International Journal of Engineering Trends and Technology (IJETT) – Volume X Issue Y- Month 2015
MODIFIED DES WITH PAIRING FUNCTIONS
Dr. S. Kiran#1, N. Subramanyan*2, Dr. T. Bhaskar Reddy#3, G. Madhavi*4
#1
Assistant Professor, Department of CSE
Y.S.R. Engineering College of YV University, Proddatur, Andhra Pradesh, India.
*2
Teaching Assistant, Department of CSE
Y.S.R. Engineering College of YV University, Proddatur, Andhra Pradesh, India.
#3
Professor & Head, Department of CST
Sri Krishna Devaraya University, Ananthapuram, Andhra Pradesh, India.
*3Assistant Professor, Department of CSE
MeRITS, Udayagiri, Andhra Pradesh, India.
1
2
3
rkirans125@gmail.com
subramanyam.neelam@gmail.com
bhaskarreddy_sku@yahoo.co.in
4
godi.madhavi@gmail.com
Abstract— The process of exchanging information in secured
way is called cryptography. Security is achieved for message
with Encryption process at the sender end and Decryption
process at the receiver end. Many Ciphers are developed to
provide data protection. The effectiveness of the Ciphers that
are being used depends mainly on their throughput and
memory constraint. Using of large key with huge number of
rounds with multiple complex operations may provide high
security. Because of this reason the proposed method consists
of 16 rounds, 512-bit key with 8-different rounding functions.
The key is generated by taking 512-bit random number.
Shifting operation is performed on random number based on
number of 1’s and 0’s in random number. Permutation will be
applied on shifted bits. Encryption will be done by taking
1024-bit plain text. Initially plain text will be permutated then
rounding function is performed.. In rounding function key and
permuted result will be encrypted to generate intermediate
cipher text. Intermediate cipher text will be given to pairing
function to generate final cipher text.
Keywords— Round Function, Pairing Function, Shifting,
Permutation.
I. INTRODUCTION
Cryptography[1,3] is the study of clandestine writing. It is
the art of transferring a decipherable message into one which
is indecipherable, and then retransforming that message back
into its original form. The message which is in intelligible
format is plaintext. The plaintext is converted into cipher text
which is in illegible form, by applying encryption algorithm.
The process of converting cipher text into plaintext is known
as decryption. The process of cryptography results in
concealing the context of message from all, except the sender
and the receiver.
Cryptography has many viable applications. Cryptography
shows alternate solutions to many problems like
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confidentiality, data integrity, authentication, non repudiation.
The main traditional cipher types are transposition ciphers and
substitution ciphers [2,4,8]. A transposition cipher is one,
which rearranges the order of letters in a message. Where as in
substitution method, each alphabet in text is replaced by other
letter methodically.
II. EXISTING METHOD
A. Encryption
Step1: Start.
Step2: Consider 64-bit key and retrieve 56-bits from it.
Step3: Perform left circular shift and take 48-bits this is the
key-N for round-N.
Step4: Continue Step3 for all rounds.
Step5: Take the plain text and perform initial permutation.
Step6: Step5 result and key-1 will be given to rounding
function-1.
Step7: Above step result and next key (key-N) is given to
next rounding function-N.
Step8: Continue the process for 16-rounds.
Step9: Perform 32-bit swap on round-16 result.
Step10: Perform inverse initial permutation on step9 which
generates final cipher text.
Step11: Stop.
B. Decryption
Reverse process of encryption.
III. LIMITATIONS OF EXISTING METHOD
It uses same round function for all the rounds.
Key length is very small.
IV. PROPOSED METHOD
A. Encryption
Step1: Start.
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International Journal of Engineering Trends and Technology (IJETT) – Volume X Issue Y- Month 2015
Step2: Consider 512-bit random number [5] and divide it
into two half‟s.
Step3: In first half number of 1‟s is even then perform left
shift otherwise perform right shift.
Step4: In second half number of 0‟s is even then perform
left shift otherwise perform right shift.
Step5: Take the result of step3 and step4 perform
permutation-2.
Step6: Result of step5 is the key for rounding function-N,
Where N=1, 2….16.
Step7: By taking key as 512-bit random number repeat the
procedure from step2 to generate keys for all the
rounds.
Step8: Input the plain text message to be transmitted.
Step9: Read 1024-bit plain text at a time and perform
permutation-1.
Step10: Result of Step9 and key1 (K1) is given to the
rounding function-1.
Step11: Result of round function-1 and key2 (K2) is given
to the rounding function-2.
Step12: Continue for all rounds, output of rounding
function-16 is given to the pairing function which
generates final cipher text.
Step13: Stop.
B. Decryption
Step1: Start.
Step2: Take 512-bit random number (Considered in
Encryption) and divide it into two half‟s.
Step3: In first half number of 1‟s is even then perform left
shift otherwise perform right shift.
Step4: In second half number of 0‟s is even then perform
left shift otherwise perform right shift.
Step5: Take the result of step3 and step4 perform
permutation-2.
Step6: Result of step5 is the key for rounding function-N
Where N=1, 2….16
Step7: By taking key as 512-bit random number repeat the
procedure from step2 to generate keys for all the
rounds.
Step8: Input the cipher text message.
Step9: Read 512-bit cipher text at a time, and given it to the
reverse pairing function.
Step10: Result of above step (1024-bit) and key16 (K16) is
given to the rounding function-16.
Step11: Result of Step10 and key15 (K15) is given to the
rounding function-15.
Step12: Continue for all rounds, Perform inverse
permutation-1 for the output of rounding function-1.
