TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4463 ~ 4
4
6
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.548
3
4463
Re
cei
v
ed
De
cem
ber 2
4
, 2013; Re
vi
sed
Febr
uary 18,
2014; Accept
ed March 3, 2
014
Improved Multi-secret Sharing Scheme Based
on
One-Wa
y Function
Geng Y
o
n
g
-J
un*
1
，
G
uo L
i
-Zheng
1
，
Z
h
eng Ming-Hui
2
1
Departme
n
t of Computer Sci
ence a
nd T
e
chnol
og
y, He
nan
Univers
i
t
y
of Urban C
onstructi
on,
Ping
din
g
sh
an
467
03
6, Hena
n, Chin
a
2
Information Ac
adem
y H
ube
i Univers
i
t
y
of Nation
aliti
e
s,
Enshi 4
4
5
000,
Hub
e
i, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: geng
@hnc
j.e
du.cn
A
b
st
r
a
ct
T
he w
eakn
e
ss
He-D
aw
son
’
s
thresho
l
d
multi
-
secret sh
arin
g
sche
m
e
is
pr
esente
d
a
n
d
a
naly
z
e
d
.
By usi
n
g
the
one-w
a
y fu
ncti
on th
ou
ght
in
the H
e
-D
aw
so
n
sch
e
m
e, a new
multi-
use
an
d multi-sec
r
e
t
shari
ng sc
he
me is
pro
pose
d
. T
he i
m
prove
d
sche
m
e
is
multi-ti
me-us
e
of onc
e se
cr
et s
hares
distri
buti
o
n
and ca
n resist consp
i
rin
g
atta
ck. F
u
rthermor
e
, the new
scheme is multi-s
e
cret s
hari
ng, grou
p secrets c
a
n
be r
e
co
nstructed
in fr
ee
ord
e
r a
n
d
differe
nt gro
u
p
secre
t
is corr
espo
n
d
in
g to
differe
nt thresh
ol
d v
a
l
u
e
w
h
ich can
mee
t
w
i
th different practica
l ap
plic
ation. At
last, the sec
u
rity an
d efficie
n
cy of the n
e
w
propos
e
d
mu
lti-secret sh
arin
g sche
m
e
are an
aly
z
e
d
.
Ke
y
w
ords
:
Lagr
ang
e int
e
r
pol
ating
poly
n
o
m
i
a
l, li
near
pro
j
ec
tive g
e
o
m
etry, secret shari
ng, thresh
old,
one-
w
a
y function
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Secret sha
r
i
ng
schem
es ba
sed
on
Lagrang
e
int
e
rpol
ating p
o
lynomial an
d
line
a
r
proje
c
tive ge
ometry were
prop
osed in
depe
ndently
by Blakley [1
] and Shami
r
[2]. In a (t,
n)
threshold
se
cret sh
arin
g scheme, secret holde
r deliv
e
r
s t
he dist
in
ct
se
cret
valu
es (call
ed share
s
or shado
ws)
to n partici
pa
nts. At least t or more p
a
rticipa
n
ts
can
combi
ne the
i
r sh
are
s
an
d
recover the
se
cret, b
u
t o
n
ly t-1 o
r
le
ss me
mbe
r
s cann’t. Based
on the
s
e
propertie
s
,
se
cret
sha
r
ing
ha
s
been
used i
n
many fiel
d
s
of m
ode
rn
crypto
graph
y and i
s
a
n
importa
nt pa
rt of
mode
rn
crypt
ogra
phy.The
motivation for se
cret shari
ng is
se
cu
re
key man
age
ment. In som
e
situation
s
, th
ere i
s
u
s
ually
a key that provides a
c
ce
ss to many im
portant file
s. If such
a key
is
lost (e.g., the pe
rson
wh
o knows th
e
key i
s
lo
s
t, or th
e
com
puter th
at st
ore
s
the
key is
destroyed
), then
all the
im
portant
files b
e
com
e
in
a
ccessible. T
he
basi
c
i
dea
in
se
cret
shari
n
g is
to divide the
se
cret
key int
o
pie
c
e
s
a
nd
distrib
u
te
the
pieces to
different
perso
n
s
so
that ce
rtain
sub
s
et
s of th
e pe
rson
s
ca
n get tog
e
th
er to
re
cove
r the key. Th
e thoug
ht ca
n be
re
alize
d
b
y
mathemati
cs
method
s. A (t, n) thre
sh
old
scheme i
s
a
techni
que to
sha
r
e a
key
among
n u
s
e
r
s.
