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2019-03-07T20:32:00.002-08:00

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Hill Cipher program in c

2018-08-03T10:27:00.001-07:00

Introduction to Hill Cipher

In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. The following discussion assumes an elementary knowledge of matrices.

This technique encrypt plaintext in matrix form of 2x2 or 3x3.when plaintext in 2x2 then key value also in 2x2 matrix and 3x3 use then 3x3 matrix key.Using matrix we can encrypt 4 or 9 plaintext letters at once.

Hill Cipher Theory

First of all need key in matrix form of 2x2 or 3x3 depends of requirement.

Here, we have formula to find Cipher text (Encryption)

CT = K*PT mod 26

Where, CT = CipherText ,

K = Key ,

PT = PlainText.

We have also formula to find Plain text from Cipher text (Decryption)

PT = K^-1*CT mod 26

Where, CT = CipherText ,

K^-1 = Inverse of key ,

PT = PlainText.

Example:

Plain text is "computer" and Key is in matrix 4 9 3 7. Apply Encryption and Decryption using Hill Cipher 2x2 matrix.

First perform Encryption:

In this we made 4-4 part of letters because we use 2x2 matrix.
Also convert plain text using below format,
a,b,c,d,........,x,y,z ==> 0,1,2,3,......,23,24,25.

Here over plain text is "computer" ==> "2 14 12 15 20 19 4 17"

In first part "comp" is encrypted for this "2 14 12 15"

Answer of CT is "12 9 12 17" convert it into letters "mjmr".

second part of text is "uter" ==>"20 19 4 17" using formula cipher text is "12 21 10 20" convert into letters "mvku".

"computer" ==>"mjmrmvku" is our cipher text.

Decryption:

We perform inverse process of encryption.
First 4-4 parts of cipher text and find value of it like...
"mjmr mvku" ==>"12 9 12 17 12 21 10 20"

Use first 4 for decryption see in below image

In this find inverse of key and multiple matrix with first 4 cipher text letters.
(how to find inverse and multiplication click here)

You can see in picture we get the plain text from cipher text.

Now we see Hill Cipher Program in c

First we see variable information:

  int key[2][2]={'\0'},p[50]={'\0'};  
  char pt[50]={'\0'};  
  int len=0,n=0,i=0,j=0,m=0;  
  clrscr();

Key is 2x2 matrix use for get key value from user.
Pt is character array that is use for store plain text.
p in this array store plain text numeric value (a,b,c...==>0,1,2...) .

Get Plaintext and key from user:

 printf("\n Enter PlainText:");  
  gets(pt);  
  printf("\n Enter key:");  
  for(i=0;i<2;i++)  
  {  
   for(j=0;j<2;j++)  
   scanf("%d",&key[i][j]);  
  }

using gets() we get plain text and use for loop for get value of key.

Add Filler

In this part we add filler to our plain text for better out put.

why need filler?
Filler is use when 4 equal parts is not possible like..
In "hello" part is "hell" and "o" that time our program's first part is run completely but in second part we have only one letter there for error is occur or program miss behave.

Therefore we use filler 'x' in program "hello" ==> "hell oxxx".

 len=strlen(pt);  
  if(len % 4 == 1)  
  {  
   n=3;  
  }else if(len % 4 == 2)  
  {  
  n=2;  
  }else if(len % 4 == 3)  
  {  
  n=1;  
  }else  
  {  
  n=0;  
  }  
  if(n != 0)  
  {  
  for(i=0;i<n;i++)  
  {  
   pt[len]='x';  
   len++;  
  }  
  }  
  printf("\n new plaintext:");  
  puts(pt);  
  n=0;  
  printf("\n Your Key is:");  
  printf("\n");  
  for(i=0;i<2;i++)  
  {  
    for(j=0;j<2;j++)  
    {  
    printf("\t %d \t",key[i][j]);  
    }  
    printf("\n \n");  
  }

Output of this:

Store plain text numeric value:

  for(i=0;i<strlen(pt);i++)  
  {  
   p[m]=pt[i]-97;  
   m++;  
  }

here substitute 97 from each letter it will give numeric value of letters and store in array p.

