A Novel Cyclic-Lower-Upper-Rectangular (CLUR) Cryptography Method

A Novel Cyclic-Lower-Upper-Rectangular (CLUR) Cryptography Method

Suyash Kandele, Veena Anand

Department of Computer Science and Engineering National Institute of Technology Raipur, India

Abstract The proposed algorithm belongs to the category of symmetric algorithm and hence the decryption process is just the reverse of encryption process. This is a keyless technique of concealing the data, thus reducing the overhead of maintaining the key and its secured transmission. Unlike conventional algorithms which break the message into square matrix, the proposed algorithm partitions and rearranges the message in horizontal rectangular matrix. Here, in the first step we apply rotation pattern on the generated matrix. This step changes the position of elements in addition to changing their relative sequence. Our next step is to alter the number of repetitions and value of characters, which has been implemented by using a part of magic square matrix. We have performed distinct operations at different places which does not form any recognizable pattern for naïve guessing. The proposed algorithm has high randomness and is, therefore, dynamically changing with the varying length of string.

KeywordsRectangular matrix; Rotation pattern; Upper magic matrix; Lower magic matrix;

1. INTRODUCTION

   Over a score of years, internet has found its applications in education, research, medical science, defense, commerce and many more besides mere communication. A significant amount of data is available on internet. In some fields, secrecy of data may not be important, but for some typical applications security is a crucial aspect. The encryption and decryption of data becomes too important while transmitting it over a shared medium from being stolen away or manipulated by any unauthorized user.

   Let us assume a situation where a message has to be sent from one army troop to another through a vulnerable medium. Since the message is of high importance and should be delivered only to its desired destination, the security of this information transfer should be very high. It should not fall in the hands of Witty and Vigilant intruder who may temper this data or intercept it. The information is more vulnerable to the attacker who is not interested in data but is passionate about cryptanalysis. In this circumstance, we need to be meticulous about the security measures.

   In todays world, where we are approaching digitization in every possible sector, each user feels the need of a novel, unique and reliable cryptography system; for his/her personalized documents; that is unknown to others. So cryptography exists to be an interminable division, where the minutest and the mightiest algorithm; which is a remarkable exploration of human mind; has its prominent contribution.

   In the present work the author has used basic but significantly important methodology to change the position of elements, break the sequence of consecutive elements and alter the number of repetitions & value of characters. Since the mathematical computations involved in the proposed algorithm are not sophisticated, thus it is also suitable for mobile devices and devices with low computational power.

2. BASIC TERMINOLOGY

   1. Horizontal Rectangular Matrix

      Horizontal rectangular matrix is a 2-Dimensional array in which the number of columns is twice the number of rows, i.e. the size will be (n x 2n).

   2. Rotation Pattern

      Rotation pattern comprises of a sequence of steps to modify the position of elements in the matrix.

   3. Magic Square Matrix

      Magic square matrix can be defined as a square matrix in which the elements are arranged in such a way that the sum of elements contained in a row, that in a column and that in the diagonals are all equal. Here we have used the magic square matrix of size 2n x 2n.

   4. Upper Magic Matrix

      The upper half of the magic square matrix is referred to, in this context, as an upper magic matrix. This matrix is formed by magic square matrix (2n x 2n) using its first half rows (1 to nth row) along with all its columns (1 to 2nth column).

   5. Lower Magic Matrix

      The lower half of the magic square matrix is referred to, in this context, as a lower magic matrix. This matrix is formed by magic square matrix (2n x 2n) using its second half rows ((n+1)th to 2nth row) along with all its columns (1 to 2nth column).

   6. XOR Operation

   Here we have performed bitwise XOR operation upon two numbers. When the two bits are identical, the result is evaluated to zero, otherwise to one.

3. PROPOSED ENCRYPTION ALGORITHM WITH EXAMPLE

   Step-1

   First and foremost, convert each element of the input string into its corresponding ASCII value and calculate its length.

