A Block Cipher Based Cryptosystem through Modified Forward Backward Overlapped Modulo Arithmetic Technique (MFBOMAT)

IOSR Journal of Computer Engineering (IOSR-JCE)
e-ISSN: 2278-0661, p- ISSN: 2278-8727Volume 13, Issue 1 (Jul. - Aug. 2013), PP 138-146
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A Block Cipher Based Cryptosystem through Modified Forward
Backward Overlapped Modulo Arithmetic Technique
(MFBOMAT)
Debajyoti Guha1
, Rajdeep Chakraborty2
, Abhirup Sinha3
1
Dept. of IT, Siliguri Institute of Technology,Darjeeling-734009, West Bengal, India.
2
Dept of CSE, Netaji Subhash Engineering College, Garia , Kolkata-700152, West Bengal, India.
3
Tata Consultancy Services, New Town, Rajarhat, Kolkata-700156,West Bengal, India.
Abstract: In this paper, a new Cryptosystem based on block cipher has been proposed where the encryption is
done through Modified Forward Backward Overlapped Modulo Arithmetic Technique (MFBOMAT). 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 last blocks are then added
where the modulus of addition is 2n
. The result replaces the last block (say Nth
block), first block remaining
unchanged (Forward mode). In the next attempt the second and the Nth
block (the changed block) are added and
the result replaces the second block(Backward mode).Again the second (the changed block) and the (N-1)th
block are added and the result replaces the (N-1)th
block (Forward mode).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: FBOMAT, Symmetric block cipher, Cryptosystem
I. 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 [2]. 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 [3] 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 I of this paper deals with the proposed scheme. A concept of key-generation is given in
Section II. Results and comparisons are illustrated in Section III. Conclusions are drawn in Section IV,
acknowledgements are shown in section V and Section VI lists the references.
1. The Modified Forward Backward Modulo Arithmetic Technique (MFBOMAT)
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.......B m where m=512/n. Starting from the MSB, the blocks are paired as
(B1,Bm), (B2,Bm), (B2,Bm-1),(B3,Bm-1) and so on. So there is a common member in any two non-adjacent block-
pairs, i.e. the block-pairs are overlapping and hence the name given to the technique The FBOMAT 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.
1.1. The Algorithm for MFBOMAT
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

A Block Cipher Based Cryptosystem Through Modified Forward Backward Overlapped Modulo
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.
In this fashion several rounds are completed till we reach Round 8 where the block size is 256 and we get the
encrypted bit-stream. The operations 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, starting from the blocks B m/2 and ((B m) /2) +1 and then ((B m)/2) and ((B m) /2) +2 and then ((B m)/2)-
1 and ((B m) /2) +2 .The process continues until all the remaining blocks are decrypted.
.
1.1. 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.
1.2. 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.
1.2.1 The Encryption Scheme
Round 1: Block size = 2, number of blocks = 8

Input
(B2, B3) mod16, Change B3
Round 3: Block size = 8, number of blocks = 2
Input
11111010 00000101
B1 B2
Output
11111010 11111111
B1 B2
(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' =.1111101011111111.For decryption the opposite method i.e. modular subtraction
is used to get back the original bit stream in S.
1.2.2 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
11111010 11111111
B1 B2
Output
11111010 00000101
B1 B2
(B1, B2) mod 256, Change B2
Round 2:Block size=4, number of blocks=4
Input
1111 1010 0000 0101
B1 B2 B3 B4
Output
1111 1010 0110 0101
B1 B2 B3 B4
Input
1111 1010 0110 0101
B1 B2 B3 B4
Output
1111 0101 0110 0101
B1 B2 B3 B4
Input
1111 0101 0110 0101
B1 B2 B3 B4
Output
1111 0101 0110 0110
B1 B2 B3 B4

Round 3:Block size=2, number of blocks =8
Input
11 11 01 01 01 10 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 11 01 01 00 10 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 11 01 01 00 10 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 11 01 11 00 10 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 11 01 11 00 10 01 10
B1 B2 B3 B4 B5 B6 B7 B8
11 11 01 11 00 01 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 11 01 11 00 01 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 11 00 11 00 01 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 11 00 11 00 01 01 10
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 11 00 11 00 01 10 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 11 00 11 00 01 10 10
B1 B2 B3 B4 B5 B6 B7 B8
Output
11 01 00 11 00 01 10 10
B1 B2 B3 B4 B5 B6 B7 B8
Input
11 01 00 11 00 01 10 10
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
The decrypted bit stream :S”=1101001100011011.So S=S”.

II. 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.
2.1. 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
Table 1 : Representation of no. of iterations in each round by bits.
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
Each round. The binary strings are concatenated together to form the 128-bit binary string :
000000000100101000000010101010000001000010110110101011011000110010101101100110111011111011
10111011000010110011101100001101100100.. 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.
III. 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 files.

Fig. 2 : Frequency Distribution of ASCII characters MFBOMAT encrypted files
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. 3 : Frequency Distribution of ASCII characters in the RSA encrypted file.
Fig. 4 : Frequency Distribution of ASCII characters in the FBOMAT encrypted file.
Although ten different text files were encrypted and decrypted using both RSA and MFBOMAT, 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 MFBOMAT, and encrypted file
with RSA and FBOMAT. A close observation will reveal that the characters in the encrypted file using
MFBOMAT are fairly well distributed throughout the character space. Hence the MFBOMAT scheme may be
comparable with 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 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.
Fig. 5 : 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.
Table 3: indicates encryption time for MFBOMAT, FBOMAT and RSA
Fig 6: shows graphically Time Complexity Analysis among MFBOMAT, FBOMAT & RSA for Encryption.

Table 4: indicates decryption time for MFBOMAT, FBOMAT and RSA
Fig 7: shows graphically Time Complexity Analysis among MFBOMAT, FBOMAT and RSA for Decryption
It can be seen that the time taken to encrypt a file using MFBOMAT is very little compared to that
using RSA and FB OMAT.
IV. Conclusion
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.
V. Acknowledgement
The authors express their deep sense of gratitude to the Department of Information Technology, Siliguri
Institute of Technology,West Bengal University of Technology. The authors also express their deep sense of
gratitude to the Department of Computer Science & Engineering, Netaji Subhash Engineering college,West
Bengal University of Technology.
VI . Reference
Journal Paper:
[1] 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.
Emai rajdeep_chak@indiatimes.com, guha_debajyoti@yahoo.com, jkmandal@sancharnet.in,
Books:
[2] W. Stallings, Cryptography and Network Security: Principles and Practices, Prentice Hall, Upper Saddle River, New Jersey,
USA, Third Edition, 2003.
[3] Atul Kahate, Cryptography and Network Security, TMH, India,2nd
Ed,2009
[4] Behroz Forouzan, Cryptography and Network Security, TMH, India, 4th
Ed,2010

Proceedings Paper:
[5] 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.

A Block Cipher Based Cryptosystem through Modified Forward Backward Overlapped Modulo Arithmetic Technique (MFBOMAT)

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