Send values to function:

 hill(p,m,key);

here send array p in this all numeric value of plaintext that is use in encryption,
m it is index of p (in c language difficult to find length of integer array)
key it is most important for encryption and decryption.

Function of Hill Cipher:

 void hill(int [50],int ,int [2][2]);

First add this function deceleration above of main function.

Variables use in function:

  int i=0,sum=0,j=0,k=0,n=0,count=0,ic=0;  
  int ipt[2][2]={'\0'},cy[2][2]={'\0'},c[50]={'\0'};  
  char fcy[50]={'\0'},fpt[50]={'\0'};  
  float ikey[2][2]={'\0'},det=0,psum=0,pt[2][2]={'\0'};  
  int tpt[2][2]={'\0'};

ipt is store 4 value of plain text that is use in matrix multiplication.
cy is cipher text value before of mod with 26.
fcy is final array of cipher text.
ikey in this store inverse of key.
pt is store value before of mod with 26.

Encryption:

 for(n=0;n<m;n++)  
  {  
   for(i=0;i<2;i++)  
   {  
   for(j=0;j<2;j++)  
   {  
    ipt[i][j]=p[count];  
    count++;  
   }  
   }  
  for(i=0;i<2;i++)  
  {  
  for(j=0;j<2;j++)  
  {  
  sum=0;  
   for(k=0;k<2;k++)  
   {  
    sum=sum+key[i][k]*ipt[k][j];  
   }  
   cy[i][j]=sum;  
  }  
  }  
  printf("\n cipher text is:");  
  sum=0;  
  for(i=0;i<2;i++)  
  {  
  for(j=0;j<2;j++)  
  {  
   fcy[sum]=(cy[i][j]%26)+97;  
   c[ic]=cy[i][j]%26;  
   ic++;  
   printf("%c \t",fcy[sum]);  
   sum++;  
  }  
  }  
  n=n+3;  
  printf("\n");  
  }

In above code first for loop use for length of plaintext using index 'm'.
Below Two for loop is use for 4-4 partition and store in ipt.

then do matrix multiplication for 2x2 matrix and store in cy array.

fcy[sum]=(cy[i][j]%26)+97; //also present in above image

this is use for mod with 26 and add 97 for get cipher text.

c[ic]=cy[i][j]%26; //also present in above image

And this store numeric value of cipher text that is use for Decryption.

Decryption:

  count=0;  
  for(n=0;n<m;n++)  
  {  
   for(i=0;i<2;i++)  
   {  
   for(j=0;j<2;j++)  
   {  
    ipt[i][j]=c[count];  
    count++;  
   }  
   }  
  det=((key[0][0]*key[1][1])-(key[0][1]*key[1][0]));  
  if(det !=0)  
  {  
  for(i=0;i<2;i++)  
  {  
  for(j=0;j<2;j++)  
  {  
   if(i==0 && j==0)  
   {  
   ikey[i][j]=key[1][1];  
   }  
   if(i==1 && j==1)  
   {  
   ikey[i][j]=key[0][0];  
   }  
   if(i != j)  
   {  
   ikey[i][j]=-key[i][j];  
   }  
  }  
  }  
  for(i=0;i<2;i++)  
  {  
  for(j=0;j<2;j++)  
  {  
  psum=0;  
   for(k=0;k<2;k++)  
   {  
    psum=psum+ikey[i][k]*ipt[k][j];  
   }  
   pt[i][j]=psum;  
   while(pt[i][j] < 0)  
   {  
   pt[i][j]=pt[i][j]+26;  
   }  
   tpt[i][j]=pt[i][j];  
  }  
  }  
  printf("\n plain text is:");  
  psum=0;  
  for(i=0;i<2;i++)  
  {  
  for(j=0;j<2;j++)  
  {  
   fpt[psum]=(tpt[i][j]%26)+97;  
   printf("%c \t",fpt[psum]);  
   psum++;  
  }  
  }  
 }  
 else  
 printf("\n Invers not possible!!!...try with diff value of key..");  
 n=n+3;  
 printf("\n");  
 }