   Here, the ASCII equivalent of the string is: [ 80 114 101 80 108 32		32 101	97
   115 101 110 116 97 116 105 111 110 32 76 97 121 11	1 114 114	32 115	111
   101 114 32 105 115 32 114 101 115 112 111 110 11	5 101 112	102 105	114
   115 105 98 108 101 32 102 111 114 32 69 110 99 98 99 114		121 115	116

   Consider the entered input string is: Presentation Layer is responsible for Encryption & Decryption.

   114 121 112 116 105 111 110 32 38 32 68 101 99

   114 121 112 116 105 111 110 46 ]

   Length of string = 62

   Step-2

   We break the sequence of input string into rectangular matrices of size n x 2n; such that n is assigned maximum possible value; and place the remaining sequence into a variable REMAINDER_STRING. Note the value of n in a variable matrix_size[ ] that maintains the sequence of division. This step is repeated using remainder REMAINDER_STRING of this step as input string, till REMAINDER_STRING contains 8 or more elements.

   In this example, the matrices generated are:

   80 114 101 115 101 110 116 97 116 105

   111 110 32 76 97 121 101 114 32 105

   115 32 114 101 115 112 111 110 115 105

   98 108 101 32 102 111 114 32 69 110

   99 114 121 112 116 105 111 110 32 38

   The matrices after rotations are:

   110 101 76 101 121 116 114 116 105 105

   112 101 110 110

   111 32 32 38

   110 69 115 105

   110 111 97 32

   121 101 116 99

   32 114 68 112

   Since, the first matrix has odd number of rows, so reversing the un-changed elements. After this step, the first matrix becomes:

   110 101 76 101 121 116 114 116 105 105

   80 108 32 32 101 97 112 101 110 110

   111 114 32 111 111 115 32 114 32 38

   115 101 112 102 105 114 110 69 115 105

   98 99 114 121 115 116 110 111 97 32

   Step-4

   We take a magic square matrix of size 2n x 2n. If the number of rows in the rectangular matrix under consideration is odd (value of n is odd) then we proceed to step-5, otherwise if the number of rows in the rectangular matrix under consideration is even (value of n is even) then we continue to step-6.

   92 99 1 8 15 67 74 51 58 40

   32 68 101 99

   114 121 112 116

   REMAINDER_STRING = [ 105 111 110 46 ]

   matrix_size = [ 5 2 ]

   Step-3

   Then we apply rotation pattern on all the generated rectangular matrices. The sequence of steps in rotation pattern

   98 80 7 14 16 73 55 57 64 41

   4 81 88 20 22 54 56 63 70 47

   85 87 1 21 3 60 62 69 71 28

   86 93 25 2 9 61 68 75 52 34

   17 24 76 83 90 42 49 26 33 65

   23 5 82 89 91 48 30 32 39 66

   79 6 13 95 97 29 31 38 45 72

   10 12 94 96 78 35 37 44 46 53

   11 18 100 77 84 36 43 50 27 59

   Upper Magic Matrix

   Lower Magic Matrix

   is:

   1. Apply single-up-shift to the even columns of the

      16 2 3 13

      Upper Magic

      matrix.

   2. Rotate the outer-most frame of elements in the matrix in anti-clock wise direction, its inner frame in clock-wise direction, and so on. If the generated matrix has odd number of rows, i.e. value of n is odd, then reverse the elements of middle row which did not participate in either of the rotations in this step.

   The matrices after single-up-shift are:

   Step-5

   5 11 10 8

   9 7 6 12

   4 14 15 1

   Matrix

   Lower Magic Matrix

   80 110 101 76 101 121 116 114 116 105

   111 32 32 101 97 112 101 110 32 105

   115 108 114 32 115 111 111 32 115 110

   98 114 101 112 102 105 114 110 69 38

   99 114 121 115 116 110 111 97 32 105

   32 121 101 116

   114 68 112 99

   We take the upper magic matrix of size n x 2n and perform operation on the corresponding element of generated rectangular matrix. If the value of element of upper magic matrix is odd then means XOR, otherwise means addition.