A thresh
old
scheme h
a
s many pra
c
tical ap
plicati
ons, such a
s
ope
ning a
bank vault
or
authenti
c
atin
g an ele
c
tro
n
i
c
fund
s tran
sf
er. Ho
weve
r,
there a
r
e
several
situation
s
in which m
a
ny
different
se
crets n
eed
to
b
e
sha
r
ed
am
ong
a g
r
o
up of
users.
In a
straightforwa
r
d app
roa
c
h, we
can
solve th
e pro
b
lem
b
y
using
any
exiting thre
shol
d sch
e
m
e
rep
eatedly
and di
strib
u
t
ing
multiple se
cret shad
ows to each
user i
n
the grou
p. Acco
rdin
g to [3], when a grou
p se
cret has
been re
co
nst
r
ucte
d,
if
ano
ther se
cret n
eed
to be
re
con
s
tru
c
ted,it
is
requi
re
d that the trust
ed
cente
r
(T
C)
redi
strib
u
te fresh
sha
r
e
s
to ev
ery parti
cipa
nt, which
is called a
one-time
-u
se
scheme. T
o
distrib
u
te sha
r
es i
s
a ve
ry
pun
ctilio
u
s
and
co
stly proce
s
s. For t
h
is rea
s
on, t
h
e
prop
erty of
multi-time-use of on
ce
secret sh
ar
es distrib
u
tion i
s
ne
ce
ssary
in se
cret sh
a
r
ing
scheme
s
. He
-Da
w
son [4]
prop
osed a
multi-sta
ge
se
cret
sha
r
in
g schem
e to
sha
r
e m
u
ltiple
se
cret
s ba
se
d on one
-wa
y
function. They use
d
the public shift techni
que to obtain the true
sha
r
e
s
a
nd t
he
su
ccessiv
e
ap
plicatio
n
s
of
one
-w
ay functio
n
to
make
the
se
crets
re
co
nstructed
stage
-by-stag
e
in sp
eci
a
l
o
r
de
r.
Th
e sch
e
me allo
ws
a g
r
o
u
p
o
f
us
er
s to
s
h
ar
e mu
ltip
le
s
e
c
r
e
t
s
and
ea
ch
use
r
o
n
ly nee
ds t
o
keep
on
e
shado
w.
L
a
ter,
Ha
rn
[5] pro
posed
an
alte
rnative
sche
me
to reali
z
e the
same
functio
n
. Cha
ng [6]
also
pro
p
o
s
e
d
a sch
e
me t
hat he
claime
d it wa
s supe
rior
to He-Da
w
so
n and
Ha
rn’
s
two sche
me
s. Ho
weve
r, Cha
ng de
cla
r
ed hi
s sche
m
e
re
con
s
truct
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4463 – 4
467
4464
grou
p
se
cret
s in th
e fixed
ord
e
r
rath
er than fr
ee order. Re
cently
,
anothe
r sev
e
ral multi-se
cret
s
c
h
e
m
e [7
-9
]
w
e
re
pr
op
os
ed
, th
e
r
a
r
e
les
s
e
ffic
i
en
t tha
n
H
e
-D
aws
o
n
’
s
sc
h
e
m
e
wh
ic
h us
es
one
-
way functio
n
to reali
z
e mult
i-se
cret sh
ari
ng.
In this pape
r, we will sho
w
He
-Dawso
n sc
heme’
s
wea
k
n
e
ss th
at it is one-time-u
se
scheme
an
d
can’t
end
ure
con
s
pi
ring
attack. At t
he same
time, we
shall also use
the one
-way
function
thou
ghts i
n
the
He-Dawso
n
scheme
to
p
r
o
pose
a
ne
w multi-secret sharin
g sche
me.