All process same as encryption.like do 4-4 partition.

then find determinate of array and check it is 0 or not.Whenever det=0 then decryption is not possible because inverse is infinite.

then find inverse.here use simple if statements for better understand.
Matrix multiplication with cipher text's numeric value and inverse of key.

pt[i][j]=psum;  
   while(pt[i][j] < 0)  
   {  
   pt[i][j]=pt[i][j]+26;  
   }  
   tpt[i][j]=pt[i][j];  //also present in above image

In this for loop store value of multiplication,but our value is also in negative therefore add value 26 till positive value not occur and store in temporary integer array 'tpt' .
why use while loop?
This while loop is for only negative value of pt because in next step we have to mod with 26.
We know that mod of negative is add value of 26 whenever positive value is not occur.

like -10 mod 256 is equal to -10+256=246.It is value of negative mod.
-275 mod 250 then -275+250 = - 25.still negative then add one more time -25+250=225.then -275 mod 250=225.

fpt[psum]=(tpt[i][j]%26)+97;  //also present in above image

in this step we store final plain text value.here add 97 into mod value.

Output of Full Program:

Use Download button for Code

Thank You!!

Playfair Cipher program in c

2018-07-24T14:23:00.000-07:00

Introduction to Playfair

The Playfair cipher or Playfair square or Wheatstone-Playfair cipher is a manual symmetric encryption technique(Use same key for encryption of plaintext and decryption of ciphertext) and was the first literal digram substitution cipher. The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair for promoting its use.

This technique encrypts pairs of letters (bigrams or digrams), instead of single letters as in the simple substitution cipher and rather more complex cipher systems then in use.

History of playfair

It was however later used for tactical purposes by British forces in the Second Boer War and in World War I and for the same purpose by the British and Australians during World War II.

This was because Playfair is reasonably fast to use and requires no special equipment - just a pencil and some paper.

A typical scenario for Playfair use was to protect important but non-critical secrets during actual combat e.g. the fact that an artillery barrage of smoke shells would commence within 30 minutes to cover soldiers' advance towards the next objective. By the time enemy cryptanalysts could decode such messages hours later, such information would be useless to them because it was no longer relevant.

Playfair Program in c

Step 1:Variables we use in program:

First of all we see deceleration of variables.
Here basic deceleration which is use full in further code...

 #include<stdio.h>  
 #include<conio.h>  
 #include<time.h>  

 void main()  
 {  
  char key[50]={'\0'};  
  char o[25]={'a','b','c','d','e','f','g','h','i','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'};  
  char k[25]={'\0'};  
  char m[5][5]={'\0'};  
  char pt[50]={'\0'},tp[50]={'\0'};  
  //variable for time complexity  
  clock_t start,end;  
  double time_used;  
  int i=0,j=0,flag=0,a=0,len=0;  
  clrscr();

Explain variable:
here use time.h for calculate time complexity of code.
key : char. array it is use for enter cipher key for encryption.
o : this is temp. array for add alpha bates
k : use for Add matrix's value in 1D(one dimension) array.
m :It is our 5x5 matrix.
pt and tp:pt is use for Plain Text and tp is temporary array.

Not understand variable don't panic...

Step 2:Enter key into 1D array:

In key we use only unique character so first of all remove space from key.In matrix which is 5x5 means 25 character store but we have 26 character therefore use i=j that mean whenever j come in key it will replace by i.you will see in below code

  start=clock();  
  printf("\n\t\t||||||||||   PLAYFAIR CIPHER   ||||||||||\n");  
  printf("\n\n");  
  printf("\nEnter key:");  
  gets(key);  
  for(i=0;i<strlen(key);i++)  
  {  
  if(key[i]=='j')  
  {  
   key[i]='i';  
  }  
  for(j=0;j<strlen(k);j++)  
  {  
   if(k[j]==key[i])  
   {  
   flag=1;  
   break;  
   }  
  }  
  if(flag != 1)  
  {  
   k[a]=key[i];  
   a++;  
  }  
  flag=0;  
  }  //remove same char from key and add into k

In above code start clock for time.using gets() retrieve value of key.First for loop is go for length of key in this check 'j' is present in key whenever find 'j' replace with 'i'.
In second for loop check character in 1D array k[25] because unique value is require.Here use of 'flag' , when flag=1 then skip character because it is present already in array k[25] .if flag !=1 then add this character and change flag=0.

