Final year project

PICTURE ARITHMETIC CRYPTOSYSTEM USING SYMMETRIC KEY

ENCRYPTION ALGORITHM WITH LEGITIMATE PICTURES.

Document explanation :

1. GENERATION OF PICTURE SORTING KEY:

On the receiver side, the picture sorting

key is generated from the secret code sent by the sender. To generate the picture

sorting key, LOCK-10(LOgical Crypto Key) operation is performed over the secret

code. LOCK-10 consists of ten different logical operations which can be done in

ten factorial (3628800) ways. The ten operations are

1. GCD (Greatest Common Divisor) of the digits

2. LCM (Least Common Multiple) of the digits

3. Sum of the digits

4. Product of the digits

5. Square of the number

6. Sum of square of digits

7. Product of square of digits

8. Sum of cube of digits

9. Product of cube of digits

10.Cube of the number

Let the secret code be 12345. Now the picture sorting key is generated as follows:

GCD of the digits (GCD (1,2,3,4,5) ) is 1.

LCM of the digits (LCM (1,2,3,4,5) ) is 60.

Sum of the digits (1+2+3+4+5) is 15.

Product of the digits (1*2*3*4*5) is 120.

Square of the number (123452) is 152399025.

Sum of square of digits (12+22+32+42+52) is 55.

Product of square of digits (12*22*32*42*52) is 14400.

Sum of cube of digits (13+23+33+43+53) is 225.

Product of cube of digits (13*23*33*43*53) is 1728000.

Cube of the number (123453) is 1881365963625.

Now the Picture sorting key can be produced in 3628800 ways (10 factorial).

Anyone of those ways is chosen at random to create the picture sorting key. E.g.

14400152399025115601881365963625225120551728000 is the new picture

sorting key generated in the order 7,5,1,3,2,10,8,4,6,9.

2. SORTING ‘N’ PICTURES:

The ‘N’ pictures in the folder are sorted using picture

sorting key (which is already generated from the secret key). We know that N

pictures can be sorted in ‘N’ factorial ways. Let the picture sorting key be

14400152399025115601881365963625225120551728000. Then the N pictures

are arranged in (14400152399025115601881365963625225120551728000 mod

‘N’ Factorial)th way in the folder. These ‘N’ pictures are sorted and pasted in a

folder by converting each picture into a BYTE array (byte []). Thus the ‘N’ pictures

are sorted in a new folder by using Picture Sorting key. Without knowing the exact

arrangement of pictures in folder, it will take a very long time for the hackers to

crack the key.

3. CONSTRUCTION OF 10X26 TABLE:

It is a table with 26 English alphabets (a-z) and

10 numbers (0-9). It is a 10x26 matrix where the 26 English alphabets are

arranged in different forms as 10 rows. This matrix is stored in a double

dimensional array. We have used four 10x26 matrices to encrypt the message

which are stored in four discrete 2d arrays. Any one of these 2d arrays is chosen

in random to encrypt the message which makes the task very hard for the hackers

to break our system.

A sample 10x26 matrix is shown below:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

0 j r z w y x f h a o m u p d g b e t v n q c i l s k

1 d c t l r a w z j h v b k e s n i x g y o m p f u q 2 p l r x s f y j t c w k q e a v b i g d n m z u o h 3 v e j x r i n k w d u y s b p h o m a c l g f z t q 4 n v z o t i x q f h m b r c g y p a e j u d l w s k 5 a w e f u b r i m g t d c j p n v x o k q s l h z y 6 d b h r k a o z p g t v n u j y m f w q c i x e s l 7 n v z f h w b e l k d g x a m c r o j y s t i q u p 8 p j i n f y e d s l q t w c r x m z u o a b g k h v 9 c z n m k x p e a l w s d r t i f u g v q b h j o y

4. CONVERSION OF PICTURES TO KEY (1st key):

To get the pictures from the key PACK (Picture

Arithmetic Crypto Key) operation is performed over the pictures. N pictures are

spitted in six groups and each group is assigned with certain specific operations.

The first group is assigned with no-operation and so the key digit will be

taken as the position of the picture mod 10. E.g.: if the picture is in 12th

place of the first group then the key digit will be taken as 12%10=2.

The second group is assigned with the operation Addition. The mod

operation is performed with the position of the picture and the result is

added with the previous key digit. If the result of the add operation exceeds

9 then mod 10 operation is performed over the result.

The third group is assigned with the operation Subtraction. The mod

operation is performed with the position of the picture and the result is

subtracted from the previous key digit. If the result of the sub operation

takes a negative value then mod 10 operation is performed over the result.

The fourth group is assigned with the operation Multiplication. The mod

operation is performed with the position of the picture and the result is

multiplied with the previous key digit. If the result of the mul operation

exceeds 9 then mod 10 operation is performed over the result.