   Using the upper magic matrix:

   92 99 1 8 15 67 74 51 58 40

   98 80 7 14 16 73 55 57 64 41

   4

   81 88 20 22 54 56 63 70 47

   85 87 19 21 3 60 62 69 71 28

   86 93 25 2 9 61 68 75 52 34

   The 1st matrix after this step is:

   202 6 77 109 118 55 188 71 163 145

   ÊMmv7¼G£²¼'.u(G\®Gs#x©XMf &2csj®¬ 4¸>k{zI²$Blro$|Sqhk

   "

   178 188 39 46 117 40 71 92 174 71

   Cipher text is:

   115 35 120 131 133 169 88 77 102 9

   38 50 99 115 106 174 172 0 52 133

   184 62 107 123 122 73 178 36 149 66

   Step-6

   We take the lower magic matrix of size n x 2n and perform operation on the corresponding element of generated rectangular matrix. If the value of element of lower magic matrix is even then means XOR, otherwise means addition.

   Using the lower magic matrix:

   9 7 6 12

   4 14 15 1

   The 2nd matrix after this step is:

   130 108 114 111

   36 124 83 113

   Step-7

   Calculate the sum of row of magic square matrix of size same as that of the value of each element in the variable matrix_size[ ] and store the sum in variable sum_of_magic_matrix[ ].

   Convert the magic square matrix of size 3 into a 1- dimensional array magic_array[ ] and then square each term in it.

   In this example, the matrices generated are:
   For all the elements in the variable REMAINDER_STRING,	202	6	77	109	118	55	188 71 163 145
   perform XOR operation with the corresponding value of	178	188	39	46	117	40	71 92 174 71
   element in sum_of_magic_matrix[ ] and then perform XOR	115	35	120	131	133	169	88 77 102 9
   operation with corresponding elements in magic_array[ ]. 38		50	99	115	106	174	172 0 52 133
   184		62	107	123	122	73	178 36 149 66
   [ 104 107 11 34 ]				130	108	114	111

   Here, sum_of_magic_matrix = [ 65 5 ] magic_array = [ 64 1 36 9 25 49 16 81 4 ]

   Step-8

4. PROPOSED DECRYPTION ALGORITHM WITH EXAMPLE

   Step-1

   First and foremost, convert each element of the input string into its corresponding ASCII value and calculate its length.

   Consider the entered input string is:

   ÊMmv7¼G£²¼'.u(G\®Gs#x©XMf &2csj®¬ 4¸>k{zI²$Blro$|Sqhk

   "

   Here, the ASCII equivalent of the string is:

   [ 202 6 77 109 118 55 188 71 163 145 178 188 39

   46 117 40 71 92 174 71 115 35 120 131 133 169 88

   77 102 9 38 50 99 115 106 174 172 0 52 133 184

   62 107 123 122 73 178 36 149 66 130 108 114 111

   36 124 83 113 104 107 11 34 ]

   Length of string = 62

   Step-2

   We break the sequence of input string into rectangular matrices of size n x 2n; such that n is assigned maximum possible value; and place the remaining sequence into a variable REMAINDER_STRING. Note the value of n in a variable matrix_size[ ] that maintains the sequence of division. This step is repeated using remainder REMAINDER_STRING of this step as input string, till REMAINDER_STRING contains 8 or more elements.

   After this step, the content of REMAINDER_STRING is:

   Step-9

   In this last step, we merge all the rectangular matrices and the variable REMAINDER_STRING, in the order they were divided, to form the cipher text.