The
ne
w sc
h
e
me
is mult
i-t
i
me-u
se of
o
n
ce se
cr
et sh
are
s
di
strib
u
tion an
d secure. Furthe
rmo
r
e,
the ne
w sch
e
m
e is
multi-secret shari
n
g
,
grou
p
secre
t
s ca
n be
re
constructe
d in
free o
r
de
r a
nd
different grou
p se
cret is co
rre
sp
ondi
ng to different
thresh
old value
whi
c
h can m
eet with different
pra
c
tical
ap
pl
ication. At la
st, the
se
cu
ri
ty
of the ne
w p
r
op
osed
multi-secret
sha
r
ing
sch
e
m
e
betwe
en the
new a
nd the
old schem
e a
r
e analy
z
ed.
2. Chara
ceri
s
tics o
f
One
-
w
a
y
Hash Fu
nction
A hash fun
c
tion
h
() is a transfo
rmatio
n that takes a
variabl
e-si
ze input m and return
s a
fixed-si
ze
stri
ng, which i
s
called th
e h
a
sh value
h
(that
is
,
h
=
h
(m)). Has
h
func
tions
with jus
t
this
prop
erty h
a
ve a va
riety of
gen
eral
com
putational
u
s
es, b
u
t
when
employed
in
cryptog
r
a
phy
the
hash fun
c
tion
s a
r
e
usually
cho
s
e
n
to
ha
ve som
e
a
ddi
tional p
r
op
erti
es. T
he b
a
si
c req
u
irement
s
for a
crypto
g
r
aphi
c
ha
sh f
unctio
n
a
r
e: t
he inp
u
t can
be of
any le
ngth, the o
u
tput ha
s a
fixed
length,
h
(x) is relatively ea
sy to comput
e for any given
x
,
h
(x) is one-way,
h
(x
) is colli
sion
-fre
e.
A hash fun
c
ti
on
h
() is said
to be
one
-wa
y
if
it is hard t
o
invert,
wher
e "ha
r
d to i
n
vert" mea
n
s th
a
t
given a ha
sh
value
h
, it is comp
utationa
lly infeasible t
o
find som
e
input
x
such that h (x) =
h
.
If
given a me
ssage
x
, it is co
mputationally
infeasi
b
le to
find a me
ssa
ge
y
not equ
al to
x
su
ch
t
hat
h
(x
) =
h
(y) t
hen
h
()
is said to be a weakly co
lli
sion-free hash function.
A strongly collision-free
hash fun
c
tion
h()
is
one fo
r whi
c
h it i
s
co
mputationally
infeasi
b
le to
find any two
messag
es x and
y s
u
ch that
h(
x)
=
h
(
y
)
. T
h
e ha
sh value
rep
r
e
s
ent
s conci
s
ely the l
onge
r me
ssa
ge or
do
cum
ent
from which it
wa
s comp
ute
d
; one
can
th
ink of a
me
ssage di
ge
st as a "digital fin
gerp
r
int" of th
e
large
r
do
cum
ent. Examples of well-kn
o
w
n ha
sh
fun
c
tions are MD2 and MD5 and SHA. Perh
aps
the main
rol
e
of a
crypto
grap
hic
ha
sh
function
i
s
i
n
the p
r
ovisi
on of digital
sign
ature
s
. T
h
e
followin
g
sch
e
mes u
s
e th
e characte
rist
ics of the
ha
sh fu
nctio
n
to re
alize effi
cient m
u
lti-se
cret
sha
r
ing.
3. He-Da
w
s
o
n’s Multi-se
cret Sharin
g Scheme
In
He
-Dawso
n’s schem
e, the
tru
s
ted center (T
C)
g
enerat
es the
gro
up
se
cre
t
s an
d
make
s g
r
ou
p
membe
r
s
re
construct g
r
ou
p se
crets in
speci
a
l order.
They claim
e
d
their sch
e
me
to
be a
multi-ti
me-u
se
sch
e
m
e of o
n
ce
se
cret
sh
ar
e
s
di
strib
u
tion.
Thei
r
sche
me notatio
ns are
defined
a
s
fol
l
ows. Let
p
p
Z
Z
h
:
be
any on
e-way
function
an
d
p is a
big
p
r
i
m
e inte
ger
while
)
(
m
h
k
denote
s
k succe
s
sive appli
c
atio
ns of h
to m; i.e.,
m
m
h
)
(
0
, and
)).