The fifth group is assigned with the operation Division. The mod operation

is performed with the position of the picture and the result is used to divide

the previous key digit. If the result of the div operation exceeds 9 then mod

10 operation is performed over the result.

The sixth group is assigned with the operation Mod. The mod operation is

performed with the position of the picture and the result is used to perform

mod operation with the previous key digit. If the result of the mod

operation exceeds 9 then mod 10 operation is performed over the result.

The above six operations are continuously applied to get the key from the

pictures. As a result of this process we get the first key. Since the key digits are

continuously changing with every picture, it will be a very tough task for the

hackers to know the key. We will send the picture-key part by part so if a cracker

is not aware of any one of this part then he cannot get even a part of the key.

5. GENERATION OF SECOND KEY:

The second key is generated from the first key by

performing LOCK-5(LOgical Crypto Key) operation. LOCK-5 consists of five

different operations. The five operations are

1. GCD (Greatest Common Divisor) of the digits

2. LCM (Least Common Multiple) of the digits

3. Sum of the digits

4. Product of the digits

5. Square of the number.

Let the 1s t key be 12345. Now the second key is generated as follows:

GCD of the digits (1,2,3,4,5) is 1.

LCM of the digits (1,2,3,4,5) is 60.

Sum of the digits (1,2,3,4,5) is 15.

Product of the digits (1,2,3,4,5) is 120.

Square of the number (12345) is 152399025.

Now the second key can be produced in 120 ways (5 factorial). Anyone of those

ways is chosen at random to create the second key. E.g. 12015115239902560 is

the new second key generated in the order 4,3,1,5,2.

6. ENCRYPTION WITH 1ST KEY USING VIGENERE CIPHER:

Encryption with Vigenere cipher is usually

performed by using the key as a string or a group of words. But here we are using

the numeric key to encrypt our message. Let the message be “hello world” and the

key be “454565”. Now encryption with vigenere cipher is done as follows:

The first character of the message is ‘h’ and it is shifted forward by 4 places

of English alphabets, since the first key digit is 4. Therefore, the first

character of the encrypted message is ‘l’.

The second character of the message is ‘e’ and it is shifted forward by 5

places of English alphabets, since the second key digit is 5. Therefore, the

second character of the encrypted message is ‘j’.

Similarly, we get the encrypted message as “ljpqu bswpi”.

Note: The encryption process follows round-robin fashion if the key reaches its

end.

7. ENCRYPTION WITH 2nd KEY USING 10x26 matrix:

Let the message be “hello world” and

the key be 324345. Now the encryption procedure is as follows:

The first letter of the message is ’h’ and first digit of the key is 3. In the

above matrix, the row 3 (i.e., 4th row) corresponding to column H has the

alphabet ‘k’. Therefore the first letter of the encrypted message is ‘k’.

The second letter of the message is ’e’ and first digit of the key is 2. In the

above matrix, the row 2 (i.e., 3rd row) corresponding to column E has the

alphabet ‘s’. Therefore the second letter of the encrypted message is ‘s’.

Similarly, for the message “hello world” we get the encrypted message as “ksbyg

lpibx”.

Note: The encryption process follows round-robin fashion if the key reaches its

end.

8. DECRYPTION WITH SECOND KEY USING 10x26 MATRIX:

The decryption process using 10x26 matrix

is just the reverse process of encryption. Let the encrypted message be “ksbyg

lpibx” and the key be 324345. Now the decryption procedure is as follows:

The first letter of the encrypted message is ’k’ and first digit of the key is 3.

In the above matrix, the row 3 (i.e., 4th row) corresponding to column H has

the alphabet ‘k’. Therefore the first letter of the decrypted message is ‘h’.

The second letter of the encrypted message is ’s’ and first digit of the key is

2. In the above matrix, the row 2 (i.e., 3rd row) corresponding to column E

has the alphabet ‘s’. Therefore the second letter of the decrypted message

is ‘s’.

Similarly, for the encrypted message “ksbyg lpibx” we get the decrypted message

as “hello world”.

Note: The decryption process follows round-robin fashion if the key reaches its

end.

9. DECRYPTION WITH 1ST KEY USING VIGENERE CIPHER:

The decryption process using vigenere

cipher is just the reverse process of encryption. Let the encrypted message be

“ljpqu bswpi” and the key be “454565”. Now decryption with vigenere cipher is

done as follows:

The first character of the message is ‘l’ and it is shifted backward by 4

places of English alphabets, since the first key digit is 4. Therefore, the first

character of the decrypted message is ‘h’.

The second character of the encrypted message is ‘j’ and it is shifted

backward by 5 places of English alphabets, since the second key digit is 5.

Therefore, the second character of the decrypted message is ‘e’.

Similarly, we get the decrypted message as “hello world”.

Note: The decryption process follows round-robin fashion if the key reaches its

end.