   [ 202 6 77 109 118 55 188 71 163 145 178 188 39

   46 117 40 71 92 174 71 115 35 120 131 133 169 88

   77 102 9 38 50 99 115 106 174 172 0 52 133 184

   62 107 123 122 73 178 36 149 66 130 108 114 111

   36 124 83 113 104 107 11 34 ]

   36 124 83 113

   REMAINDER_STRING = [ 104 107 11 34 ]

   matrix_size = [ 5 2 ]

   Step-3

   We take a magic square matrix of size 2n x 2n. If the number of rows in the rectangular matrix under consideration is odd (value of n is odd) then we proceed to step-4, otherwise if the number of rows in the rectangular matrix under consideration is even (value of n is even) then we continue to step-5.

   92 99 1 8 15 67 74 51 58 40

   98 80 7 14 16 73 55 57 64 41

   4 81 88 20 22 54 56 63 70 47

   Step-6

   Upper

   Then we apply rotation pattern on all the generated rectangular matrices. The sequence of steps in rotation pattern

   85 87 19 21 3

   60 62 69 71 28

   Magic

   Matrix

   is:

   86 93 25 2 9 61 68 75 52 34

   17 24 76 83 90 42 49 26 33 65

   79 6	13	95	97	29	31	38	45	72
   10 12	94	96	78	35	37	44	46	53
   11 18	100	77	84	36	43	50	27	59
   			16	2	3	13		Upper Magic

   23 5 82 89 91 48 30 32 39 66

   Lower Magic Matrix

   1. Rotate the outer-most frame of elements in the matrix in clock-wise direction, its inner frame in anti-clock wise direction, and so on. If the generated matrix has odd number of rows, i.e. value of n is odd, then reverse the elements of middle row which did not participate in either of the rotations in this step.

   2. Apply single-down-shift to the even columns of the matrix.

      Step-4

      5 11 10 8

      9 7 6 12

      4 14 15 1

      Matrix

      Lower Magic Matrix

      The matrices after rotations are:

      80 110 101 76 101 121 116 114 116 105

      111 32 32 101 97 112 101 110 32 105

      115 108 32 111 111 115 32 114 115 110

      98 114 101 112 102 105 114 110 6938

      99 114 121 115 116 110 111 97 32 105

      We take the upper magic matrix of size n x 2n and perform operation on the corresponding element of generated rectangular matrix. If the value of element of upper magic matrix is odd then means XOR, otherwise means subtraction.

      Using the upper magic matrix:

      92 99 1 8 15 67 74 51 58 40

      98 80 7 14 16 73 55 57 64 41

      32 121 101 116

      114 68 112 99

      Since, the first matrix has odd number of rows, so reversing the un-changed elements. After this step, the first matrix becomes:

      80 110 101 76 101 121 116 114 116 105

      111 32 32 101 97 112 101 110 32 105

      4 115 108 114 32 115 111 111 32 115 110

      81 88 20 22 54 56 63 70 47

      85 87 19 21 3 60 62 69 71 28

      86 93 25 2 9 61 68 75 52 34

      The 1st matrix after this step is:

      116	114	116	105	105
      97	112	101	110	110
      115	32	114	32	38
      114	110	69	115	105
      116	110	111	97	32

      110 101 76 101 121

      80 108 32 32 101

      98 114 101 112 102 105 114 110 69 38

      99 114 121 115 116 110 111 97 32 105

      The matrices after single-down-shift are:

      80 114 101 115 101 110 116 97 116 105

      111 110 32 76 97 121 101 114 32 105

      115 32 114 101 115 112 111 110 115 105

      111 114 32 111 111

      115 101 112 102 105

      98 99 114 121 115

      Now, continue to Step-6

      98 108 101 32 102 111 114 32 69 110

      99 114 121 112 116 105 111 110 32 38

      32 68 101 99

      114 121 112 116

      Step-5

      We take the lower magic matrix of size n x 2n and perform operation on the corresponding element of generated rectangular matrix. If the value of element of lower magic matrix is even then means XOR, otherwise means subtraction.

      Using the lower magic matrix:

      9 7 6 12

      4 14 15 1

      The 2nd matrix after this step is:

      121 101 116 99

      32 114 68 112

      Step-7

      Calculate the sum of row of magic square matrix of size same as that of the value of each element in the variable matrix_size[ ] and store the sum in variable sum_of_magic_matrix[ ].

