Combining cryptography with channel coding to reduce complicity
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This document summarizes a research paper that proposes combining cryptography and channel coding to increase security and reduce complexity. It describes how a linear feedback shift register can be used to generate a sequence to select different encoding matrices for different blocks of an input signal. This makes it difficult for intruders to decode the signal without knowing the key and matrix sequence. The encoding process multiplies each block with a selected matrix. Decoding detects and corrects errors using a parity check matrix and comparison to a reference array. Combining encryption and coding in this way could improve performance without increasing complexity.
![International Journal of Electronics and Communication Engineering & TechnologyAND
INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 2, July- September (2012), pp. 346-351
IJECET
© IAEME: www.iaeme.com/ijecet.html
Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME
www.jifactor.com
COMBINING CRYPTOGRAPHY WITH CHANNEL CODING TO
REDUCE COMPLICITY
Sunaina Sharma
Electronics and Communication
Sunaina.sh39@gmail.com
ABSTRACT
Cryptography is a form of hiding the text so to increase the security of the information. On
the other hand the main purpose of using coding is to reduce the error probability and to
increase the efficiency of the channel. As the word complicity means criminal offence. This
paper presents an overview how complicity can be reduce by combining Channel coding with
cryptography with the use of LFSR shift register
Keywords: Include at least 5 keywords or phrases
I. INTRODUCTION
The general communication system consist separate block for channel coding and for
encryption [1]. The general diagram for has been shown below:
Source Quantization
Digital Data Input
Source Encrypti Channel Modul
Coding on Coding ation
Channel
Source Channel Equaliza Demodul
Decoding Decoding tion ation
D/A Digital Data
Convertor Output
Fig 1.1: Communication System
346](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-1-320.jpg)
![International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
This paper provides the information how to merge channel coding with the cryptography
to provide more security to the signal. In the network security and cryptography, the study of
confidentiality, authenticity and error correction are very important [4][6]. Many of the
modern communication systems are limited in resources such as battery power and
computational power. Mobile sensor networks, smart cards etc., are some examples. Hence a
major research in communication concentrates on designing systems with low computational
or hardware complexity. To reduce the computational and communication cost of two major
cryptographic operations say channel coding and cryptography has been combined. And the
proposed work as [1] [2]:
Source Quantization Combining
Blocks
Source Encrypti Channel Modul
Coding on Coding ation
Channel
Source Channel Equaliza Demodul
Decoding Decoding tion ation
D/A
Convertor
Fig 1.2: Purposed Communication System
II.COMBINING CRYPTOGRAPHY WITH CHANNEL CODING
The objective of the paper is to combine Cryptography with channel coding to reduce the
computational and communication cost and to increase the security per bit [7] [8]. The block
diagram shows how encryption and coding has been done on the signal [2]:
LFSR G Matrix
Sound Signal Digital Signal Channel Noise
is converted divided into (White Gaussian
into digital bits of 4 (i) Noise)
Comparison Received
between Word
Coded and
Uncoded word
Finding out
Calculating Coset Leader Standard
Error Vector and Array
Syndrome
Fig 1.3: Block dig of channel coding with LFSR
347](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-2-320.jpg)
![International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
An approach to improve the performance of a communication system without increase in
complexity is to embed encryption within channel coding. For this, programming has been
done in Matlab. Since Matlab is commonly used for programming purposes, it provides
several of inbuilt functions and tools used for programming purposes. A voice signal is first
converted into digital and then encoded and encrypted. And at the receiver side it is decoded
and decrypted. The flow diagram for this is as under [2]:
LFSR Start
XORing the Sound Signal
tapes and
generating the
sequence Digital Signal
Signal Divided
Selecting G into Bit of 4(i)
Matrix
according to
the sequence Codeword
generated CW = i×G
LFSR
Channel
Received
word Standard
valid Array
Syndrome & G
Coset leader matrix
(errV)
CW = i- errV
Decoded Word
Comparison
between
Coded and
Un-coded
Signal
Stop
Fig 14: Flow dig of cryptography with channel coding
348](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-3-320.jpg)
![International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
III. LINEAR FEEDBACK SHIFT REGISTER
A linear feedback shift register (LFSR) is a shift register whose input bit is a linear
function of its previous state. The most commonly used linear function of single bits is XOR.
