S
V
o
l
.
2,
No
. 3,
N
o
vem
b
er
2
0
1
3
:
99
– 10
5
10
4
The
fi
rst
5
0
and
2
0
0
0
0
P
s
eud
o
ran
d
o
m
num
bers
ge
ne
rat
e
d as
di
sc
u
ssed i
n
sect
i
o
n I
I
fo
r a
n
ar
b
itr
ar
ily ch
o
s
en
inpu
ts in_
s
eed
1
400
00
,
a is 16
807
, m
is 2
1
474
836
47
r
e
su
ltin
g
p
l
o
t
s are sho
w
n
i
n
Fi
gu
r
e
6
an
d in
Fi
gu
re
7
resp
ectiv
ely. Th
e
p
l
o
t
shown in
Fi
g
u
re
6
rand
o
m
in
natu
re.
To v
e
rify th
e fu
n
c
tionality o
f
beha
vi
o
r
al
de
s
c
ri
pt
i
o
n o
f
t
h
e
al
go
ri
t
h
m
simul
a
t
i
on i
s
ca
rri
ed o
u
t
f
o
r sa
m
e
i
nput
s i
n
_s
eed, m
and
ob
t
a
i
n
ed
Mo
d
e
lsim
results is p
e
rfectly
match
i
n
g
with
MATLAB
results
Fi
gu
re
8.
M
o
d
e
l
s
im
sim
u
l
a
ti
on
resul
t
of
ge
n
e
rat
e
d
ran
d
o
m
num
bers a
n
d E
n
cry
p
t
i
o
n
-
De
cry
p
t
i
o
n
of
Pl
ai
n
Text.
Th
e
p
s
eu
do
ran
d
o
m
n
u
m
b
e
rs g
e
nerated from Park
–
Miller algo
rith
m
are u
s
ed
to
en
cry
p
t th
e tex
t
u
a
l
messag
e
.
Gen
e
rated
sequ
en
ce is con
v
e
rted into
32
b
it leng
th. The ob
tain
ed
3
2
b
it leng
th of k
e
ys
XOR ed
wit
h
pl
ai
n t
e
xt
ual
m
e
ssage c
o
nve
rt
ed i
n
t
o
A
S
C
I
I
di
gi
t
s
. T
h
e
gr
o
up
o
f
4
A
S
C
I
I
di
gi
t
f
o
rm
a fr
am
e of l
e
n
g
t
h
32
bi
t
.
In
t
h
i
s
pa
per
“NA
G
A
R
J
U
N
C
O
LLE
GE”
i
s
ch
ose
n
as
a
pl
ai
n t
e
xt
an
d
enc
r
y
p
t
e
d
wi
t
h
t
h
e
32
bi
t
r
a
nd
om
num
bers.
The
obt
ai
ne
d
3
2
bi
t
t
o
bec
o
m
e
a ci
phe
r t
e
xt
whi
c
h i
s
c
o
n
v
ert
e
d
back
t
o
t
e
xt
. T
o
decry
p
t
t
h
e c
i
phe
r
t
e
xt
sam
e
sequ
ence
of
key
s
a
r
e use
d
a
n
d re
v
e
rse
pr
ocess
us
ed t
o
get
bac
k
an
ori
g
i
n
al
pl
ai
n t
e
xt
Tab
l
e 1
.
Dev
i
ce
Utilizatio
n
R
e
p
o
rt o
f
PRNG
Th
e
Xilin
x FPGA RTL sch
e
m
a
t
i
c an
d syn
t
h
e
sis
repo
rt o
f
propo
sed Pseudo
Ran
d
o
m
n
u
m
b
e
r
Gene
rat
o
r i
s
s
h
ow
n i
n
Fi
gu
re
9,
Fi
g
u
re
1
0
a
n
d i
n
Ta
bl
e 1
.
M
a
xi
m
u
m
operat
i
n
g
f
r
eq
ue
nc
y
i
s
1
9
1
.
1
3
1
M
H
z.