(
(
)
(
1
m
h
h
m
h
k
k
A
ssum
e
t
he TC want
s t
o
sha
r
e k
se
cret
s
i
s
(for
)
,
,
2
,
1
k
i
and at
least t pa
rtici
pants
ca
n re
con
s
tru
c
t the
se
cret
s. Th
en, the T
C
randomly
cho
o
se
s
n distin
ct
integers
i
ID
(
f
o
r
)
*
p
i
Z
ID
as the
parti
cipa
nts’ pu
bli
c
identity informatio
n and
performs th
e
f
o
llowin
g
st
ep
s:
Step 1: Rand
omly choo
se
n
x
x
x
,
,
,
2
1
)
(
*
p
i
Z
x
as the secret
sha
r
e
s
.
Step 2: For
k
i
,
,
2
,
1
execute
s
the followin
g
step
s:
1. Con
s
tru
c
ts a polynomial
)
(
x
P
i
of degree (t
-1) and
i
i
s
P
)
0
(
.
2. Compute
s
)
(
j
i
ij
ID
P
Z
,for
n
j
,
,
2
,
1
.
3. Compute
s
)
(
1
j
i
ij
ij
x
h
Z
d
as the shift value
s
and
)
(
1
j
i
x
h
as the
pse
udo share
s
, for
n
j
,
,
2
,
1
.
Step 3:
Delivers
i
x
to each partici
pant se
cretly and pu
blish
e
s all
ij
d
, f
o
r
k
i
,
,
2
,
1
and
n
j
,
,
2
,
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Im
proved Mul
t
i-se
cret Sharing Schem
e
Bas
ed o
n
On
e-Way F
u
n
c
tion (Ge
ng Yo
ng-Jun
)
4465
At least t
parti
cipa
nts provid
e th
eir p
s
e
udo
sha
r
e
s
in
the spe
c
i
a
l order:
)
(
,
),
(
),
(
0
2
1
j
j
k
j
k
x
h
x
h
x
h
(for
t
j
,
,
2
,
1
),
to recons
truc
t the
polynomials
)
(
x
P
i
for
.
1
,
,
1
,
k
k
i
Then ea
ch
se
cret i
s
re
con
s
tructed th
rou
gh the followi
ng formul
a (
.
1
,
,
1
,
k
k
i
):
l
a
b
b
b
a
b
t
a
ia
a
l
i
i
ID
ID
ID
d
x
h
P
s
,
1
1
1
)
)
(
(
)
0
(
(1)
The se
cret are re
co
nstruct
ed in the sp
e
c
ial orde
r;
1
1
,
,
,
s
s
s
k
k
.
4. The Shortage of
He-Da
w
s
o
n’s Sche
me
He-Da
w
son’
s Schem
e isn’
t multi-time-u
se
schem
e.
To re
con
s
tru
c
t the final
se
cret
1
s
, at lea
s
t t p
a
rticip
ants m
u
st p
r
ovide
t
heir pseud
o
sha
r
e
s
)
(
0
i
x
h
for
t
i
,
,
2
,
1
. Note that
i
i
x
x
h
)
(
0
. So, after
rec
o
ns
truc
ting
all the
s
e
cret
s
,
the
TC mu
st di
strib
u
te n
e
w
se
cret
sh
ado
w
'
i
x
to each pa
rti
c
ipa
n
t over a
se
cret ch
ann
el
be
cau
s
e ol
d
memb
er se
cret sh
are
s
i
x
has
bee
n
publi
c
ized. Thus, their
sch
e
mes b
e
lon
g
s
to the one
-time-u
s
e
sche
me.
He-Dawso
n’
s sch
e
me can’t endu
re
con
s
pi
ring
attack. If someone first p
r
ovide
s
her/hi
s
pseu
do sh
are
)
(
1
1
x
h
, the other
partici
pant
s can
e
a
sily
obtain he
r/hi
s pseud
o
s
h
ar
es
)
(
,
),
(
),
(
1
1
1
3
1
2
x
h
x
h
x
h
k
. Th
en o
n
ly (t-1
) othe
r
part
i
cipa
nts
can
co
ope
rate
to
rec
o
n
s
t
r
u
c
t
t
he se
cret
s
k
s
s
s
,
,
,
3
2
.
