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International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963

A LOGARITHM ENCRYPTION (EA-LOG) OF SYMMETRIC
CRYPTOGRAPHY
Mohammed Abdulridhu Hussain and Zaid Ameen Abduljabbar
Department of Computer Science, College of Education, Basrah University, Basrah, Iraq

ABSTRACT
Cryptography is an area of computer science which is developed to provide security for the senders and
receivers to transmit and receive confidential data through an insecure channel. In this paper an Encryption/
Decryption method will be proposed to enhance the frequency latter performance. To protect information from
disclosed by the attacker encryption must be apply on the information, the encryption propose is based on
logarithm equation, where the logarithm base will be act as the secret key of the algorithm. The strength of the
result values for a plaintext is the long key range, but the problem with the relative frequency of the letters.
Solving frequency distribution for a language three different methods propose to hide the relative frequency of
the letters. However, the methods will add a second level of security on the encrypted information that produces
from the logarithm which enhances the security.

KEYWORDS: Cryptography, Encryption, Decryption, Secret key, symmetric cryptography

I.

INTRODUCTION

Cryptography is the science of making communication unintelligible to everyone except the intended
receivers. Cryptography offers efficient solution to protect sensitive information in a large number of
applications including personal data security, internet security, diplomatic and military
communications security, etc. A cryptosystem is a set of algorithm, indexed by some keys(s), for
encoding messages into cipher text and decoding them back into plaintext [1]. Manly encryption
algorithms can be classified into two broad categories- Symmetric and Asymmetric key encryption.
In symmetric Cryptography the key used for encryption is similar to the key used in decryption. Thus
the key distribution has to be made prior to the transmission of information. The key plays a very
important role in symmetric cryptography since their security directly depends on the nature of key
i.e. the key length etc. There are various symmetric key algorithms such as DES, TRIPLE DES, AES,
RC4, RC6, BLOWFISH [2].
In Asymmetric Key encryption, two different keys are used for encryption and decryption- Public and
Private. The public key is meant for general use so it is available to anyone on the network. Anyone
who wants to encrypt the plaintext should know the Public key of receiver. Only the authorized
person can be able to decrypt the cipher text through his own private key. Private Key is kept secret
from the outside world.
Symmetric Encryption Algorithm runs faster as compared to Asymmetric key algorithms. Also the
memory requirement of Symmetric algorithm is lesser as compared to asymmetric.
The core of the encryption algorithm in cryptography is the mathematical equations; the complexity
of the equation does not mean that the algorithm is good. Almost all algorithms based on the modular
arithmetic because each result has a variety of possibility to discover the original number.
Encryption algorithms are used to handle the first security goal which is confidentiality. The attacker
has two methods to break a cipher text, the first method is trying every possible key on a cipher text
until an intelligible translation into plaintext is obtained [3] but with one condition when the algorithm
is known, the second method is determine the relative frequency of the letters in a cipher text and

1977

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
compare to a standard frequency distribution for the language in used and this strategy usually work
for the substituted encryption algorithm.
In this paper we instructed a symmetric encryption algorithm based on the same idea of the modular
but by using mathematic logarithm function with different methods. The propose algorithm is
sophisticate to be broken by the relative frequency method. Moreover, the key is difficult to be
predicted.
The rest of the paper is organized as follows: Section 2 presents the literature review. Section 3 the
propose encryption and decryption algorithms. Section 4 case study as an example. Section 5gives the
test result and discussion. Section 6 conclusion.

II.

