An odd even block cipher based cryptosystem through

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 212
AN ODD-EVEN BLOCK CIPHER BASED CRYPTOSYSTEM THROUGH
MODULO ARITHMATIC TECHNIQUE (OEMAT)
Debajyoti Guha1
, Alok Basu2
1
Assistant Professor, Dept of IT, 2
Assistant Professor, Dept of CSE, Siliguri Institute of Technology, West Bengal, India
guha_debajyoti@yahoo.com, basualok@rediffmail.com
Abstract
In this paper, a new Cryptosystem based on block cipher has been proposed where the encryption is done through Odd Even Modulo
Arithmetic Technique (OEMAT). The original message is considered as a stream of bits, which is then divided into a number of
blocks, each containing n bits, where n is any one of 2, 4, 8, 16, 32, 64, 128, 256. The first and the penultimate blocks are then added
where the modulus of addition is 2n
. The result replaces the penultimate block (say (N-1th
) block), first block remaining unchanged. In
the next attempt the second and the ultimate blocks (say Nth
block) are added and the result replaces the Nth
block. This process
continues until all the blocks are executed. The modulo addition has been implemented in a very simple manner where the carry out of
the MSB is discarded to get the result. The technique is applied in a cascaded manner by varying the block size from 2 to 256. The
whole technique has been implemented by using a modulo subtraction technique for decryption.
Keywords: MFBOMAT, FBOMAT, Symmetric block cipher, Cryptosystem
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1. INTRODUCTION
Lack of security may exist when a volume of data is
transferred from its source to the destination if no measure is
taken for its security. For one reason or the other, most of the
data being transmitted must be kept secret from others [4]. A
very important reason to encode data or messages is to keep
them secret. From e-mail to cellular communication, from
secured web access to digital cash, cryptography [5] is an
essential part of today’s information systems. It can prevent
fraud in electronic commerce and assure the validity of
financial transactions. It can prove one’s identity and protect
one’s anonymity. These electronic commerce schemes may
fall fraud through forgery, misrepresentation, denial of service
and cheating if we do not add security to these systems. In
fact, computerization makes the risks even greater by allowing
attacks that are impossible in non-automated systems. Only
strong cryptography can protect against these attacks.
The Section 2 of this paper deals with the proposed scheme. A
concept of key-generation is given in Section 3. Results and
comparisons are illustrated in Section 3. Conclusions are
drawn in Section 4, Acknowledgements are given in section 5
and Section 6 lists the references.
2. THE ODD EVEN MODULO ARITHMETIC
TECHNIQUE (OEOMAT)
In the proposed scheme the source file is input as streams of
binary bits. For our implementation we have taken the stream
size to be 512 bits though the scheme may be implemented for
larger stream sizes also. The input stream, S, is first broken
into a number of blocks, each containing n bits (n=2k
,
k=1,2,3,......,8) so that S = B1B2B3.......Bm where m=512/n.
Starting from the MSB, the blocks are paired as (B1,Bm-1),
(B2,Bm), (B3,Bm-2),(B4,Bm--3) and so on. So block pairing is
done between non adjacent odd numbered blocks and even
numbered blocks separately and hence the name given to the
technique. The OEMAT operation is applied to each pair of
blocks. The process is repeated, each time increasing the block
size till n=256.The proposed scheme has been implemented by
using the reverse technique, i.e. modulo subtraction technique,
for decryption. Section 1.1 explains the operation in detail.
2.1. The Algorithm for OEOMAT
After breaking the input stream into blocks of 2 bits each and
pairing the blocks as explained in Section 1, the following
operations are performed starting from the most significant
side:
Round 1: In each pair of blocks, the first member of the pair
is added to the second member where the modulus of addition
is 2n
for block size n. Therefore for 2-bit blocks, the modulus
of addition will be 4.
This round is repeated for a finite number of times and the
number of iterations will form a part of the session key as
discussed in Section 3.
Round 2: The same operation as in Round 1 is performed
with block size 4.