5. The Improv
ed
Multi-time-use Multi-secret Sharing Scheme
5.1. Sy
stem
parame
ters I
n
itialization
and Secre
t
Shado
w
s dis
t
ribution
The p
r
op
ose
d
sche
me n
o
t
ations a
r
e
d
e
fined a
s
foll
ows. Let
p
p
Z
Z
h
:
be
a se
cu
re
one-way fun
c
tion and p i
s
a big p
r
ime in
teger
while
)
(
m
h
k
denote
s
k
su
ccessive appli
c
ations
of
h to m and g is a primitive element of
*
p
Z
.
A
ssu
me t
he TC wa
nt
s t
o
sha
r
e k g
r
ou
p se
cret
s
i
s
(for
)
,
,
2
,
1
k
i
and diffe
rent t parti
cip
ants
can
reconstr
uct the
corre
s
p
ondin
g
gro
up secrets.
the
tru
s
ted cente
r
(TC)
ran
domly
cho
o
s
e
s n dist
in
ct
int
e
g
e
rs
i
ID
(
)
*
p
i
Z
ID
as th
e
partici
pant
s’ publi
c
inform
ation and p
e
rf
orm
s
the follo
wing
step
s:
Step 1: Rand
omly choo
se
n
x
x
x
,
,
,
2
1
)
(
*
p
i
Z
x
as the mem
b
er se
cret sh
ares.
Step 2: For
n
i
,
,
2
,
1
execute
s
the
followin
g
step
s:
1) Con
s
tru
c
t
a
polynomial
)
(
x
P
i
of degree
(t-1) an
d comp
ute gro
up
se
cret
s
i
s
,
)
0
(
i
P
v
,
p
g
s
v
i
mod
.
2) Comp
ute
)
(
j
i
ij
ID
P
Z
, for
n
j
,
,
2
,
1
.
3) Comp
ute,
p
x
h
c
j
i
ij
mod
)
(
1
,
)
(
1
j
i
ij
ij
x
h
Z
d
and
p
g
q
ij
c
ij
mod
as the pse
udo
s
h
ares
, for
n
j
,
,
2
,
1
.
4) Comp
ute
p
g
r
ij
d
ij
mod
for
n
j
,
,
2
,
1
.
Step 3: Deliver
i
x
to each particip
ant se
cretly and pub
lish all
ij
r
for
k
i
,
,
2
,
1
and
n
j
,
,
2
,
1
.
5.2. Group Secre
t
Re
con
s
truc
tion
Without l
o
si
n
g
ge
ne
rality, assume
that
n
different g
r
oup
se
crets reco
nstructio
n
poli
c
y
exit in the gro
up. For e
a
ch
policy, there is a
corre
s
po
n
d
ing g
r
ou
p se
cret a
nd thre
shol
d value.
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4463 – 4
467
4466
(
)
,
,
2
,
1
n
i
are g
r
ou
p
se
cret
s. Assum
e
to recon
s
truct the
group
se
cret
l
s
by the co
-op
e
ration
of at least
l
particip
ants . T
hey provide t
heir p
s
eu
do
share
s
lj
q
(for
l
j
,
,
2
,
1
) to the gro
up
se
cret
combi
ner. After the
group
se
cret combin
er re
ceive
s
pseud
o sha
r
e
s
lj
q
, he reconst
r
u
c
ts
the grou
p se
cret
l
s
throug
h the followi
ng formul
a:
l
j
b
b
b
j
b
ID
ID
ID
lj
lj
l
j
l
q
r
s
,
1
)
(
1
l
j
l
j
b
b
b
j
b
j
l
j
l
lj
ID
ID
ID
x
h
x
h
Z
g
1
,
1
1
1
))
(
)
(
(
p
g
l
P
mod
)
0
(
(2)
The group
se
cret
s can be reco
nstructe
d in the free order.
6. Analy
ses
of the Impro
v
ed
Scheme’s Securit
y
6.1.
The Scheme is Multi-time-use
To re
con
s
tru
c
t the gro
up
se
cret
l
s
, at least l parti
cip
ants mu
st provide their p
s
eu
do
s
h
ar
es
lj
q
. From
p
g
q
lj
c
lj
mod
, attacker can’t get
p
x
h
c
j
l
lj
mod
)
(
1
be
ca
use
it is
a discrete log
a
rithm proble
m
. Though at
tacker can ge
t
lj
c
, he still can’t get
i
x
beca
u
se of one-
way functio
n
’
s
ch
ara
c
te
r. On the other
hand, to
sha
r
e k se
crets in
our sche
me, each parti
cip
ant
only need to
kee
p
one
se
cret sha
r
e
i
x
.