RELATED WORK

Visual Cryptography is a technique to make data secure. After dividing image into ‘n’ shares, the
individual shares are sent via different communication channels to destination such that intruder has
less chance to get whole information [4].
Ranjan kumar, et al. [4] this paper focuses on one particular popular technique, Least Significant Bit
(LSB) embedding, using digital images as the medium. The terminology is that a message is hidden
within a cover image to produce a stego-image. Security issue in this paper is encrypting the resulting
Stego-image using symmetric encryption method before share creation. The encryption based on
additive modulo 255 algorithms. Keys are generated using a unique technique called Mixed Key
Generation (MKG). In this method block of size of 8 byte keys are generated using PRN generation
algorithm and individual bits from every bytes is selected.
Janailin, et al. [5] propose a new symmetric key algorithm called as KED (Key Encryption
Decryption) and a new key generation method. The proposed algorithm is used for encryption and
decryption process, using modulo69 and inverse modulo69. The encryption algorithms based on
multiply with key1 and adding with key2. Where key1 is entered by the user, key2 is calculated and
the reverse of key1 will be found for decryption purpose. The decryption algorithm is the reverses of
encryptions which is done through subtraction with key2 and multiply with the reverse value of key1
act as division.
Vishwa gupta, et al. [6] propose an advance cryptography algorithm for improving data security. This
algorithm essentially based on combination of XOR operation and circular shift between the 16
character blocks which is operate on the key and to produce the cipher.
Prof. K. Ravindra Babu, et al. [7] propose new substitution algorithm where the plaintext is
substituted with a color block form the available 18 Deucalion’s of colors in the world, the algorithm
named Play Color Cipher (PCC). Each character from the plaintext will be map into four colors in one
pixel, where the size of the result cipher image will be more than the original plaintext four times.
Ayushi [4] propose a symmetric key cryptographic algorithm which is based on reversing the ASCII
code of a character and divide the result by 4 digits divisor as the key. The algorithm is simple to
implement.
Ankita Agarwal [5] in this paper, a new approach of Genetic Algorithm is proposed in which, the
operations of GA (Crossover and Mutation) are exploited to produce this encryption method. Where
Crossover is swapping two bytes in each 8-byte and Mutation is subtraction of one byte from the
number 255, the selection of bytes to apply the operation on based on a key.

III.

THE PROPOSE ALGORITHM

The propose encryption algorithm embedded the mathematical logarithm function to encrypt the
plaintext as shown in equation (1), where this algorithm can be categorized as substitution method. In
another word each character in plaintext will be replaced with another character. Thus, to cover all
probability of plaintext character, ASCII code is used.
𝑝

ln⁡(𝑝)

𝐶 = 𝑙𝑜𝑔𝑘 = ln⁡(𝑘)

…………………… (1)

where c is the cipher text, p is the plaintext and k is the secret key.

1978

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Input
Plaintext

Encryption
Algorithm

Deccryption
Algorithm

EA-LOG

DA-LOG

Output
Plaintext

Figure 1: Symmetric cryptography model

3.1 Encryption Algorithm
Step1: Consider a plaintext with PL length and k as secret key.
Step2: For i = 1 to PL Do
Read the plaintext character by character as Plaintext (i)
Apply Equation (1) save result in Cipher
Step3: Transform the variable cipher to a ciphertext, three methods are proposed;
Method 1:
- Each integer number converts to one character from the alphabetic string variable.
- Replace all the recurrence characters with the previous position of the same character. The
position will be converted to a character; the maximum position value is equal to the
alphabetic variable length.
Method 2:
- convert each two integer number to one ASCII character
- Replace all the recurrence characters with the previous position of the same character. The
position will be converted to a character; the maximum position value is greater than 127
which is ASCII number.
Method 3:
- convert the cipher numbers to binary and then each 6-bit binary number convert to ASCII
characters
- Replace all the recurrence characters with the previous position of the same character. The
position will be converted to a character; the maximum position value is greater than 127
which is ASCII number.
3.1.1 EA-LOG Method 1
The result of cipher variable is a real number with a maximum length of five digits. Therefore, to
produce a ciphertext each integer number will be replaced with a character from the alphabetic string
variable.
The Encryption ALGORITHM for method 1
Step1: Append the length (number of digit) for each number in the variable cipher save the result in
variable cipher1.
Step2: For i = 1 to length(cipher1) Do
For j=1 to length(cipher1(i)) do
Each digit number acts as position to the alphabetic variable for produce the
ciphertext, save as cc1 variable.
End for
End for
Step3: For i = 1 to length(cc1) Do
Find the position of cc1(i) in cc1(1 to i-1)
If true (the character is found) and position <= length(alphabetic) then
Replace the character with the position

