An attempt on Hill Cipher.

An attempt on Hill Cipher.

It has been a possible attempt to write on Hill Cipher Step by step in order to not only makes it a child’s play but also strive to makes it more and more understandable.

Why it is Hill Cipher?

It is Hill Cipher because the mathematician Laster Hill developed at in 1929.

Points should be kept in mind!

Ø  It is a classical cipher, as if Caesar cipher, Play fair cipher and so on.

Ø  It is a symmetric cipher, which means key is shared between both parties- sender and receiver-.

Ø  It is a substitution and matrix based cipher, means with the help of using mathematics matrix operation the position of letters are be changed.

Let’s play the game now.

Step 1: first of all select a key. But, select the key in matrix, as I selected:

[2 3]

[3 4] Note: This key will be shared BTW both parties.

Step 2:

Just select a plain text which you want to encrypt. As I selected “RACEY”.

Step 3:

Break the message into pairs of letter which means create the pair of letters. Start pairing from left to right.

As I do so.

RA	CE	Y
1st pair	2nd pair	What about Y?

 How long your message will be, you should break and pair it.

Considerable: But Y is a single letter how a single letter can create a pair?

Step 4:

It’s very interesting as we know that the hill cipher needs to break the message and create pairs. But, if, the message is break and created pairs where still a letter remains for pairing, which have no other extra letter to fulfill the pair demand. In such case we use the concept of Pillar Letter

Step 4: what is pillar letter?

The pillar is a helper which helps the other letter to fulfil the requirements of pairing. In our case the pillar letter will help” Y” to create its pair. You can select any letter which is used as a pillar but the second party must be informed which is your pillar letter. Mostly, “X” is used as pillar letter. I am also using X is pillar letter. Now the pairs will be.

This is the sequence of pairing the letters.

RA	CE	YX
1st pair	2nd pair	3rd pair

 Step 5:

Now put the letters into their position. Mostly, the letters position started from 0 and end 25 like array.

As I put them like.

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
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

Step 6:

Start putting the letters:

1^st pair: R {17} A {0} second pair: C {2} E {4} third pair: Y {24} X {22}.

Step 7:

Now apply the Matrix operation with the help of key on each pair.

As I did so.

1^st pair:

  [2 3] [17] Mode 26

 [3 4] [0]                                         

 Perform the matric like this: multiply the row of First table with the column of second table. AS,

(2*17) + (3*0) =34+0=34

(3*17)+ (4*0) =51+0=51

 As you know we are using 26 mode because of total letters are 26.

Use the mode 26 and get the output.

[34] Mode 26 =8

[51] =====     =25

 What come after the mode find the position of that letter. Which will be your cipher letter. As I did for 1^st which is on 8^th and second is on 25^th.

 8[I] and 25[Z]. It Will be first pair output.

Your first Pair cipher: 8[I] and 25[Z] =IZ

Note: Don’t worry if you don’t know how to perform the mode operation. Just wait or see below. In last step.

Second pair:

Second pair: C {2} E {4}

  [2 3] [2] Mode 26 = [16]

 [3 4] [4] ------------ = [22]

(2*2) + (3*4) =4+12=16

(3*2) + (4*4) =6+16=22

The output of second pair will be: 16[Q] and 22[W]. Or QW.

 3^rd pair:

Third pair is: Y {24} X {22}.

  [2 3] [24] Mode 26 = [114] = [10]

 [3 4] [22] ------------ = [162] = [6]

(2*24) + (3*22) =48+66=114

(3*22) + (4*24) =66+96=162

Output will be: [10] =K and [6] =G.

Finally, we have encrypted our message. Pair by pair and step by step. Which is.

Plain text is “RACEY”.

Cipher text is: “IZQWKG”.

Last:

How to perform Mode operation?

 Keep in mind we have length of 26 letters, 0-25. If we multiply the Matrix key with the letter’s position which can exceed the length of 26. Therefore, we need to put a limit through which we will be able to not let the letters to cross the length of 26.

But how really this mode magical operation work?

It is really too simple, just get the product of multiplied letters with key. And divide them with 26. Get the reminder, the reminder will be your cipher letter position as I did with first pair:

Output of multiplied “R”, (2*17) + (3*0) =34+0=34

Now I divided 34/26.

34 will be divided by 26 only one time.

Reminder will be 8 (try and confirm it). Take the 8 [I] in place of 17[R].

But what if the multiplied product is less than 26?

No matter, get relaxed. If, it is not greater than 26, then simply put the same number of letter in place of plain text. As I did in 2^nd pair. Where both 16 and 22 are not greater than 26. Simply put both of them as: 16[Q] and 22[W] in place of C [2] E [4].

Got? If still have confusion, don’t hesitate just put your question and get the possible Anwser.