6.2.
The Ne
w
S
c
heme is Multi-secr
et Shar
ing
It improves the flexibility of
t
he scheme and
can meet
with di
fferent practical
appl
ication
becau
se diffe
rent g
r
ou
p
se
cret
s i
s
corre
s
po
ndin
g
to
different
se
cret polynomi
a
l function
in t
he
scheme i
n
itial
i
zation. T
he
grou
p secret
i
s
(
)
,
,
2
,
1
k
i
can b
e
re
constructe
d in
free o
r
de
r. If
l
s
is b
e
recon
s
tructed,
1
l
s
and
1
l
s
isn’t influ
e
n
c
ed be
ca
use a
ttacke
r
can’t
get mem
ber
se
cret
sha
r
ing a
c
co
rding to discre
te logarithm p
r
oble
m
.
6.3.
Less than T
h
reshold Val
u
e Members
can’t Recon
s
truc
t Corre
sponding Gr
oup Secre
t
Attac
k
e
r
s
c
an’t
r
e
cover
s
e
cr
et
polynomial
)
(
j
l
ID
P
becau
se th
ese
pro
b
lem
s
are
ba
sed
on discrete lo
garithm p
r
obl
em se
cu
rity
and Shamir’
s
secret sha
r
in
g scheme.
6.4.
The Scheme
can Resis
t
Cons
piring Attac
k
If some gro
up memb
ers want to co
nspi
ring atta
ck to ge
nerate grou
p secret, the
recons
truc
ting formula
c
a
n’t work
s
u
cc
es
s
f
u
lly be
ca
u
s
e attacke
r
can’t imperso
n
a
te right
lj
r
.
7. Analy
ses
of the Impro
v
ed
Scheme’s Performan
c
e
Shamir’
s
se
cret sha
r
ing, d
i
screte l
oga
rithm p
r
oble
m
and
one
way
functio
n
a
r
e
use
d
in
the multi-se
cret shari
ng
scheme
so
that
their co
mputation co
mplexity
is different.
Th
eir
differen
c
e
of
perfo
rman
ce
i
s
li
sted in
the
followin
g
Ta
ble 1.
√
repre
s
ent
s the
se
curity me
chani
sm
is used an
d ×rep
re
sent
s the se
curity me
cha
n
ism i
s
n’t use
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Im
proved Mul
t
i-se
cret Sharing Schem
e
Bas
ed o
n
On
e-Way F
u
n
c
tion (Ge
ng Yo
ng-Jun
)
4467
Table 1. Perf
orma
nce Co
mpari
s
o
n
of Schem
e 1 [4], Scheme 2 [10] and Improved Sche
me
Securit
y
mechani
sm
Improved schem
e
Scheme 1 [4]
Scheme 2 [10]
Shamir’s secret sharing
√
√
√
discrete logarithm problem
√
×
√
one w
a
y
function
√
√
×
The three
scheme i
s
em
u
l
ated in
su
ch
runt
ime envi
r
onm
ent
a
s
Cele
ron 1.4G
Hz +
1
G
RAM + Wi
n
dows XP + VC8.0. The
experim
ent
ma
inly comp
ares mem
ber
se
cret
shad
o
w
distrib
u
tion a
nd sh
arin
g se
cret recon
s
truction’
s e
ffici
ency in the th
ree
sch
eme.
Sha1 is
sele
cted
as o
ne way functio
n
, mod
u
lo p of 51
2
,
768,102
4 an
d 1280
bit is sele
cted.Th
e
comp
ari
s
on
of
efficien
cy in tne three
sche
me is a
s
following Fig
u
re 1
.