1979

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Replace the position with the character from the alphabetic.
Save the result as cc11
End if
End for
3.1.2 EA-LOG METHOD 2
This method converts each two integer numbers to one ASCII character.
The Encryption ALGORITHM for method 2
Step1: Append the length (number of digit) for each number in the variable cipher save the result in
variable cipher1.
Step2: For i = 1 to length(cipher1) Do
For j=1 to length(cipher1(i)) step 2 do
Each two digits converted into one ASCII character, save as cc2 variable.
End for
End for
Step3: For i = 1 to length(cc2) Do
Find the position of cc2(i) in cc2(1 to i-1)
If true (the character is found) and position + 101 > 127 then
Replace the character with the position
Replace the position value with the character from the ASCII.
Save the result as cc22
End if
End for
3.1.3 EA-LOG METHOD 3
This method will treat the Cipher numbers as binary numbers by taken each time six bit and convert
them to character from the ASCII.
The Encryption ALGORITHM for method 3
Step1: For i = 1 to length(cipher) Do
Convert cipher(i) to binary, save as no variable.
For j=1 to length(no) step 6 do
converted into one ASCII character, save as cc3 variable.
End for
Append the number of characters for each cipher(i) will produces.
End for
Step2: For i = 1 to length(cc3) Do
Find the position of cc3(i) in cc3(1 to i-1)
If true (the character is found) and position + 63 > 127 then
Replace the character with the position
Replace the position value with the character from the ASCII.
Save the result as cc33
End if
End for

3.2 Decryption algorithm
The decryption algorithm in the symmetric cryptography is reverse procedure of the encryption and it
can be written as:
𝑝 = 𝑘𝑒𝑦 𝑐
…………………… (2)
where c is the cipher number and the cipher number will be generated from the ciphertext depending
on the method.
3.2.1 DA-LOG Method 1
Step1: Read the key
For i = 1 to length(cc11) Do
Convert the position characters to the original characters, save the result as cc12
variable.
End for
Step2: For i = 1 to length(cc12) Do

1980

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Convert the characters to the original value from the variable alphabetic by its
location.
End for
Step3: For i=1 to length(cc12) Do
Read the length of each number.
Combine the number (based on the above which is the number of digits)
Save the result as no2.
Apply Equation (2) to produce the plaintext characters.
End for
3.2.2 DA-LOG Method 2
Step1: Read the key
For i = 1 to length(cc22) Do
Convert the position characters to the original characters, save the result as cc23
variable.
End for
Step2: For i = 1 to length(cc23) Do
Each character will be converted to two digit numbers.
End for
Step3: For i=1 to length(cc23) Do
Read the length of each number.
Combine the number (based on the above which is the number of digits)
Save the result as no2.
Apply Equation (2) to produce the plaintext characters.
End for
3.2.3 DA-LOG Method 3
Step1: Read the key
For i = 1 to length(cc33) Do
Convert the position characters to the original characters, save the result as cc34
variable.
End for
Step3: For i=1 to length(cc34) Do
Read the number of characters for the real number.
Convert the characters to binary numbers and combine the number (based on the
above which is the number of digits) to produce one real number.
Save the result as no2.
Apply Equation (2) to produce the plaintext characters.
End for

IV.

CASE STUDY

In this section given a details example to express the EA-LOG process. The algorithm implemented in
MATLAB. Assume the following variables:
Plaintext = “network security”
Key = 99
Alphabetic='abcdefghijklmnopqrstuvwxyz';
After applying equation (1) the cipher variable will be:
Cipher = [10229
10043
10344
10400
10248
10307
10169
7542
10326
10043
10000
10363
10307
10128
10344
10436]
Each number represents one plaintext character.

4.1 Method 1 Encryption Process
Cipher1 = [510229
510326 510043

1981

510043
510344
510400
510000 510363 510307

510248
510128

510307
510344

510169
510436]

47542

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Cc1=
[fbaccjfbaaedfbadeefbaeaafbaceifbadahfbabgjehfecfbadcgfbaaedfbaaaafbadgdfbadahfbabcifbadeefbae
dg]
Cc11=
[fbackjpppkedpponpkpppnlkppmcqipppdlhppnlgjxrrmcmsudovpppkvrppokkkppmtglpppnlhppnlcipnp
vekpppnqg]

4.2 Method 1 Decryption Process
Cc12=
[fbaccjfbaaedfbadeefbaeaafbaceifbadahfbabgjehfecfbadcgfbaaedfbaaaafbadgdfbadahfbabcifbadeefbae
dg]
No2 = [10229
10043
10344
10400
10248
10307
10169
7542
10326
10043 10000
10363
10307
10128
10344
10436]
Plaintext = network security

4.3 Method 2 Encryption Process
Cipher1 = [510229
510326 510043

510043
510344
510400
510248
510000 510363 510307 510128

510307
510344

510169
510436]