E.g :"computer" is our key here duplicate not present therefore in k enter 'computer'

Step 3:Enter extra character into 1D array:

First enter key value then we also add remaining character in array.

 for(i=0;i<=strlen(o);i++)  
  {  
  for(j=0;j<strlen(k);j++)  
  {  
   if(k[j]==o[i])  
   {  
   flag=1;  
   break;  
   }  
  }  
  if(flag != 1)  
  {  
   k[a]=o[i];  
   a++;  
  }  
  flag=0;  
  }  //add extra character

using Two for loop, one for length of alpha bates and second for 1D array.simply check character is present in k[25] or not.Not present then add character when present then skip.

E.g : our key is already enter in k[25] which is "computer" then remaining character "a b c d f g h i k l n q s v w x y z" is enter in key here 'i/j' enter in one place.

Step 4:One Dimension array to Two Dimension:

 a=0;  
  printf("Matrix of 5x5 is:\n");  
  for(i=0;i<5;i++)  
  {  
  for(j=0;j<5;j++)  
  {  
   m[i][j]=k[a];  
   if(m[i][j]=='i')  
   {  
   printf("\t i/j");  
   }else  
   {  
   printf("\t %c",m[i][j]);  
   }  
   a++;  
  }  
  printf("\n");  
  }

Here 'a' is use for index of 1D array.using this for loop we store 1D array value into 2D array and also print that value.

Below picture of output for step 1 to 4.

In above output we see that character of key enter first then sequence wise entered in non repeated form.

Step 5: Enter plain text and remove space

  printf("\n");  
  printf("\n Enter PlainText:");  
  gets(pt);  
  a=0;  
  for(i=0;i<strlen(pt);i++)  
  {  
  if(pt[i]!=' ')  
  {  
   tp[a]=pt[i];  
   a++;  
  }  
  } //remove space

Here when space is occur then skip it.And store new string in temporary variable 'tp'.

Step 6:Divide into pair of two

Playfair is work on pair of character.Here divide into two pair and check pair characters are same when character are same then add x after first character. Understand ?? No It's Ok...

E.g: Our Plan Text is "information"

First divide into two of pair "in fo rm at io n" but we need two pair here 'n' is alone therefore we enter 'x' after 'n' so new plaintext is "in fo rm at io nx".

second example: our plain text is "hello" then

"he ll o" is divide in pair but 'll' is same character in pair therefore add 'x' after 'l'.then new plaintext pair is "he lx lo".

 len=strlen(tp);  
  a=0;  
  for(i=0;i<len;i++)  
  {  
  if(tp[i]==tp[i+1])  
  {  
   pt[a]=tp[i];  
   pt[a+1]='x';  //add x when two same character 
   a=a+2;  
  }else  
  {  
   pt[a]=tp[i];  
   pt[a+1]=tp[i+1];  
   i=i+1;  
   a=a+2;  
  }  
  }  
  if(strlen(pt)%2 !=0)  
  {  
  pt[a-1]='x';  
  }  // add x when last character is alone
  printf("\n New PlainText:");  
  puts(pt);

Step 7:Call Playfair function:

First add function above main function:

 void playfair(char [50],char [5][5]);

then write below code in main:

 playfair(pt,m);  
  end=clock();  
  time_used=((double)(end-start))/CLOCKS_PER_SEC;  
  printf("\n time taken=%f sec",time_used);  
  getch();  
 }

In function we send plain text which is 'pt' and 2D array 'm'.