      Convert the magic square matrix of size 3 into a 1- dimensional array magic_array[ ] and then square each term in it.

      Here, sum_of_magic_matrix = [ 65 5 ] magic_array = [ 64 1 36 9 25 49 16 81 4 ]

      Step-8

      For all the elements in the variable REMAINDER_STRING, perform XOR operation with the corresponding value of element in magic_array[ ] and then perform XOR operation with corresponding elements in sum_of_magic_matrix[ ].

      Take Rectangular Matrix

      After this step, the content of REMAINDER_STRING is: [ 105 111 110 46 ]

      The flow chart of rotation pattern for encryption is:

      Start

      Step-9

      Perform single-up-shift on Even columns

      In this last step, we merge all the rectangular matrices and the variable REMAINDER_STRING, in the order they were divided, to form the plain text.

      [ 80 114 101 115 101 110 116 97 116 105 111 110

      32 76 97 121 101 114 32 105 115 32 114 101 115

      112 111 110 115 105 98 108 101 32 102 111 114

      32 69 110 99 114 121 112 116 105 111 110 32 38

      32 68 101 99 114 121 112 116 105 111 110 46 ]

      Plain text is:

      Presentation Layer is responsible for Encryption &

      No. of rows is Odd

      No Stop

      Reverse the unchanged elements of middle row

      Perform Cycling Operation (ACW-CW-ACW-CW)

      Yes

      Decryption.

5. FLOWCHART OF ENCRYPTION ALGORITHM The flow chart of encryption algorithm is:

   Get length and ASCII value of Plain Text

   Get length and ASCII value of Cipher Text

   Start Input Plain Text

   Fig. 2. Flow Chart of Rotation Pattern for Encryption.

6. FLOWCHART OF DECRYPTION ALGORITHM The flow chart of decryption algorithm is:

   Start

   Input Cipher Text

   Break the string into rectangular matrix till there are more than 7 elements

   Break the string into rectangular matrix till there are more than 7 elements

   Apply Rotation Pattern on Rectangular Matrices

   No. of No rows is

   XOR with sum_of_magi c_matrix[ ]

   Odd

   No. of No rows is

   XOR with magic_array[]

   Even

   XOR with sum_of_magi c_matrix[ ]

   No. of No

   No. of No

   Yes Yes

   rows is Odd

   rows is Even

   Take Upper Magic Matrix

   Yes Yes

   Take Lower Magic Matrix

   Take Upper Magic Matrix

   XOR with magic_array[]

   Element of Magic Matrix is Odd

   Take Lower Magic Matrix

   Element of Magic Matrix is Even

   Element of Magic Matrix is Odd

   Element of Magic Matrix is Even

   No Yes No Yes

   Merge all the Rectangular Matrices & Remainder Elements

   Perform XOR

   Perform Subtraction

   Perform XOR

   Perform Subtraction

   No Yes No Yes

   Perform Addition

   Perform XOR

   Perform Addition

   Perform XOR

   Apply Rotation Pattern

   Merge all the Rectangular Matrices & Remainder Elements

   Output Cipher Text Stop

   Fig. 1. Flow Chart of Encryption Algorithm.

   Output Plain Text Stop

   Fig. 3. Flow Chart of Decryption Algorithm.

   Plain Text	Length	Time (in second)	Cipher Text
   the above passage, just enjoy it and bang your head here.with lots of jerks!!!!!!!

   The flow chart of rotation pattern for decryption is:

   Start

   Take Rectangular Matrix

   Perform Cycling Operation (CW-ACW-CW-ACW)

   No. of rows is Odd

   No

   Yes

   On enormously increasing the length of string, the time required to encrypt it, is still changed by a negligible amount. We have plotted a graph Encryption Time Graph to represent the encryption time taken by the strings of various

   Perform single-down-shift on Even columns

   lengths.