Figure 2: cc2 value
Double(cc2) = [51 2 29 51 100 43 51 3 44 51 4 100 51 2
51 1 69
47 54 20 51 3 26 51 100 43 51 100 100 51
7 51 1 28 51 3 44 51 4 36]

47542

48 51 3
3 63 51

7
3

Figure 3: cc22 value
Double(cc22) = [51 2 29 104 100 43 104 3 44 104 4 108 104 113 48 104
110 7 104 1 69 47 54 20 107 110 26 104 118 125 104 104 102 104 110
63 104 104 122 104 122 28 104 107 44 104 4 36]

4.4 Method 2 Decryption Process

No2 = [10229
10043
10344
10043 10000
10363
10307
Plaintext = network security

Figure 4: cc23 value
10400
10248
10307
10128
10344
10436]

10169

7542

10326

4.5 Method 3 Encryption Process
Figure 5: cc3 value
Double(cc3) = [3 2 31 53 3 2 28 59 3 2 33 40 3 2 34 32 3 2 32
8 3 2 33 3 3 2 30 57 3 1 53 54 3 2 33 22 3 2 28 59 3
2 28 16 3 2 33 59 3 2 33 3 3 2 30 16 3 2 33 40 3 2 35
4]
Figure 6: cc33 value
Double(cc33) = [3 2 31 53 67 67 28 59 67 67 33 40 67 67 34 32 67
67 66 8 67 67 75 66 64 67 30 57 67 1 90 54 67 71 75 22 67 67
95 95 67 67 67 16 67 67 75 71 67 67 67 66 64 67 91 75 67 67 71
111 67 67 35 4]

4.6 Method 3 Decryption Process

1982

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Figure 7: cc34 value

No2 = [10229
10043
10344
10043 10000
10363
10307
Plaintext = network security

V.

10400
10128

10248
10344

10307
10436]

10169

7542

10326

RESULT & DISCUSSION

Experiment 1
Plaintext = symmetric Cryptography
Key= 99
Table 1: experiment (1) - ciphertext ASCII for method 1

102
106
112
107
108
117
111
112

98
112
107
107
120
119
100
108

97
112
112
107
112
107
108
108

100
110
112
101
112
112
104
104

99
112
112
120
110
112
120
112

103
108
112
114
120
112
106
110

112
112
108
109
113
118
107
110

112
112
104
118
103
111
115
101

112
112
112
108
112
118
107
100

101
110
112
106
112
112
107
119

113
107
110
118
112
112
117
109

112
101
108
112
99
112
115
114

112
100
99
116
111
107
99
114

112
112
105
108
105
111
122
109

112
112
112
110
112
103
105
99

117
111
110
109
112
112
112

108
110
112
100
112
112
112

Figure 8: experiment (1) - Ciphertext for method 1
Table 2: experiment (1) - ciphertext ASCII for method 2

51 3
26
104 104 7
104 4 36
125 95 50

104 4
104 1
104 2
107 113

36
28
68
119

104
104
104
104

2
113
110
1

9
102
44
110

104 104 104
47 54 20
104 107 48
104 4 36

104
49
104
47

100
15
118
54

43 104 116 44
107 110 116 116
86 104 110 119
20

Figure 9: experiment (1) - Ciphertext for method 2
Table 3: experiment (1) - ciphertext ASCII for method 3

3
67
67
67
67

2
67
71
67
67

33
70
14
71
79

22
40
62
8
127

67
67
67
67
67

67
67
67
67
67

35
67
83
29
74

4
66
66
38
99

67
64
64
67
67

67
67
67
67
115

31
30
107
75
115

72
16
107
66
115

67
67
67
64

67
67
67
67

67
79
32
27

67
67
84
88

67
67
67
67

67 28 59
1 53 54
67 75 99
67 79 87

Figure 10: experiment (1) - Ciphertext for method 3

Experiment 2
Plaintext = symmetric Cryptography
Key= 31

1983

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Table 4: experiment (2) - ciphertext ASCII for method 1

