# Shift cipher

## Modular Math and the Shift Cipher

The Caesar Cipher is a type of

**shift cipher**. Shift Ciphers work by using the modulo operator to encrypt and decrypt messages. The Shift Cipher has a**key K**, which is an**integer from 0 to 25**. We will only share this key with people that we want to see our message.## How to Encrypt:

For every letter in the message

**M**:**1.**Convert the letter into the number that matches its order in the alphabet starting from 0, and call this number

**X**.

( A=0, B=1, C=2, ...,Y=24, Z=25)

**2.**Calculate:

**Y**=

**(X + K)**mod

**26**

**3.**Convert the number

**Y**into a letter that matches its order in the alphabet starting from 0.

(A=0, B=1, C=2, ...,Y=24, Z=25)

**For Example:**We agree with our friend to use the Shift Cipher with

**key K=19**for our message.

We encrypt the message

**"KHAN",**as follows:

So, after applying the Shift Cipher with key K=19 our message text "

**KHAN**" gave us**cipher text**"**DATG**".We give the message "DATG" to our friend.

## How to decrypt:

For every letter in the cipher text

**C**:1. Convert the letter into the number that matches its order in the alphabet starting from 0, and call this number Y.

(A=0, B=1, C=2, ..., Y=24, Z=25)

(A=0, B=1, C=2, ..., Y=24, Z=25)

2. Calculate:

**X= (Y - K)**mod**26**3. Convert the number

(A=0, B=1, C=2, ..., Y=24, Z=25)

**X**into a letter that matches its order in the alphabet starting from 0.(A=0, B=1, C=2, ..., Y=24, Z=25)

Our friend now decodes the message using our agreed upon

**key K=19.**As follows:So, after decrypting the Shift Cipher with key K=19 our friend deciphers the cipher text "

**DATG**" into the message text "**KHAN**".## Why is the Shift Cipher insecure?

A cipher should prevent an attacker, who has a copy of the cipher text but does not know the key, from discovering the contents of the message. Since

**we only have 26 choices for the key**, someone can easily__try all of the 26 keys__, one by one, until they recover the message. This type of attack is called a**brute force attack**.