RSA Encryption Example

RSA Encryption Demo

Classroom RSA Keys

Public Key: 
  e = 7
  n = 187
Private Key: 
  d = 23
  n = 187




RSA Encryption

RSA is famous for its security and uses mathematical operations based on exponents and modular arithmetic.

→ Uses two keys: Public Key to Encrypt and Private Key to Decrypt.

→ RSA begins with two prime numbers. A prime number is a natural number greater than 1 that has only two factors: 1 and itself.

For this classroom example:
p = 11, q = 17, so N = 11 × 17 = 187.
The (public key) which is used as exponent is e = 7 and the (private key) used as exponent is d = 23
We have:
Prime number: p=11
Prime number: q=17
N = p*q = 11*17 = 187

Encrypt

encrypted = messagee mod N

The Public Key is used as the exponent. mod N means take the remainder after dividing by N.

Decrypt

message = encryptedd mod N

The Private Key is used as the exponent. mod N again means take the remainder after dividing by N.

Example: Encrypt "Hello" and Decrypt Cyphertext

Public Key: e = 7
Private Key: d = 23
N = 187
A B C D E F G H K L M N O P R S T U V W X Y Space
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hello = 8   5   10   10   13

Encrypt:

H = (87) mod 187 = 134
E = (57) mod 187 = 146
L = (107) mod 187 = 175
L = (107) mod 187 = 175
O = (137) mod 187 = 106
Hello encrypted: 134 | 146 | 175 | 175 | 106

Decrypt:

Cipher text: 134 | 146 | 175 | 175 | 106

134 = (13423) mod 187 = 8 → H
146 = (14623) mod 187 = 5 → E
175 = (17523) mod 187 = 10 → L
175 = (17523) mod 187 = 10 → L
106 = (10623) mod 187 = 13 → O
Decrypted: Hello