102
110
113
107
100
112
112
97
113

98
112
99
105
104
112
112
112
119

100
108
112
110
118
105
112
112

105
112
112
112
114
112
118
112

109
111
112
108
112
99
112
109

104
107
104
97
112
112
99
118

112
110
117
107
112
112
112
113

109
112
112
106
111
112
112
109

112
108
112
118
103
118
112
112

106
112
112
112
111
109
107
112

103
101
112
112
107
113
111
106

111
108
109
109
112
112
110
103

107
106
107
107
112
109
112
111

112
112
112
101
118
112
108
107

112
112
108
107
101
110
111
112

111
110
112
112
97
106
118
121

107
105
112
112
112
103
101
107

Figure 11: experiment (2) - Ciphertext for method 1
Table 5: experiment (2) - ciphertext ASCII for method 2

51
38 17
104 37 92
104 124 65
104 33 21

104
104
104
104

39
35
107
107

65
52
40
119

104
104
104
104

36 61 104 104 104
33 81 104 100 110
38 42 104 107 14
35 24 104 39 65

104
104
104
104

34
22
34
100

111 104 116 42
44 104 116 107
96 104 107 119
116

Figure 12: experiment (2) - Ciphertext for method 2
Table 5: experiment (2) - ciphertext ASCII for method 3

3
66
67
66
66

64
64
67
64
64

23
24
86
71
115

57
18
20
67
103

66
66
67
66
66

64
64
64
64
64

26
87
83
66
99

65
32
83
56
99

66
66
66
66
66

64
64
64
64
111

21 29
19 48
107 107
87 87
115 75

66 64
66 64
66 64
66 64

67 67 66 64 17 63
79 5
66 2
86 44
22 79 66 64 99 99
16 9 66 64 79 87

Figure 13: experiment (2) - Ciphertext for method 3

Experiment 3
Plaintext = net!_work.@
Key= 26
Table 6: experiment (3) - ciphertext ASCII for method 1

102
109
112
112

98
112
112
112

101
109
112
107

107
122
107
76

99
100
110
110

104
110
108
109

112
112
108
108

112
108
112
108

111
110
109
115

108
117
109
112

103
113
68
65

111 107 110 112 109 106 97
107 112 112 66 71 107 105
119 109 112 112 111 108 99
119

Figure 14: experiment (3) - Ciphertext for method 1
Table 7: experiment (3) - ciphertext ASCII for method 2

51
44 27 104 41 65 104 45 90
104 119 54 104 116 36 104 43 42

104 7 31 104 39 77 104 46 68
104 17 103 102 27 64

Figure 15: experiment (3) - Ciphertext for method 2

1984

Vol. 6, Issue 5, pp. 1977-1987

International Journal of Advances in Engineering & Technology, Nov. 2013.
©IJAET
ISSN: 22311963
Table 8: experiment (3) - ciphertext ASCII for method 3

3 64
66 64
67 64

33 27 66 64 29 21 66 64 35 62 66
37 12 66 64 87 54 66 64 83 8 66
7 28

2 39 43 67 64 26 25
64 32 6 66 87 55 88

Figure 16: experiment (3) - Ciphertext for method 3

In this work we proposed a schema in symmetric cryptography named as EA-LOG, where encryption
and decryption algorithms are described with three main methods. The result of the propose schema
provide a secure ciphertext by providing infinite key length.
The general problem of the symmetric cryptography algorithms is the sharing of the secret key. The
solution of such problem by using either RSA or Diffie-Hellman key exchange which is produces a
single number on each side and it suitable for the above algorithm. Figure 17 shows the cipher vs. the
key length for character (a). Increasing the key Length will decrease the result of the encryption
algorithm, and that will result reducing the ciphertext characters.

Figure 17: key and the cipher value for character (a)

The first method consumes the bandwidth but it is the simplest. However, to make the method more
difficult simply change the sequence of character in the alpha variable.
The second method increasing the key value will result smaller value of the cipher variable which is
in term reduce the ciphertext characters, in other word, the cipher value less than five integer number.
The problem in the receiver side how to discover how many character for each number, one solution
is to add the length to the ciphertext.
The third method will handle the result in binary level. The best way to combine the binary result for
all numbers then converts them to characters, to reduce the ciphertext characters.
The result ASCII code from the above methods could be unknown character where it must handle
through programming.

VI.

CONCLUSIONS

The aim of this paper is creating a symmetric algorithm for encryption and decryption, to protect the
information from discloses by the attacker and defeats the frequency distributed for the language.
The EA - LOG on the basis of the logarithm equation with three different methods to deal with the
outcome that results from the logarithm. This paper demonstrated the relative frequency of the letter is

1985

Vol. 6, Issue 5, pp. 1977-1987


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