Thus, an LFSR is most often a shift register whose input bit is driven by the exclusive-or
(XOR) of some bits of the overall shift register value. The initial value of the LFSR is called
the seed, and because the operation of the register is deterministic, the stream of values
produced by the register is completely determined by its current (or previous) state. Likewise,
because the register has a finite number of possible states, it must eventually enter a repeating
cycle [9]. A 12 bit key is given as input to the filter then this filter will generate 4095 (212-1)
number of sequence. According to which the G matrix is selected. There are approximately
6000 equivalent G matrixes generated by applying different linear process on the basic matrix
[2].
Key Define XORing Generating
(As input) Tapping Tapings Numbers
Fig 1.5: LFSR
IV. ENCODING AND ENCRYPTING
The Number of G matrix has been created using permutation and linear expirations. Such
as addition of scalar multiple of one row to another, permutation of columns. Then using this
numbers generated by the LFSR the respective matrix from the set of matrix has been
selected. Then that particular matrix is multiplied with that codeword only [2].
Information
Signal i (4 bits)
Creating Choosing
number G matrix Codeword
of G according CW
matrix LFSR
Fig 1.6: Generating codeword using G matrix and LFSR
Note: It must be noted here that for every 4 bit of information signal different G matrix is
multiplied every time according to LFSR.
As the intruder is not known to the key and the actual sequence of the number generated
by the LFSR and the matrix to which the codeword is being multiplied he/she won’t be able
to reconstruct the signal even if the codeword is known to them. And the reverse process has
been employed to reconstruct the signal again at the receiver [8].
Coding rate R= k/n
349](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-4-320.jpg)
![International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
Block
k n
k n-k
Information Bits Parity Bits
n digital codewords
Fig 1.7: Generating Codeword
V. DECODING AND DECRYPTING
The signal is received at the receiver end. And the standard array has been created. Once
the standard array has been created, now next step is to check if the received word is correct
or not. Now divide the received signal in bits of 7. This is the codeword. Now first step is to
multiply the codeword with the parity check matrix if the resulted is zero that means no error
has occurred otherwise the signal is in error. Compare this codeword with the standard array
that the codeword falls in which column. The coset leader of that column is in error. Subtract
the coset leader of the error vector with every received word the resultant is the actual
codeword which has been send [2] [8].
Standard array has been created, now next step is to check if the received word is correct or
not. Now divide the received signal in bits of 7. This is the codeword. Now first step is to
multiply the codeword with the parity check matrix if the resulted is zero that means no error
has occurred otherwise the signal is in error. Compare this codeword with the standard array
that the codeword falls in which column. The coset leader of that column is in error. Subtract
the coset leader with every received word the resultant is the actual codeword which has been
send [5].
Note: It must be noted here that the weight which is being added should not be a codeword
and the resultant should not be a repeating number i.e. all the numbers in the standard array
should be unique and non repeating number.
Received
word
Comparing
Multiplied code with
with Standard array
Parity
H matrix
Column multiplied
multiplied with according
HT (syndrome) to LFSR
Codeword = Error
vector – received Define error
word vector according
to syndrome
Fig 1.8: Decoding diagram
350](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-5-320.jpg)
![International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
VI. CONCLUSIONS
Till now the work on channel coding consist of the single G matrix which is been
multiplied with the complete data to produce the codewords but in this paper the number of G
matrix has been produced by permutation and adding of one row with another. These G
matrixes are randomly selected by LFSR register and multiplied with the block of data. For
every new block different G matrix is selected and codeword is generated. As different G
matrix is used every time it would be very hard for intruder to guess the right G matrix every
time and to interpret the right information.
ACKNOWLEDGMENT
I would like to thank my Parents to provide financial and emotional spot to me and
standing with me in every even and odds. I would like to thank almighty for showing me the
right direction out of the blue, to help me stay calm in the oddest of the times and keep
moving even at times when there was no hope.
REFERENCES
[1] Sunaina Sharma, Combining Cryptography with Channel Coding, ISOR, vol. 2. July
2012.
[2] Sunaina Sharma, Combining Cryptographic Operation for complexity reduction, Lovely
Professional University Jalandhar, M.Tech, 2012.
[3] Natasa Zivic And Christoph Ruland, Channel coding as cryptographic Enhancer, Wseas
Transactions On Communications, Issue 2, Volume 7, February 2008.