Step13: Output of inverse permutation-1 is the plain text.
Step14: Stop.
C. Pairing Function
A pairing function[6,7] on a set A associates each pair of
members from A with a single member of A, so that any two
distinct pairs are associated with two distinct members.
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D. Cantor pairing function
When x and y are non−negative integers, CantorPair[x, y]
outputs a single non−negative integer that is uniquely
associated with that pair.
Fig 1. Cantor pairing
E. Elegant pairing function
When x and y are non−negative integers, ElegantPair[x, y]
outputs a single non−negative integer that is uniquely
associated with that pair.
Fig 2. Elegant pairing
F. Rounding Function
The proposed structure recommends 16 rounds and
different round functions which are selected using Multiplexer
Circuit. Let the rounding function for round 1 to round 16 be
RF1, RF2, etc. up to RF8 and again from RF1 to RF8. The
user can incorporate their own round functions for designing
the cipher[4]. The round function which have been selected in
the present Design includes: EX-OR,EX-NOR, NOT (Key
bits „0‟), NOT (Key bits „1‟), CIRCULAR LEFT SHIFT(Key
bits „0‟), CIRCULAR LEFT SHIFT(Key bits „1‟),
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International Journal of Engineering Trends and Technology (IJETT) – Volume X Issue Y- Month 2015
CIRCULAR RIGHT SHIFT(Key bits „0‟), CIRCULAR
RIGHT SHIFT(Key bits „1‟)
Selection
S3 S2 S1 S0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
H. Flow Chart for Encryption and Decryption:
Round Function
RF1
RF2
RF3
RF4
RF5
RF6
RF7
RF8
RF1
RF2
RF3
RF4
RF5
RF6
RF7
RF8
G. Flow Chart for Key Generation:
Fig 4. Flow chart for encryption and decryption
I. Flow Chart for Single Round Encryption:
Fig 5. Flow chart for single encryption
J. Result:
For encryption and decryption process following key 512
bit random number is considered as key:
Fig 3. Flow chart for key generation
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93846850055346952473693261358674973005706669900250
87889452229210992649003087234541419063293183209107
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International Journal of Engineering Trends and Technology (IJETT) – Volume X Issue Y- Month 2015
31896143537510130467171983464486246753893459865583
5953
Consider plaintext as: “To understand steganography, one
must first understand its predecessor: cryptography.
Cryptography is the art of protecting info”
Intermediate Cipher text
Character
Character
1,3,…127
2,4,….128
Cipher
text
Intermediate Cipher text
Character
Character
1,3,…127
2,4,….128
Cipher
text
187
152
115634
115
9
15730
236
213
202522
51
103
23972
0
209
43890
138
69
43332
54
100
23978
129
167
88170
4
12
280
122
164
82326
191
209
160782
117
90
43290
240
146
149862
74
60
18238
184
125
96158
88
9
9682
63
130
37568
35
246
79312
146
151
88798
196
5
40994
85
172
66476
108
98
42858
152
77
52974
181
76
66668
138
174
97932
170
202
139096
49
206
65378
88
184
74432
77
144
49216
138
167
93606
69
134
41550
140
185
106230
74
30
11068
48
215
69528
143
138
79528
241
91
111038
41
192
54604
76
88
27212
9
134
20610
104
117
49270
237
55
86030
90
248
114762
240
122
131886
132
165
88770
14
108
15034
135
41
31422
54
164
47850
176
193
136882
72
235
94700
26
133
25492
176
101
77358
59
196
65398
96
97
37634
241
211
205238
172
81
64606
73
197
73316
193
171
133246
245
126
138502
32
77
12054
30
197
51816
76
19
9272
13
143
24518
144
145
84098
148
249
158302
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V. FEATURES OF PROPOSED ALGORITHM
Vigorous key- uses maximum of 2512 possibilities to
guess the key.
Different round functions and Pairing functions.
Fast transmission.
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International Journal of Engineering Trends and Technology (IJETT) – Volume X Issue Y- Month 2015
VI. CONCLUSION
The role of cryptography is to provide a very high degree of
security for the information. In the proposed method 16
rounds of encryption is done with different rounding functions
to increase the security. The final cipher text is reduced to half
of the plain text with pairing functions. Further the length of
the key can be increased to more than 512. The number of
rounding functions may also be increased to enhance the
security. New pairing functions may be derived from the
existing which makes more complex in cipher generation.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
William Stallings. Cryptography and Network Security, Principles and
Practices, Forth Edition, Prarson Education, 2008.
Introduction to Modern Cryptography, Jonathan Katz, Yehuda Lindell
Chapman & Hall /CRC Taylor RFrancisGroup.
Information Security: Text Encryption and Decryption with Poly
Substitution method and combining features of cryptography.R.Venkateswaram, Dr.V.Sundaram ,June 2010.
Applied Cryptography Protocols, Algorithms and Source Coding
BRUE SCHNEIER, Second Edition, John Wiley & Sons, Inc.
S G Srikantaswamy, Dr. H D Phaneendra, “Improved Caesar Cipher
with Random Number Generation Technique and Multistage
Encryption”, International Journal on Cryptography and Information
Security (IJCIS). Vol. 2, No.4. pp. 39-49, December 2012.
PairingFunction, http://en.wikipedia.org/ wiki/Pairing_function.
pairinglattices,books.google.co.in/books.
Encipher, A Text Encryption and Decryption Technique using
Substitution-Transposition and Basic Arithmetic and Logical Operation.
Devendra Prasad, Govind Prasad Arya, Chirag Chaudhary, Vipin
Kumar, IJCSIT.
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