Figure 1. Co
mpari
s
o
n
of Membe
r
Secret
Shadow
Di
stributio
n and
Sharing Se
cret
Rec
o
ns
truc
tion’s
Effic
i
enc
y
in the Three Sc
heme
8. Conclusio
n
The
sh
ortag
e
s
of
He-Da
w
son’
s m
u
lti-se
cret
sha
r
i
ng
sch
e
me
wa
s an
alyzed a
n
d
pre
s
ente
d
in
this a
r
ticle,
which i
s
o
n
e
-
time-u
se
sche
me an
d can’t
re
sist
con
s
p
i
ring
attack. A
improve
d
ne
w multi-se
cret shari
ng schem
e wa
s
prop
osed by
using the o
ne-way funct
i
on
thought
s
in
t
he He-Da
w
son scheme. The
im
prove
d
sch
e
me i
s
multi-time
-u
se
of on
ce
secret
sha
r
e
s
di
stri
bution an
d can re
si
st con
s
piri
ng
atta
ck. Furthermore, the new
schem
e is m
u
lti-
se
cret
sha
r
in
g, grou
p se
crets ca
n be
re
con
s
tru
c
ted i
n
free o
r
de
r
and different grou
p secret
is
corre
s
p
ondin
g
to diffe
rent
thre
shol
d val
ue
which
can
meet with
different
practi
ca
l appli
c
ation.
At
last, the se
cu
rity and efficiency of the n
e
w propo
se
d multi-secret sharin
g sche
m
e
are an
alyze
d
.
Referen
ces
[1]
GR
Blakley
.
Sa
feguar
din
g
cryptogra
phic k
e
y
s
. Nationa
l Co
mputer Co
nfer
enc
e. 19
79; 48
(1): 165-1
72.
[2]
A Shamir. Ho
w
to share a secret.
Commu
n
ic
ations of the A
C
M
. 1979; 22(
11): 612-
61
3.
[3]
Wen-ai J
a
ckson, Keith M Mar
t
in
, Christine M
O’Keefe. On s
haring
many
s
e
crets. Asiacr
ypt’94. 1994:
42-5
4
.
[4]
J He, E
Da
w
s
on. Mu
ltistag
e
secret s
hari
n
g b
a
sed
o
n
o
ne-
w
a
y functi
o
n
.
Electronics Letters.
199
4;
30(1
9
): 159
1-1
592.
[5]
L Harn. Multist
age secr
et sha
r
ing b
a
sed
on
one-
w
a
y functi
on.
Electron
ics
Letters
. 1995;
31(4): 26
2.
[6]
T
i
ng-Yi Ch
an
g, Min-S
h
ia
ng
H
w
a
n
g
, W
e
i-Pa
ng Y
a
n
g
. A
ne
w
multi-st
age
s
e
cret sh
arin
g s
c
heme
usi
n
g
one-
w
a
y functi
on.
Association for Co
mp
utin
g
Machin
ery
. 20
05; 39(2): 4
8
-5
5.
[7]
Z
hou Yous
he
ng. D
y
namic
multi-secret
s
hari
ng schem
e base
d
on cellu
lar a
u
toma
ta.
Journal o
f
computer res
e
arch an
d dev
el
op
me
nt.
2012;
49(9): 19
99-
20
04.
[8]
Hou
Jia
n
ch
un
. Improved
v
e
rifia
b
le
multi-
secret sh
arin
g
schem
e.
Co
mp
uter
E
ngi
n
eeri
ng an
d
Appl
icatio
ns.
2
012; 48(
14): 94
-97.
[9]
Han H
u
i
y
i
ng. Varia
b
le thres
h
o
l
d muti-secret
s
hari
ng schem
e, Natural sci
e
n
ce jo
urna
l of harb
i
n norm
a
l
univ
e
rsit
y
.
2
0
1
2
; 28(3): 29-3
1
.
[10]
Z
hao JJ, Z
han
g JZ
, Z
hao R. A practi
ca
l veri
fiabl
e multis
ecr
e
t shari
ng sch
eme.
Co
mp
ute
r
Standar
ds
&
Interfaces
. 200
7; 29(1): 13
8-1
41.
mem
be
r s
ec
ret
s
had
ow
di
str
ib
uti
on
0
50
0
10
00
15
00
20
00
25
00
30
00
51
2
7
6
8
10
24
12
80
the
l
eng
th
of
m
odu
lo
p
(bi
t)
tim
e c
o
st
(μ
s
)
sch
eme
2
imp
rov
ed
sch
eme
1
sha
ring secret
reconstructi
o
n
0
20
0
40
0
60
0
80
0
10
00
12
00
14
00
16
00
512
7
68
1
024
1280
the l
ength of modu
lo p (bit)
ti
me c
ost
(μ
s)
sche
me2
impr
oved
sche
me1
Evaluation Warning : The document was created with Spire.PDF for Python.