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In this fashion several rounds are completed till we reach
Round 3 where the block size is 256 and we get the encrypted
bit-stream. The operation of the non adjacent block-pairs
increases the complexity of the algorithm resulting in the
enhancement of security.
During decryption, the reverse operation, i.e. modulo
subtraction, is performed instead of modulo addition, between
the odd and even block pairs until all the remaining blocks are
decrypted.
2.2. The Modulo Addition
An alternative method for modulo addition is proposed here to
make the calculations simple. The need for computation of
decimal equivalents of the blocks is avoided here since we
will get large decimal integer values for large binary blocks.
The method proposed here is just to discard the carry out of
the MSB after the addition to get the result. For example, if we
add 1101 and 1001 we get 10110. In terms of decimal values
13+9=22, since the modulus of addition is 16 (24
) in this case,
the result of addition should be 6 (22-16=6). Discarding the
carry from 10110 is equivalent to subtracting 10000 (i.e. 16 in
decimal). So the result will be 0110, which is equivalent to 6
in decimal. The same is applicable to any block size.
2.3 Example of the Scheme
Although the proposed scheme is applied to a 512-bit input
stream, for the sake of brevity, consider a stream of 32 bits,
say S = 1101001100011011 each round is performed only
once to make the process simple for understanding.
2.3.1 The Encryption Scheme
Round 1: Block size = 2, number of blocks = 8
Input
11 01 00 11 00 01 10 11
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 01 00 11 00 00 01 00
B1 B2 B3 B4 B5 B6 B7 B8
Operation: (B1, B7) mod4 Change B7;
(B2, B8) mod4 Change B8;
Input
1101 0011 0000 0100
B1 B2 B3 B4
Output:
1101 0011 1101 0111
B1 B2 B3 B4
Operation: (B1, B3) mod16, Change B3;
(B2, B4) mod16, Change B4;
Input
11010011 11010111
B1 B2
Output
11010011 10101010
B1 B2
Operation: (B1, B2) mod 256, Change B2
Since we have considered only a 16-bit stream we cannot
proceed further. The output from Round 3, say S', is the
encrypted stream, i.e. S' =.1101001110101010.For decryption
the opposite method i.e. modular subtraction is used to get
back the original bit stream in S.
2.3.2 The Decryption Scheme
For decryption the opposite method i.e. modular subtraction
is used to get back the original bit stream in S.
Round 1: Block size=8, number of blocks =2
Input
11010011 10101010
B1 B2
Output
11010011 11010111
B1 B2
Operation: (B1, B2) mod 256, Change B2
Round 2: Block size=4, number of blocks=4
Input
1101 0011 1101 0111
B1 B2 B3 B4
Output
1101 0011 0000 0100
B1 B2 B3 B4
Operation: (B1, B3) mod16, Change B3;
(B2, B4) mod16, Change B4;

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Round 3: Block size=2, number of blocks =8
Input
11 01 00 11 00 00 01 00
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 01 00 11 00 01 10 11
B1 B2 B3 B4 B5 B6 B7 B8
Operation: (B1, B7) mod4 ChangeB7;
(B2, B8) mod4 ChangeB8;
The decrypted bit stream: S”=1101001100011011.So S=S”.
3. KEY GENERATION
In the proposed scheme, eight rounds have been considered,
each for 2, 4, 8, 16, 32, 64, 128, and 256 block size. As
mentioned in Section 2.1, each round is repeated for a finite
number of times and the number of iterations will form a part
of the encryption-key. Although the key may be formed in
many ways, for the sake of brevity it is proposed to represent
the number of iterations in each round by a 16-bit binary
string. The binary strings are then concatenated to form a 128-
bit key for a particular key. Example in Section 3.1 illustrates
the key generation process.
3.1. Example of Key Generation
Consider a particular session where the source file is
encrypted using iterations for block sizes 2, 4, 8, 16, 32, 64,
128, and 256 bits, respectively. Table 1 shows the
corresponding binary value for the number of iterations in
each round. The binary strings are concatenated together to
form the 128-bit binary
string:000000000100101000000010101010000001000010110
11010101101100011001010110110011011101111101110111
011000010110011100001101100100. This 128-bit binary
string will be the encryption-key for this particular session.
During decryption, the same key is taken to iterate each round
of modulo-subtraction for the specified number of times.
Table 1: Representation of no. of iterations in each round by
bits
3.2. Results and Comparisons
The variation of frequencies of all the 256 ASCII characters
between the source file and the encrypted file are given in this
section. The evenly distribution of character frequency over
the 0-255 region of the encrypted file
Fig. 1: Frequency Distribution of ASCII characters in the
source file.
Fig.2: Frequency Distribution of ASCII characters in the
OEMAT encrypted file.
Round
No.
Block
Size
No. of Iterations
Decimal Binary
1 2 74 0000000001001010
2 4 680 0000001010101000
3 8 4278 0001000010110110
4 16 44428 1010110110001100
5 32 44443 1010110110011011
6 64 48878 1011111011101110
7 128 49870 1100001011001110
8 256 50020 1100001101100100

