### An algorithm to solve the Caesar Cipher problem.

**Caesar Cipher**: An earlier encryption technique which used to substitute the current alphabets with alphabet after a number of count.

#### Example

Input: text = ABCD , Key = 13 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 13 shift to A is N 13 shift to B is O 13 shift to C is P 13 shift to D is Q Output: NOPQ

We will implement a simple algorithm with different approaches to implement Caesar cipher. Everything will be written in ES6.

## First Approach

#### Implementation

- We will create an object with decoded letter for every alphabet.
- Then we will loop through the string and creat the deciphered string with the corresponding decoded letters.

let ceaserCipher = (str) => { //Deciphered reference letters let decoded = { a: 'n', b: 'o', c: 'p', d: 'q', e: 'r', f: 's', g: 't', h: 'u', i: 'v', j: 'w', k: 'x', l: 'y', m: 'z', n: 'a', o: 'b', p: 'c', q: 'd', r: 'e', s: 'f', t: 'g', u: 'h', v: 'i', w: 'j', x: 'k', y: 'l', z: 'm' } //convert the string to lowercase str = str.toLowerCase(); //decipher the code let decipher = ''; for(let i = 0 ; i < str.length; i++){ decipher += decoded[str[i]]; } //return the output return decipher; }

Input: console.log(ceaserCipher('attackatonce')); console.log(ceaserCipher('prashantyadav')); Output: "nggnpxngbapr" "cenfunaglnqni"

Time complexity: O(n).

Space complexity: O(1).

#### Time and Space complexity

- We are just deciphering each letter of the string, so Time complexity is O(n).
- We are using constant space, so Space complexity O(1).

This approach is good but there are few problems with this method.

1). The cipher is fixed for 13 letter substitution.

2). Also, we are just doing it for lowercase letters.

## Second Approach

#### Implementation

- We will solve the above problem with different keys or dynamic keys and mathematical calculation.
- We will use string inbuilt methods and regular expressions.

let caesarCipher => (str, key) { return str.toUpperCase().replace(/[A-Z]/g, c => String.fromCharCode((c.charCodeAt(0)-65 + key ) % 26 + 65)); }

Input: console.log(ceaserCipher('ATTACKATONCE', 13)); console.log(ceaserCipher('PRASHANTYADAV', 13)); Output: "NGGNPXNGBAPR" "CENFUNAGLNQNI"

Time complexity: O(n).

Space complexity: O(1).

#### Time and Space complexity

- We are just deciphering each letter of the string, so Time complexity is O(n).
- We are using constant space, so Space complexity O(1).

This approach is also good but there is still one problem with this method. It is still not handling case sensitive strings.

## Handling Case Sensitive

#### Implementation

- We will loop through each letter of the string and check if its uppercase or lowercase.
- Then we will decipher it accordingly using mathematical computation.

//check if letter is uppercase function isUpperCase(str) { return str === str.toUpperCase(); } //decipher the string let ceaserCipher = (str, key) => { let decipher = ''; //decipher each letter for(let i = 0; i < str.length; i++){ //if letter is uppercase then add uppercase letters if(isUpperCase(str[i])){ decipher += String.fromCharCode((str.charCodeAt(i) + key - 65) % 26 + 65); }else{ //else add lowercase letters decipher += String.fromCharCode((str.charCodeAt(i) + key - 97) % 26 + 97); } } return decipher; }

Input: console.log(ceaserCipher('ATTACKATONCE', 13)); console.log(ceaserCipher('prashantyadav', 13)); Output: "NGGNPXNGBAPR" "cenfunaglnqni"

Time complexity: O(n).

Space complexity: O(1).

#### Time and Space complexity

- We are just deciphering each letter of the string with mathematical computation, so Time complexity is O(n).
- We are using constant space, so Space complexity O(1).

Learn more about the String.fromCharCode() and charCodeAt().

Gorreri Franco says:

Hi! Great post!

I have a question in the second approach. Why you have to subtract 65 before adding the key and then doing the mod 26 and finally adding 65?

String.fromCharCode((c.charCodeAt(0)-65 + key ) % 26 + 65)

Why can’t i just do?

String.fromCharCode(c.charCodeAt(0) + key)

chars says:

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Prashant Yadav says:

I designed it myself

Bill says:

Hi,

This is great! Thanks for posting, I found it very useful.

What would you do to handle negative key values?

Prashant Yadav says:

We are deciphering alphabets not numbers so there are no negative numbers i guess.