Step 8:Playfair Function:

 void playfair(char pt[50],char m[5][5])  
 {  
  int i=0,j=0,k=0,a=0;  
  char cy[50]={'\0'};  
  int x1=0,y1=0,x2=0,y2=0;

First of all see variable that is use in this function
cy: it is character array for ciphertext.

Here Three Rule of cipher text:

Same Column
Same Row
Rectangle

Take one pair and check in 5x5 matrix for this rule.

1) Same Column: When pair characters are in same column then use down character for cipher text.

2) Same Row: When pair in same row then use next character for cipher text.

3) Rectangle: When pair make rectangle then use corner of character match in matrix.

code for this rule:

 for(k=0;k<strlen(pt);k++)  
  {  
   for(i=0;i<5;i++)  
   {  
   for(j=0;j<5;j++)  
   {  
    if(m[i][j]==pt[k])  
    {  
      x1=i;  
      y1=j;  
    }  
    if(m[i][j]==pt[k+1])  
    {  
     x2=i;  
     y2=j;  
    }  
   }  
   }  
       if(y1==y2) //.............same column rule:1  
       {  
            x1++;  
            x2++;  
           if(x1>4)  
           {  
                x1=0;  
           }  
           if(x2>4)  
           {  
                 x2=0;  
           }  
            cy[a]=m[x1][y1];  
            a++;  
            cy[a]=m[x2][y2];  
            a++;  
       }     //.............rule:1 done  
      else if(x1==x2) //..............................rule:2 same row  
      {  
            y1++;  
            y2++;  
            if(y1>4)  
            {  
                 y1=0;  
            }  
            if(y2>4)  
            {  
                 y2=0;  
            }  
            cy[a]=m[x1][y1];  
            a++;  
            cy[a]=m[x2][y2];  
            a++;  
      }else if(x1!=x2 && y1!=y2) //..........rule:3  
      {  
       cy[a]=m[x1][y2];  
       a++;  
       cy[a]=m[x2][y1];  
       a++;  
      } //.........................rule:3 done  
   k=k+1;  
  }  
  printf("\n Cipher text is:");  
  puts(cy);

here we have ciphertext: "in fo rm at io nx" ==> "gs le gr be fu xm"

Here encryption is done...
But also we have convert ciphertext into plaintext at receiving side therefore use Decryption.

"Decryption is inverse process of encryption"

Step 9: Decryption

 a=0;  
  for(k=0;k<strlen(cy);k++)  
  {  
      for(i=0;i<5;i++)  
      {  
           for(j=0;j<5;j++)  
           {  
            if(m[i][j]==cy[k])  
            {  
             x1=i;  
             y1=j;  
            }  
            if(m[i][j]==cy[k+1])  
            {  
             x2=i;  
             y2=j;  
            }  
           }  
      }  
      if(y1==y2) //.........rule:1  
      {  
           if(x1==0)  
           {  
            x1=4;  
           }else  
           {  
            x1--;  
           }  
           if(x2==0)  
           {  
            x2=4;  
           }else  
           {  
            x2--;  
           }  
           pt[a]=m[x1][y1];  
           a++;  
           pt[a]=m[x2][y2];  
           a++;  
      }else if(x1==x2) //..........rule:2  
      {  
           if(y1==0)  
           {  
            y1=4;  
           }else  
           {  
            y1--;  
           }  
           if(y2==0)  
           {  
            y2=4;  
           }else  
           {  
            y2--;  
           }  
           pt[a]=m[x1][y1];  
           a++;  
           pt[a]=m[x2][y2];  
           a++;  
      }else if(x1!=x2 && y1!=y2)  //............rule:3  
      {  
       pt[a]=m[x1][y2];  
       a++;  
       pt[a]=m[x2][y1];  
       a++;  
      }  
      k=k+1;  
  }  
  printf("\n Plain Text:");  
  puts(pt);  
 }

Using cipher text 'cy' and inverse of encryption we can generate plaintext.

Here Main Output of code :

Below You Can download code in .txt file:

Thank you!!