[4] G. Julius Caesar, John F. Kennedy, Security Engineering: A Guide to Building
Dependable Distributed Systems.
[5] Anonym, Coding In Communication System.
[6] Gary C. Kessler, An Overview of Cryptography, Auerbach, September 1998.
Books
[7] Richard E. Blahut, Algebraic code for data transmission (Cambridge University Press,
2003).
[8] Ranjan Bose, Information theory, Coding and Cryptography (Tata McGraw Hill, 2008).
Websites
[9] www.wekipedia.com
351](https://image.slidesharecdn.com/combiningcryptographywithchannelcodingtoreducecomplicity-121125075142-phpapp02/85/Combining-cryptography-with-channel-coding-to-reduce-complicity-6-320.jpg)
Combining cryptography with channel coding to reduce complicity
- 1. International Journal of Electronics and Communication Engineering & TechnologyAND INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 3, Issue 2, July- September (2012), pp. 346-351 IJECET © IAEME: www.iaeme.com/ijecet.html Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME www.jifactor.com COMBINING CRYPTOGRAPHY WITH CHANNEL CODING TO REDUCE COMPLICITY Sunaina Sharma Electronics and Communication Sunaina.sh39@gmail.com ABSTRACT Cryptography is a form of hiding the text so to increase the security of the information. On the other hand the main purpose of using coding is to reduce the error probability and to increase the efficiency of the channel. As the word complicity means criminal offence. This paper presents an overview how complicity can be reduce by combining Channel coding with cryptography with the use of LFSR shift register Keywords: Include at least 5 keywords or phrases I. INTRODUCTION The general communication system consist separate block for channel coding and for encryption [1]. The general diagram for has been shown below: Source Quantization Digital Data Input Source Encrypti Channel Modul Coding on Coding ation Channel Source Channel Equaliza Demodul Decoding Decoding tion ation D/A Digital Data Convertor Output Fig 1.1: Communication System 346
- 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME This paper provides the information how to merge channel coding with the cryptography to provide more security to the signal. In the network security and cryptography, the study of confidentiality, authenticity and error correction are very important [4][6]. Many of the modern communication systems are limited in resources such as battery power and computational power. Mobile sensor networks, smart cards etc., are some examples. Hence a major research in communication concentrates on designing systems with low computational or hardware complexity. To reduce the computational and communication cost of two major cryptographic operations say channel coding and cryptography has been combined. And the proposed work as [1] [2]: Source Quantization Combining Blocks Source Encrypti Channel Modul Coding on Coding ation Channel Source Channel Equaliza Demodul Decoding Decoding tion ation D/A Convertor Fig 1.2: Purposed Communication System II.COMBINING CRYPTOGRAPHY WITH CHANNEL CODING The objective of the paper is to combine Cryptography with channel coding to reduce the computational and communication cost and to increase the security per bit [7] [8]. The block diagram shows how encryption and coding has been done on the signal [2]: LFSR G Matrix Sound Signal Digital Signal Channel Noise is converted divided into (White Gaussian into digital bits of 4 (i) Noise) Comparison Received between Word Coded and Uncoded word Finding out Calculating Coset Leader Standard Error Vector and Array Syndrome Fig 1.3: Block dig of channel coding with LFSR 347
- 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME An approach to improve the performance of a communication system without increase in complexity is to embed encryption within channel coding. For this, programming has been done in Matlab. Since Matlab is commonly used for programming purposes, it provides several of inbuilt functions and tools used for programming purposes. A voice signal is first converted into digital and then encoded and encrypted. And at the receiver side it is decoded and decrypted. The flow diagram for this is as under [2]: LFSR Start XORing the Sound Signal tapes and generating the sequence Digital Signal Signal Divided Selecting G into Bit of 4(i) Matrix according to the sequence Codeword generated CW = i×G LFSR Channel Received word Standard valid Array Syndrome & G Coset leader matrix (errV) CW = i- errV Decoded Word Comparison between Coded and Un-coded Signal Stop Fig 14: Flow dig of cryptography with channel coding 348