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Fig.3: Frequency Distribution of ASCII characters
MFBOMAT encrypted file
against the source file ensures better security provided by the
proposed algorithm and it also shows the heterogeneity
between the two files. The frequency distribution graph is
drawn according to the percentage of occurrence of a
particular character, not the total number of occurrence.
Fig. 4: Frequency Distribution of ASCII characters in the
RSA encrypted file.
Fig.5: Frequency Distribution of ASCII characters in the
FBOMAT encrypted file.
Although ten different text files were encrypted and decrypted
using both RSA and OEMAT, only one such file is considered
here for analyzing the results. Figs. 1,2,3and 4 illustrate the
frequencies of occurrence of all the 256 ASCII characters in
the source file, encrypted file with OEMAT and encrypted file
with MFBOMAT, RSA and FBOMAT. A close observation
will reveal that the characters in the encrypted file using
OEMAT are fairly well distributed throughout the character
space. Hence the OEMAT scheme may be comparable with
MFBOMAT,RSA and FBOMAT. Another way to analyze the
scheme is to test the homogeneity of the source and the
encrypted file. The Chi-Square test has been performed for
this purpose. Table 2 and fig 5 shows the source file name,
size and the corresponding Chi-Square values (using OEMAT,
MFBOMAT, RSA, FBOMAT) for ten different files. Barring
some exceptions we see that the Chi-Square value increases
with the increase in file size. Further, the high values prove
that Chi-Square is highly significant at 1% level of
significance.
Table 2: Test for homogeneity using Chi-Square method.
Chart 1: Graph showing Chi-Square values for MFBOMAT,
FBOMAT and RSA
Hence the source and the corresponding encrypted files are
considered to be heterogeneous.
Another way to analyze the scheme is to analysis the
encryption and decryption time.

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Table 3: indicates encryption time for OEMAT, MFBOMAT,
FBOMAT and RSA
Chart 2: shows graphically Time Complexity Analysis among
MFBOMAT, FBOMAT & RSA for Encryption.
Table 4: indicates decryption time for OEMAT, MFBOMAT,
FBOMAT and RSA
Chart 3: shows graphically Time Complexity analysis among
OEMAT, MFBOMAT, FBOMAT and RSA for Decryption
It can be seen that the time taken to encrypt a file using
OEMAT is very little compared to that using MFBOMAT,
FBOMAT and RSA.
CONCLUSIONS
The technique proposed takes little time to encode and decode
though the block length is high. The encoded string will not
generate any overhead bits. The block length may further
increased beyond 256 bits, which may enhance the security.
Selecting the block pairs in random order, rather than taking
those in consecutive order may enhance security. The
proposed scheme may be applicable to embedded systems.
ACKNOWLEDGEMENTS
The authors express their deep sense of gratitude to the
Department of Computer Science & Engineering and
Department of Information Technology, Siliguri Institute of
Technology.
REFERENCES
[1]Debajyoti Guha, Rajdeep Chakraborty, and Abhirup Sinha,
“A Block Cipher Based Cryptosystem Through Modified
Forward Backward Overlapped Modulo Arithmetic Technique
(MFBOMAT)”, published in International Organization of
Scientific Research Journal of Computer Engineering (IOSR-
JCE), e-ISSN: 2278-0661, p- ISSN: 2278-8727 accepted and
published in Volume 13-Issue 1 (Jul. - Aug. 2013)issue,
Article number 22, PP- 138-146.
Email:rajdeep_chak@indiatimes.com,
guha_debajyoti@yahoo.com,sinha.abhirup@gmail.com.
[2] Rajdeep Chakraborty, Debajyoti Guha and J. K. Mandal,
“A Block Cipher Based Cryptosystem Through Forward
Backward Overlapped Modulo Arithmetic Technique
(FBOMAT)”, published in International Journal of
Engineering & Science Research Journal (IJESR), ISSN 2277
– 2685, accepted & published in Volume 2 – Issue 5 (May
2012) ,Article number 7, pp-349 – 360.
Email:rajdeep_chak@indiatimes.com,
guha_debajyoti@yahoo.com,
jkmandal@sancharnet.in,

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[3] Mandal, J. K., Sinha, S., Chakraborty, R., " A
Microprocessor-based BlockCipher through Overlapped
Modulo Arithmetic Technique (OMAT)",Proceedings of 12th
International Conference of IEEE on Advanced Computing
and Communications - ADCOM-2004, December 15-
18,Ahmedabad, India, pp. 276 - 280, 2004.
[4] W. Stallings, Cryptography and Network Security:
Principles and Practices, Prentice Hall, Upper Saddle River,
New Jersey, USA, Third Edition, 2003.
[5] Atul Kahate, Cryptography and Network Security, TMH,
India, 2nd Ed, 2009
[6] Behroz Forouzan, Cryptography and Network Security,
TMH, India, 4th Ed, 2010
BIOGRAPHIES:
Debajyoti Guha has obtained B.Tech.in
Information Technology and M.Tech.in
Computer Science from West Bengal University
of Technology. Presently he is working as an
Assistant Professor in the dept. of IT in Siliguri Institute of
Technology. His research interest is in Computer Networking,
Cryptography and Network Security.
Alok Basu has started his career as a
Mechanical Engineer, at Alloy Steels Plant,
SAIL in 1983. He worked there in different
sections of his field in various capacities. Later
he got a scope to be trained in COBOL and to
work with the in-house software development and
maintenance team for more than seven years. He was mainly
involved in the development of Production Information &
Order Servicing System in COBOL on MV 15000 (AOS/VS-
II) platform. He joined in Siliguri Institute of Technology after
completion of M. Tech in Information Technology. He is
serving this institute for more than 10 years and presently
holding the chair of HOD.

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