Fi
gu
re
9.
X
I
LI
NX
R
TL
Sche
m
a
t
i
c
of PR
N
G
Fi
gu
re
1
0
. Ti
m
i
ng R
e
p
o
rt
of
P
R
NG
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RES I
S
SN
:
208
9-4
8
6
4
FPGA Imp
l
emen
ta
tion
o
f
Pa
rk-Miller Algo
rith
m t
o
Gen
e
ra
t
e
S
e
q
u
e
n
ce
o
f
3
2
-Bit Pseu
do… (Bh
a
r
a
t
esh
N
)
10
5
5.
CO
NCL
USI
O
N
In
t
o
d
a
y
’
s world
,
all th
e e-co
mmerce tran
saction
h
a
ppen
s
o
v
e
r th
e
in
tern
et.
Th
e
d
a
ta th
at is
trans
f
erred
ove
r the internet needs to be sec
u
red
before
the t
r
ansm
ission process ha
ppens. For these
purposes,
the data
needs
to enc
r
ypte
d
while tra
n
sm
is
sion a
n
d dec
r
y
p
ted at recei
vi
ng e
n
d wit
h
suitable key. T
h
e
m
a
in
in
pu
t to th
ese
alg
o
rith
m
s
is t
h
e
k
e
ys th
at are u
s
ed
for t
h
e
encry
p
tion and dec
r
yption
purposes. T
h
e
ke
ys ne
e
d
to
b
e
as random
as p
o
ssib
l
e i
n
o
r
d
e
r to
avo
i
d
an
y h
a
ck
ing
o
f
t
h
e
d
a
ta.
o
n
th
e o
t
h
e
r
h
a
nd
th
e I
m
p
l
e
m
en
tatio
n
,
Spee
d o
f
t
h
e e
n
cry
p
t
i
on
pr
oc
ess i
s
m
a
jor c
h
al
l
e
nge. T
h
e si
m
p
l
e
al
gori
t
h
m
m
a
y
be wo
r
k
ve
ry
fast
b
u
t
m
a
y
not
secu
re th
e d
a
ta. At
th
e
sam
e
t
i
m
e co
m
p
lex
alg
o
rith
m
m
a
y p
r
ov
id
e
b
e
tter
secu
rity
b
u
t
pro
cessing
tim
e may b
e
larg
e. Th
is lead
s t
o
Hard
ware d
e
scrip
tion
o
f
th
e algo
rith
m
.
In
th
is p
a
p
e
r
o
n
e
su
ch
Hard
ware d
e
scrip
t
io
n
of Park
-Miller alg
o
r
ithm to
g
e
n
e
rate th
e ran
d
o
m
num
ber i
s
di
scusse
d. T
h
e i
m
pl
em
ent
a
t
i
on of t
h
i
s
al
g
o
ri
t
h
m
has been
do
ne
usi
n
g t
h
e Veri
l
o
g.
The
desi
g
n
provides a random
num
ber on each cloc
k cycle. The random
nu
m
b
er ge
nerate
d are abl
e
to
m
eet the standa
rds
set
by
t
h
e NIS
T
and h
e
nce c
a
n be di
rect
l
y
use
d
fo
r C
r
y
p
t
o
g
r
a
phi
c al
g
o
r
i
t
h
m
key
s
. Thi
s
PR
NG i
s
bas
e
d o
n
sim
p
l
e
al
gori
t
h
m
and i
t
can be depl
oy
e
d
o
n
gener
a
l
FPG
A de
vel
o
pm
ent
boar
d
f
o
r de
s
i
gn ve
ri
fi
cat
i
o
n. The
d
e
sign
can
b
e
i
m
p
l
e
m
en
ted
com
p
le
tely in
d
i
gital circu
it an
d
d
o
e
s
n
o
t
requ
ire ex
tern
al co
mp
on
en
ts.
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NC
ES
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o
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lica
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e
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ans.
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e
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Evaluation Warning : The document was created with Spire.PDF for Python.