- 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME III. LINEAR FEEDBACK SHIFT REGISTER A linear feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is XOR. Thus, an LFSR is most often a shift register whose input bit is driven by the exclusive-or (XOR) of some bits of the overall shift register value. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle [9]. A 12 bit key is given as input to the filter then this filter will generate 4095 (212-1) number of sequence. According to which the G matrix is selected. There are approximately 6000 equivalent G matrixes generated by applying different linear process on the basic matrix [2]. Key Define XORing Generating (As input) Tapping Tapings Numbers Fig 1.5: LFSR IV. ENCODING AND ENCRYPTING The Number of G matrix has been created using permutation and linear expirations. Such as addition of scalar multiple of one row to another, permutation of columns. Then using this numbers generated by the LFSR the respective matrix from the set of matrix has been selected. Then that particular matrix is multiplied with that codeword only [2]. Information Signal i (4 bits) Creating Choosing number G matrix Codeword of G according CW matrix LFSR Fig 1.6: Generating codeword using G matrix and LFSR Note: It must be noted here that for every 4 bit of information signal different G matrix is multiplied every time according to LFSR. As the intruder is not known to the key and the actual sequence of the number generated by the LFSR and the matrix to which the codeword is being multiplied he/she won’t be able to reconstruct the signal even if the codeword is known to them. And the reverse process has been employed to reconstruct the signal again at the receiver [8]. Coding rate R= k/n 349
- 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME Block k n k n-k Information Bits Parity Bits n digital codewords Fig 1.7: Generating Codeword V. DECODING AND DECRYPTING The signal is received at the receiver end. And the standard array has been created. Once the standard array has been created, now next step is to check if the received word is correct or not. Now divide the received signal in bits of 7. This is the codeword. Now first step is to multiply the codeword with the parity check matrix if the resulted is zero that means no error has occurred otherwise the signal is in error. Compare this codeword with the standard array that the codeword falls in which column. The coset leader of that column is in error. Subtract the coset leader of the error vector with every received word the resultant is the actual codeword which has been send [2] [8]. Standard array has been created, now next step is to check if the received word is correct or not. Now divide the received signal in bits of 7. This is the codeword. Now first step is to multiply the codeword with the parity check matrix if the resulted is zero that means no error has occurred otherwise the signal is in error. Compare this codeword with the standard array that the codeword falls in which column. The coset leader of that column is in error. Subtract the coset leader with every received word the resultant is the actual codeword which has been send [5]. Note: It must be noted here that the weight which is being added should not be a codeword and the resultant should not be a repeating number i.e. all the numbers in the standard array should be unique and non repeating number. Received word Comparing Multiplied code with with Standard array Parity H matrix Column multiplied multiplied with according HT (syndrome) to LFSR Codeword = Error vector – received Define error word vector according to syndrome Fig 1.8: Decoding diagram 350
- 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME VI. CONCLUSIONS Till now the work on channel coding consist of the single G matrix which is been multiplied with the complete data to produce the codewords but in this paper the number of G matrix has been produced by permutation and adding of one row with another. These G matrixes are randomly selected by LFSR register and multiplied with the block of data. For every new block different G matrix is selected and codeword is generated. As different G matrix is used every time it would be very hard for intruder to guess the right G matrix every time and to interpret the right information. ACKNOWLEDGMENT I would like to thank my Parents to provide financial and emotional spot to me and standing with me in every even and odds. I would like to thank almighty for showing me the right direction out of the blue, to help me stay calm in the oddest of the times and keep moving even at times when there was no hope. REFERENCES [1] Sunaina Sharma, Combining Cryptography with Channel Coding, ISOR, vol. 2. July 2012. [2] Sunaina Sharma, Combining Cryptographic Operation for complexity reduction, Lovely Professional University Jalandhar, M.Tech, 2012. [3] Natasa Zivic And Christoph Ruland, Channel coding as cryptographic Enhancer, Wseas Transactions On Communications, Issue 2, Volume 7, February 2008. [4] G. Julius Caesar, John F. Kennedy, Security Engineering: A Guide to Building Dependable Distributed Systems. [5] Anonym, Coding In Communication System. [6] Gary C. Kessler, An Overview of Cryptography, Auerbach, September 1998. Books [7] Richard E. Blahut, Algebraic code for data transmission (Cambridge University Press, 2003). [8] Ranjan Bose, Information theory, Coding and Cryptography (Tata McGraw Hill, 2008). Websites [9] www.wekipedia.com 351