   Stop

   Fig. 4. Flow Chart of Rotation Pattern for Decryption.

7. RESULT

   We have applied the proposed algorithm on string of various lengths, and aroused with astonishing and remarkable results. The structure of plain text is found to be entirely changed. The following table enlists the sample plain text, their length, encryption time and the corresponding cipher text generated.

   Plain Text	Length	Time (in second)	Cipher Text
   Password	8	0.093	xzb Typs
   aaaaaaaaaaaaa	13	0.095	jhgmeopb$e@m}
   Money is 5000$ take it	22	0.107	Po;#NPs539v9q6~u*.Br
   Network Security is essential	29	0.120	ukf M~F~kt{gl4nlr w }/o&eG
   National Institute of Technology Raipur, C.G.	45	0.115	iVuG~w sB2IQ/aR¤_~ T|YsmRh~h*e$~asBG( K
   Presentation Layer is responsible for Encryption & Decryption.	62	0.127	ÊMmv7¼G£²¼'.u(G\® Gs#x©XMf &2csj®¬ 4¸>k{zI²$Blro$|Sqhk "
   Calculating efficiency of the algorithm to check the success. Its my success too.. feeling greatyahoooo!! !!	112	0.124	تtxréæùCѬ"úºj~~rëøI Úl±§üþvQQÍ× éÈv`ÔÂÌYG ²!~ÀÂÃR Yñù£[ÚÌÚWenáõñýË\ ximpfpª-
   My name is Suyash Kandele, and I am not a terrorist, but I am a student. I live in my house and not in the entire city Bhilai. Studies are my hobbies and I have no time for hobbies. I like greenery, and wherever I find it, I remove it from there. Dont read	341	0.110	`y?NRÁ{¤ÙF>L© kÈ|¬=T«*Û_³;ÀG á\:ÉU õ)ÈEßüùlÓ¢°ü äåæûÄ+Qæçÿ&; Ý_óñúv4DÎÔìtq_Ì¿ ûó½osU- ³Äv1@\-ù

   • Zw&Qì¬(TÖLGpz

   TABLE I. RESULTS OF CLUR ENCRYPTION ALGORITHM

   Reverse the unchanged elements of middle row

   Encryption Time Graph

   100

   90

   83.422

   86.81

   10 20

   50 100 200 300 400 500 600 700 800 900 1000 1200 1500 1800 2000

   Length of String

   40

   30

   20

   10

   0

   58.363

   50

   60.552

   57.664

   65.776

   60

   73.536

   70.966

   65.33 65.628

   70

   71.434

   80

   79.532

   79.498

   Time (in milliseconds)

   Fig. 5. Encryption Time Graph.

   3000

   2000

   3266.5

   5000

   4000

   Time (in microsecond)

   On the basis of above observations, we have calculated and plotted the value of time required to encrypt a single character, for each string, in Time per Character Graph, and found drastic minimization in time.

   Time per Character Graph

   7000

   6000

   5836.3

   0

   10 20 50 100 200 300 400 500 600 700 800 900 1000 1200 1500 1800 2000

   Length of String

   43.4

   177.415 132.497 75.69 73.536 55.615

   288.32

   1000

   1279.34

   Fig. 6. Time per Character Graph.

8. CONCLUSION

   In this proposed work, we have introduced a novel technique of encrypting text without using any key. The plain text is broken into rectangular matrices of varying sizes, with each matrix encrypted separately and distinctly. To change the number of times a character is repeated, we have employed the modified form of magic matrix. The values in the applied magic matrix directs the further encryption operation to be performed, and hence provides dynamism to this work. The basic and easy to implement mathematical and logical operations are used in this algorithm which makes it highly suitable for mobile devices and devices with low computation power.

9. FUTURE SCOPE

This algorithm, though small, introduces a novel, less time consuming approach and is self sufficient for all kind of data encryption where processor utilization is a constraint. This algorithm provides a frame work and can be used for the innovation of much more unpredictable algorithms.

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