CaesarCipher

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Caesar Cipher

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# Caesar Cipher

## History and usage

The Caesar Cipher was named after Julius Caesar (100 B.C. – 44 B.C.), who used it for secret military communication. The Caesar Cipher is a substitution cipher. Julius Caesar originally used a shift of three to encrypt and decrypt messages. The encryption is performed using an affine function: f(x)=x+b.

## Detailed Explanation : How it works?

1. Firstly, each character of the initial text (message to encrypt) is converted in a number from 0 to 25, corresponding to its position in the Latin alphabet which contains 26 letters --> (a = 0, b = 1 ... z = 25 ).

2. Then, each number obtained is transformed by an affine function (f(x) = 1x + b). "x" is representing the number while "b" is defined during the encryption. "b" is the key used to decrypt the final message.

3. If we take all the images and put them in a list, we obtain n numbers corresponding to n characters of the initial text. The next step consists in finding the values of modulo 26 of each number. (**Modulo means remainder**)

> Example : Modulo 4 of 19 is **3** because `19 = 4 * 4 + 3` In the other hand, modulo 26 of 26 is **0** because `26 = 26 * 1 + 0`

1. Therefore, we obtain a new list with n element, each between 0 and 25 both included. All these numbers are converted in letters of the Latin Alphabet using the tables below.

2. We finally create the final message by putting all the letters side by side.

Steps 1 and 4 can be done with these tables :

**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     | 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

## Weaknesses

- If an attacker knows that the message has been encrypted using Caesar Cipher, he can try all shifts (b values from 1 to 25) to decrypt the message. This is called the **bruteforce method**.

- We can also use **frequency analysis** to decrypt the message as each letter is encrypted with the same algorithm and the most common letters in english are :

![](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/English_letter_frequency_%28alphabetic%29.svg/340px-English_letter_frequency_%28alphabetic%29.svg.png)

## Example

### Encrypting

- Message to encrypt : **ZATTACKZ**
- Shift used : 4 (f(x) = 1x + 4)
- That means that **b = 4**

Using the above tables, **ATTACK** can be written as : **25 0 19 19 0 2 10 25** Images of each number :

- f(25) = 29
- f(0) = 4
- f(19) = 23
- f(2) = 6
- f(10) = 14

The new list is : **29 4 23 23 4 6 14 29**

Using the **modulo 26 method**, we obtain:

- Mod(29,26) = 3
- Mod(4,26) = 4
- Mod(23,26) = 23
- Mod(6,26) = 6
- Mod(14,26) = 14

The final message is **3 4 23 23 4 6 14 3** and using the tables again, we convert them in the encrypted message :

> **DEXXEGOD**

**ZATTACKZ** is encrypted with the function **x + 4** and becomes **DEXXEGOD**.

### Decrypting

#### First method : Knowing the key (value of the shift used)

- Message to decrypt : **DEXXEGOD**
- Shift used : 4 (f(x) = 1x - 4)
- That means that **b = -4**

Using the above tables, **DEXXEGOD** can be written as : **3 4 23 23 4 6 14 3** Images of each number :

- f(3) = -1
- f(4) = 0
- f(23) = 19
- f(6) = 2
- f(14) = 10

The new list is : **-1 0 19 19 0 2 10 -1**

Using the **modulo 26 method**, we obtain :

- Mod(-1,26) = 25
- Mod(0,26) = 0
- Mod(19,26) = 19
- Mod(2,26) = 2
- Mod(10,26) = 10

The final message is **25 0 19 19 0 2 10 25** and using the tables again, we convert them in the encrypted message :

> **ZATTACKZ**

**DEXXEGOD** is decrypted with the function **1x - 4** and becomes **ZATTACKZ**.

#### Second method : Not knowing the key (value of the shift used)

This is called the bruteforce method.

- Message to decrypt : **DEXXEGOD**

Using the above tables, **DEXXEGOD** can be written as : **3 4 23 23 4 6 14 3**

a is a number between 0 and 25\. (a = 0 would mean the message is already decrypted)

Using the function f(x) = Mod(1x + a, 26) :

We can get all these results :

a  | Decrypted text
-- | --------------
1  | fgzzgiqf
2  | ghaahjrg
3  | hibbiksh
4  | ijccjlti
5  | jkddkmuj
6  | kleelnvk
7  | lmffmowl
8  | mnggnpxm
9  | nohhoqyn
10 | opiiprzo
11 | pqjjqsap
12 | qrkkrtbq
13 | rsllsucr
14 | stmmtvds
15 | tunnuwet
16 | uvoovxfu
17 | vwppwygv
18 | wxqqxzhw
19 | xyrryaix
20 | yzsszbjy
21 | zattackz
22 | abuubdla
23 | bcvvcemb
24 | cdwwdfnc
25 | dexxegod

The only text that makes sense is zattackz so we can deduce that the key is 21 (25 - b = 21).

**DEXXEGOD** is decrypted with the function **f(x) = 1x - 4** or **f(x) = 1x + 21** and becomes **ZATTACKZ**.

# Implementations

Language   | Encrypt                             | Decrypt
---------- | ----------------------------------- | ----------------------------
C          | [caesar.c](c/caesar.c)              | _Coming Soon_
C#         | [Caesar.cs](c#/CaesarLib/Caesar.cs) | _Coming Soon_
C++        | [main.cpp](cpp/main.cpp)            | [main.cpp](cpp/main.cpp)
JavaScript | [encrypt.js](js/encrypt.js)         | [decrypt.js](js/decrypt.js)
Python     | [encrypt.py](py/encrypt.py)         | [decrypt.py](py/decrypt.py)
Swift      | [lib.swift](swift/lib.swift)        | [lib.swift](swift/lib.swift)

## Package Managers

### NPM (for JS):

```bash
npm i @cryptoolsorg/caesarcipher
```

## License

This project is licensed under the MIT License - see the [LICENSE.md](LICENSE.md) file for details

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