In this article, based on a network IDEA32-16, we have developed 5 new networks:RFWKIDEA32-16,RFWKIDEA32-8, RFWKIDEA32-4, RFWKIDEA32-2, RFWKIDEA32, that do not use round keys in round functions. It shows that in offered networks such Feistel network, encryption and decryption using the same algorithm as a round function can be used any transformation.

1. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
DOI:10.5121/ijcis.2015.5102
TO THE NETWORKS
4, 32–2 AND RFWKIDEA
NETWORK
ABSTRACT
In this article, based on a network IDEA32
RFWKIDEA32-16, RFWKIDEA32
not use round keys in round functions. It shows that in offered networks such Feistel network,
encryption and decryption using the same algorithm as a round function can be used any
transformation.
KEYWORDS
Feystel network, Lai–Massey scheme, encryption, decryption, encryption algorithm, round
function, round keys, output transformation, block, subblock, multiplication, addition,
multiplicative inverse, additive inverse
1.INTRODUCTION
H. Lai. and J. Massey replace the
PES [2]. However, after the publication of works by E. Biham and A. Shamir on the application
of the method of differential cryptanalysis to the algorithm PES, it was modified by increasing its
resistance and called IPES. A year later it was renamed IDEA [
schema Lai-Massey and the basis for the design of these algorithms is the "mixing operations
different algebraic groups".
Encryption PES and IDEA, similarly as in D
into four 16-bit sub-blocks and operations are carried out on these 16
process of encryption PES and IDEA to pairs of 16
operations:
In algorithms PES and IDEA, similarly as in DES, the block length is 64 bits. 64
divided into four 16–bit subblocks, and operations are performed on 16
process ofencryptionPESand IDEAto pairsof 16
groupoperations
− bitwise exclusive–OR (XOR), denoted as
− addition of integers modulo
representation of an integer on the basis of two. Operation is denoted as
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
2
ETWORKS RFWKIDEA32–16, 32–
FWKIDEA32–1, BASED ON
ETWORK IDEA32–16
Tuychiev G.N.
In this article, based on a network IDEA32-16 we have developed 5 new networks:
16, RFWKIDEA32-8, RFWKIDEA32-4, RFWKIDEA32-2, RFWKIDEA32, that do
not use round keys in round functions. It shows that in offered networks such Feistel network,
encryption and decryption using the same algorithm as a round function can be used any
Massey scheme, encryption, decryption, encryption algorithm, round
function, round keys, output transformation, block, subblock, multiplication, addition,
multiplicative inverse, additive inverse
H. Lai. and J. Massey replace the DES algorithm developed a new block encryption algorithm
PES [2]. However, after the publication of works by E. Biham and A. Shamir on the application
of the method of differential cryptanalysis to the algorithm PES, it was modified by increasing its
tance and called IPES. A year later it was renamed IDEA [3]. These algorithms are based on
Massey and the basis for the design of these algorithms is the "mixing operations
Encryption PES and IDEA, similarly as in DES, the block length is 64 bits. 64 bit block is divided
blocks and operations are carried out on these 16-bit sub-blocks. In the
process of encryption PES and IDEA to pairs of 16-bit sub-blocks used three different group
In algorithms PES and IDEA, similarly as in DES, the block length is 64 bits. 64
bit subblocks, and operations are performed on 16–bit subblocks.
process ofencryptionPESand IDEAto pairsof 16–bitsubblocksapplies thre
OR (XOR), denoted as ⊕ (xor);
addition of integers modulo
16
2 , when the subblock is considered as a typical
representation of an integer on the basis of two. Operation is denoted as (add);
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
2 9
–8, 32–
THE
16 we have developed 5 new networks:
2, RFWKIDEA32, that do
not use round keys in round functions. It shows that in offered networks such Feistel network,
encryption and decryption using the same algorithm as a round function can be used any
Massey scheme, encryption, decryption, encryption algorithm, round
function, round keys, output transformation, block, subblock, multiplication, addition,
DES algorithm developed a new block encryption algorithm
PES [2]. However, after the publication of works by E. Biham and A. Shamir on the application
of the method of differential cryptanalysis to the algorithm PES, it was modified by increasing its
]. These algorithms are based on
Massey and the basis for the design of these algorithms is the "mixing operations
ES, the block length is 64 bits. 64 bit block is divided
blocks. In the
blocks used three different group
In algorithms PES and IDEA, similarly as in DES, the block length is 64 bits. 64–bit block is
bit subblocks. In the
bitsubblocksapplies threedifferent
, when the subblock is considered as a typical

2. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
10
− multiplication of integers modulo 1216
+ , when the subblock is considered as a typical
representation of an integer in base two, except that the subblock of all zeros is assumed to be
16
2
. Operation is denoted as ⊗ (mul).
In encryption algorithms PES and IDEA round keys are multiplied by modulo 1216
+ and added
by modulo 16
2 with the corresponding subblocks. In MA the transformation is limited to the
operation of multiplication by modulo 1216
+ and addition by modulo 16
2 , i.e. not used
operations such as shift, substitution with S–box, etc. In the work [1, 4–6] by the authors based on
the structure of the encryption algorithm IDEA developed networks IDEA4–2, IDEA8–4,
IDEA16–8, IDEA32–16 consisting of two, four, eight and sixteen round functions. In developed
networks encrypted and decrypting, similarly as Feystel network, use the same algorithm. And as
round functions, it is possible to use any transformation.
In network IDEA32–16 in each round are applied 48 round keys, and 16 round keys are applied in
round functions, 32 round keys are multiplied and summed with the subblocks. Through the use
of 32 round key subblocks, round functions the network IDEA32–16 can be used without a key.
In addition, the network IDEA32–16 round functions have one input and output subblock. As
round functions you can use functions in which there are two input and output subblocks, four
input and output subblocks, eight input and output subblocks and sixteen input and output
subblocks. Scheme of n–rounded network IDEA32–16 shown in Figure 1.

3. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
Fig. 1. Scheme of n
In Fig. 1 zioperation ⊗ (mul),
, 8
2 ), ⊗–multiplication of integers modulo
In this paper on base of the network IDEA32
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
Fig. 1. Scheme of n–rounded network IDEA32–16
(add) or⊕ (xor). Here – addition of integers modulo
multiplication of integers modulo 1232
+ ( 1216
+ , 128
+ ).
on base of the network IDEA32–16 is developed:
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
11
addition of integers modulo 32
2 ( 16
2

4. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
12
− a network RFWKIDEA32–16 (round function without key IDEA32–16), consisting of
sixteen round functions,
− a network RFWKIDEA32–8 (round function without key IDEA32–8), consisting of eight
round functions,
− a network RFWKIDEA32–4 (round function without key IDEA32–4), consisting
of four round functions,
− a network (RFWKIDEA32–2 round function without key IDEA32–2), consisting
of two round functions,
− a network RFWKIDEA32–1 (round function without key IDEA32–1), consisting
of one round functions.
2.STRUCTURE OF THE NETWORK RFWKIDEA32–16
In the network RFWKIDEA32–16 length of the subblocks 0
X , 1
X , …, 31
X , length of the round
keys )1(32 −iX , 1)1(32 +−iX , …, 31)1(32 +−iX , 1...1 += ni , as well as the length of the input and output
subblocks round functions 0F , 1F , …, 15F equal to 32 (16, 8) bits. Scheme of n–rounded network
RFWKIDEA32–16 shown in Fig. 2, and the encryption process is given in the following formula.


















⊕=
⊕⊕⊕=
⊕⊕=
⊕=
⊕⊕⊕⊕⊕=
⊕⊕⊕=
⊕⊕=
⊕⊕⊕⊕⊕=
+−−
+−−
+−−
+−−
+−−
+−−
+−−
−−
0
31)1(320
31
1
31
210
13)1(3213
13
1
18
10
14)1(3214
14
1
17
0
15)1(3215
15
1
16
15210
16)1(3215
16
1
15
210
29)1(322
29
1
2
10
30)1(321
30
1
1
15210
)1(320
0
1
0
))((
..............................................................
))((
))((
))((
...))((
...............................................................
))((
))((
...))((
YKzXX
YYYKzXX
YYKzXX
YKzXX
YYYYKzXX
YYYKzXX
YYKzXX
YYYYKzXX
iii
iii
iii
iii
iii
iii
iii
iii
, ni ...1= (1)

5. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
13

















=
=
=
=
=
=
=
=
++
++
++
++
++
++
++
+
))((
........................................
))((
))((
))((
))((
........................................
))((
))((
))((
31320
3131
1
183213
1318
1
173214
1417
1
163215
1516
1
153215
1615
1
2322
292
1
1321
301
1
320
00
1
nnn
nnn
nnn
nnn
nnn
nnn
nnn
nnn
KzXX
KzXX
KzXX
KzXX
KzXX
KzXX
KzXX
KzXX
, in output transformation
Round function can be represented as )( 0
0
0
iTFY = , )( 1
1
1
TFY = , )( 3
2
2
TFY = ,…,
)( 15
15
15
TFY = . Here ⊕= +−− ))(( )1(321 jij
j
i
j
KzXT ))(( 16)1(3215
16
1 jij
j
i KzX ++−−
+
− , 15...0=j –
input subblocks of round functions and 0
Y , 1
Y , …, 15
Y – output subblocks of round functions

6. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
14
Fig. 2. Scheme of n–rounded network RFWKIDEA32–16
3.THE STRUCTURE OF THE NETWORK RFWKIDEA32–8,
RFWKIDEA32–4, RFWKIDEA32–2, RFWKIDEA32–1.
In the network RFWKIDEA32–16 round functions has one input and output subblock.In
addition, in block ciphers are used round function with two input and output subblocks.
On the basis network RFWKIDEA32–16 it is possible to build a network in which the
round function has four input and output subblock, eight input and output subblock and
the sixteen input and output subblocks. Network for which the round functions have two
input and output subblocks, and applies the eight round functions, called RFWKIDEA32–

7. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
15
8. Similarly, the network to which the round function has four input and output
subblocks, and applies four round distance functions is called RFWKIDEA32–4, etc. In
the same way the network RFWKIDEA32–2 and RFWKIDEA32–1.Scheme of the round
functions of the networks RFWKIDEA32–8, RFWKIDEA32–4, RFWKIDEA32–2,
RFWKIDEA32–1 shown in Fig. 3, 4, 5, 6.
In the network RFWKIDEA32–8 round functions 0F , 1F , 2F ,…, 7F have two input and output
subblocks, the length of subblocks is equal to 32 (16, 8) bits. If as the input subblock is put
],[0 10
TTT = , ],[1 32
TTT = , ],[2 54
TTT = , ..., ],[7 1514
TTT = , and as the output subblock of
the round functions take ],[0 10
YYY = , ],[1 32
YYY = , ],[2 54
YYY i = , ..., ],[7 1514
YYY = , the
round functions can be represented as )0(0 0 TFY = , )1(1 1 TFY = , )2(2 2 TFY = , ...,
)7(7 7 TFY = . For the correctness of the encryption process round function )0(0 0 TFY = can be
written as ),( 100
0
0
TTFY = , ),( 101
0
1
TTFY = , and round function )1(1 1 TFY = can be written as
),( 320
1
2
TTFY = , ),( 321
1
3
TTFY = and so on, round function )7(7 7 TFY = can be written as
),( 15140
7
14
TTFY = , ),( 15141
7
15
TTFY = .
Fig.3. Scheme of the round function of the network RFWKIDEA32–8
In the network RFWKIDEA32–4 round function 0F , 1F , 2F , 3F have four input and output
subblocks of 32 (16, 8) bits. If ],,,[0 3210
TTTTT = , ],,,[1 7654
TTTTT = ,
],,,[2 111098
TTTTT = , ],,,[3 15141312
TTTTT = –input subblock, ],,,[0 3210
YYYYY = ,
],,,[1 7654
YYYYY = , ],,,[2 111098
YYYYY = , ],,,[3 15141312
YYYYY = –output subblock of
round function, the round function can be represented as )0(0 0 TFY = , )1(1 1 TFY = ,
)2(2 2 TFY = , )3(3 3 TFY = . For the correctness of the encryption process round function
)0(0 0 TFY = can be written as ),,,( 32100
0
0
TTTTFY = , ),,,( 32101
0
1
TTTTFY = , …,
),,,( 32103
0
3
TTTTFY = , )1(1 1 TFY = rounder function can be written as
),,,( 76540
1
4
TTTTFY = , ),,,( 76541
1
5
TTTTFY = ,…, ),,,( 76543
1
7
TTTTFY = and so on,

8. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
16
rounder function ),3(3 3 KTFY = can be written as ),,,( 151413120
3
12
TTTTFY = ,
),,,( 151413121
3
13
TTTTFY = , …, ),,,( 151413123
3
15
TTTTFY = .
Fig.4. Scheme of the round function of the network RFWKIDEA32–4
Similarly, in the network RFWKIDEA32–2 round functions 0F , 1F have eight input and output
subblocks of 32 (16, 8) bits. If ],...,,[0 710
TTTT = , ],...,,[1 1598
iTTTT = –input subblock and
],...,,[0 710
YYYY = , ],...,,[1 1598
YYYY = –output subblock of round function, the round
function can be represented as )0(0 0 TFY = , )1(1 1 TFY = . For the correctness of the encryption
process round function )0(0 0 TFY = can be written as ),...,,( 7100
0
0
iTTTFY = ,
),...,,( 7101
0
1
TTTFY = , ….., ),...,,( 7107
0
7
TTTFY = ,round function )1(1 1 TFY = can be written
as ),...,,( 15980
1
8
TTTFY = , ),...,,( 15981
1
9
TTTFY = ,……., ),...,,( 15987
1
15
TTTFY = .
Fig.5. Scheme of the rounder function of the RFWKIDEA32 network
As the network RFWKIDEA32–2, if in the network RFWKIDEA32–1, as the input subblock take
],...,,[ 1510
TTTT = and as output subblock round function taking ],...,,[ 1510
YYYY = , the
round function can be represented as )(TFY = . For the correctness of the encryption process
round function )(TFY = can be written as ),...,,( 151000
TTTFY = , ),...,,( 151011
TTTFY = , ...,
),...,,( 15101515
TTTFY = .

9. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
17
Fig.6. Scheme of the round function of the network RFWKIDEA32–1
In networks RFWKIDEA32–8, RFWKIDEA32–4, RFWKIDEA32–2, RFWKIDEA32–1 j
iF – is
output 1+j subblock of round functions iF .
Encryption process networks RFWKIDEA32–8, RFWKIDEA32–4, RFWKIDEA32–2,
RFWKIDEA32–1 similar on (1) formula, but instead 10
YY ⊕ put 1
Y , instead 210
YYY ⊕⊕ put
2
Y and so on, instead 15210
... YYYY ⊕⊕⊕⊕ put 15
Y .
4.ROUND KEYS GENERATION OF THE NETWORKS
RFWKIDEA32–16, RFWKIDEA32–8, RFWKIDEA32–4,
RFWKIDEA32–2 AND RFWKIDEA32–1.
In −n roundednetworks RFWKIDEA32–16, RFWKIDEA32–8, RFWKIDEA32–4,
RFWKIDEA32–2 and RFWKIDEA32–1 in each round apply 32 round keys in the output
transformation 32 round keys, i.e. the number of all round keys equal to 3232 +n . When
encryption in Figure 1 is used instead of iK encryption round keys c
iK , while decryption round
decryption key d
iK .
In networks RFWKIDEA32–16, RFWKIDEA32–8, RFWKIDEA32–4, RFWKIDEA32–2,
RFWKIDEA32–1 decryption round keys the first round associated with the encryption round
keys by the formula (2).
))(,)(,)(
,)(,)(,)(,)(,)(,)(,)(
,)(,)(,)(,)(,)(,)(,)(
,)(,)(,)(,)(,)(,)(,)(
,)(,)(,)(,)(,)(,)(,)(
,)((),,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,(
012
3456789
10111213141515
141312111098
7654321
0
313230322932
2832273226322532243223322232
2132203219321832173216321532
14321332123211321032932832
732632532432332232132
323130292827262524232221201918
17161514131211109876543210
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
zc
n
dddddddddddddd
dddddddddddddddddd
KKK
KKKKKKK
KKKKKKK
KKKKKKK
KKKKKKK
KKKKKKKKKKKKKKK
KKKKKKKKKKKKKKKKKK
+++
+++++++
+++++++
+++++++
+++++++
=
(2)

10. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
If as operation zi, 15...0=i applies the operation mul, then
add, then KK −= and applies the operation xor, then
inversion K by modulo 1232
+ (
( 16
2 , 8
2 ).For 32, 16 and 8 bit numbers calculated
)12mod(1 161
+=⊗ −
KK , ⊗K
Decryption round keys output transformation associated with the encryption round key as
follows:
))(,)(,)(
(,)(,)(,)(
(,)(,)(,)(
(,)(,)(()
,,,
,,,
,,,,(
012
101112
11109
10
313029
212019
1211109
103132
32233222322132
32133212321132
33223213232
zczczc
zczczc
czczczc
zczcd
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
KKK
KKKK
KKKK
KKKK
KKKK
KKKK
KKKK
=+
+++
+++
+++
Similarly, the decryption round keys of the second, third, and n
round keys by the formula (3).
KK
KK
KK
KK
KK
KK
KKK
KKK
KKK
KKK
KKK
c
in
zc
in
c
in
zc
in
c
in
zc
in
c
in
zc
in
c
in
zc
in
c
in
zc
in
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
(,)(
(,)(
(,)(
(,)(
(,)(
(,)(
,,
,,
,,
,,
,,(
3
8
13
13
8
3
2)1(323)1(32
7)1(328)1(32
)1(3213)1(32
)1(3218)1(32
)1(3223)1(32
)1(3228)1(32
(3230)1(3229)1(32
(3223)1(3222)1(32
(3216)1(3215)1(32
)1(329)1(328)1(32
)1(321)1(32)1(32
++−++−
++−++−
++−++−
++−++−
++−++−
++−++−
+−+−
+−+−
−+−+−
−+−+−
+−+−−
As can be seen from equation (3) for decryption keys of encryption used in the reverse order, only
requires the computation of the inversion in accordance operation
in the first round encryption keys
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
applies the operation mul, then 1−
= KK , applies the operation mul
and applies the operation xor, then KK = , here 1−
K – multiplicative
( 1216
+ , 128
+ ), K− – additive inverse K by modulo
For 32, 16 and 8 bit numbers calculated mod(11
=⊗ −
KK
)12mod(1 81
+=⊗ −
K and K− K =0, =⊕ KK
Decryption round keys output transformation associated with the encryption round key as
(,)(,)(,)(,)(,)(,)
(,)(,)(,)(,)(,)(,)
)(,)(,)(,)(,)(,)(,)
,,,,,,
,,,,,,
,,,,,,
456789
141515141312
765432
272625242322
171615141312
8765432
322932283227322632253224
20321932183217321632153214
1032932832732632532432
zczczczczczc
zczczczczczc
czczczczczczc
d
n
d
n
d
n
d
n
d
n
d
nn
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
KKKKKKK
KKKKKK
KKKKKKK
KKKKKK
KKKKKK
KKKKKKK
+++++++
+++++++
+++++++
Similarly, the decryption round keys of the second, third, and n–round associated with encryption
niKK
KKK
KKK
KKK
KKK
KKK
KKK
KKKK
KKKK
KKKK
KKKKK
zc
in
zc
in
z
zc
in
zc
in
zc
in
z
c
in
zc
in
zc
in
z
c
in
zc
in
zc
in
z
c
in
zc
in
zc
in
z
c
in
zc
in
zc
in
z
c
in
zc
in
zc
in
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
d
i
...2),)(,)(,)
,)(,)(,)(,)
)(,)(,)(,)
(,)(,)(,)
(,)(,)(,)
)(,)(,)(,)
(,)(,)(()
,,,,,
,,,,,
,,,,,
,,,,,,
012
4567
101112
151514
11109
654
10
31)1(321)1(322
4)1(325)1(326)1(327
9)1(3210)1(3211)1(3212
14)1(3215)1(3216)1(3217
19)1(3220)1(3221)1(3222
24)1(3225)1(3226)1(3227
29)1(3230)1(32)1(3231)1
28)1(3227)1(3226)1(3225)1(3224)1
21)1(3220)1(3219)1(3218)1(3217)1
14)1(3213)1(3212)1(3211)1(3210)
7)1(326)1(325)1(324)1(323)1(322
=
=
++−++−
++−++−++−
++−++−++−+
++−++−++−+
++−++−++−+
++−++−++−+
++−++−+−+−
+−+−+−+−+−
+−+−+−+−+−
+−+−+−+−+
+−+−+−+−+−+
As can be seen from equation (3) for decryption keys of encryption used in the reverse order, only
requires the computation of the inversion in accordance operation zi, 15...0=i .When encryption
in the first round encryption keys c
K0 , c
K1 , …, c
K15 into subblocks are used in a operation
International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
18
applies the operation mul
multiplicative
by modulo 32
2
)12mod( 32
+ ,
1.
Decryption round keys output transformation associated with the encryption round key as
,)
,)
,)
,
,
,
3
13
8
28
18
30
20
10
zc
zc
z
K
K
+
(3)
with encryption
z
z
z
z
z
,)
,)
,)
,)
,)
,
9
14
12
7
2
14
(4)
As can be seen from equation (3) for decryption keys of encryption used in the reverse order, only
.When encryption
into subblocks are used in a operation zi,

11. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
19
then decryption the output transformation requires the computation of inversion operation, ie.,
0
)( 032
zcd
n KK = , 1
)( 1132
zcd
n KK =+ , ..., 15
)( 151532
zcd
n KK =+ . If z0= z3= z6= z9= z12= z15=mul, z1= z4=
z7= z10= z13= add, z2= z5=z8= z11= z14=xor, then (3) the formula is as follows:
))(,,
,)(,,,)(,,,)(,,,)(,,
,)(,)(,,,)(,,,)(,,,)(
,,,)(,,,)((),,,
,,,,,,,,,
,,,,,,,,,
,,,,,,,,,,(
1
313029
1
282726
1
252423
1
222120
1
191817
1
16
1
151413
1
121110
1
987
1
6
54
1
321
1
03132303229322832
273226322532243223322232213220321932
183217321632153214321332123211321032
93283273263253243233223213232
−
−−−−
−−−−−
−−
++++
+++++++++
+++++++++
+++++++++
−
−−−−
−−−
−−=
ccc
cccccccccccc
ccccccccccc
ccccccd
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
d
n
KKK
KKKKKKKKKKKK
KKKKKKKKKKK
KKKKKKKKKK
KKKKKKKKK
KKKKKKKKK
KKKKKKKKKK
5.CONCLUSION
In paper on the basis of the network IDEA32–16 developed networks RFWKIDEA32–16,
RFWKIDEA32–8, RFWKIDEA32–4, RFWKIDEA32–2 and RFWKIDEA32–1. In developed
networks, as round functions you can choose any transformation, including one–way functions.
Because when decrypting no need to calculate inverse functions so to round functions, ie,
Based on these networks, when the length of the subblocks is equal to 32 bits, you can construct
the encryption algorithm is the block length of 1024 bits, while the length of the subblocks is
equal to 16 bits, you can construct the encryption algorithm is the block length of 512 bits and the
length of the subblocks is equal to 8 bits, we can construct the encryption algorithm is the block
length of 256 bits. If you choose as operations zi, 15...0=i operation mul, add and xor, all
possible variants of this choice is equal to 16
3 .
The advantage of the developed networks is that the encryption and decryption using the same
algorithm. It gives comfort for creating hardware and software–hardware tools.
In addition, as the round function using the round function of the existing encryption algorithms
for example, encryption algorithms based on Feistel network, you can developed these algorithms
on the basis of the above networks.
REFERENCES
[1] Aripov M.M. Tuychiev G.N. The network IDEA4–2, consists from two round functions //
Infocommunications: Networks–Technologies –Solutions. –Tashkent, 2012. №4 (24), pp. 55–59.
[2] Lai X., Massey J.L. A proposal for a new block encryption standard //Advances in Cryptology – Proc.
Eurocrypt’90, LNCS 473, Springer–Verlag, 1991, pp. 389–404
[3] Lai X., Massey J.L. On the design and security of block cipher //ETH series in information
processing, v.1, Konstanz: Hartung–GorreVerlag, 1992.
[4] Tuychiev G.N. The network IDEA8–4, consists from four round functions // Infocommunications:
Networks–Technologies –Solutions. –Tashkent, 2013. №2 (26), pp. 55–59.

12. International Journal on Cryptography and Information Security (IJCIS), Vol. 5, No. 1, March 2015
20
[5] Tuychiev G.N. The network IDEA16–8, consists from eight round functions // Bulletin TSTU. –
Tashkent, 2014, №1, pp. 183–187.
[6] Tuychiev G.N. The network IDEA16–8, consists from sixteen round functions // Bulletin NUUz. –
Tashkent, 2013, №4/1, pp. 57–61.
Authors
TuychievGulomNumonovich – teacher of National university of Uzbekistan, Ph.D. in technics, Republic
of Uzbekistan, Tashkent, e-mail: blasterjon@mail.com