Public Key Cryptography using RSA algorithm

by: Syed Umar Anis

Purpose of the page is to demonstrate how RSA algorithm works - generates keys, encrypts message and decrypts it.

Step # 1: Generate Private and Public keys

Enter two prime numbers below (P, Q), then press calculate:

P:   Q:      Some prime numbers: 11, 13, 17, 19, 23, 29, 191, 193, 197, 199, etc.


Variable Value Name Formula Description
N modulus N: P * Q Product of 2 prime numbers
L length L: (p - 1) * (q - 1) Another way of calculating 'L' is to list of numbers from 1 to N, remove numbers which have common factor which N and count the remaining numbers.
E encryption key Find a number between 1 and L that is coprime with L and N.
D decryption key D * E mod L = 1 Remainder of the product of D and E when divided by L should be 1 (D * E % L = 1)

Private Key (E, N):
Public Key (D, N):

Step # 2: Encrypt a message

Enter a message to encrypt:


Message converted to ASCII code:

Encrypted message: message^E % N      (PowerMod can be used to calculate this very fast. Formula is applied on ASCII code of each character.)

Encrypted Message:

Step # 3: Decrypt a message

Enter a encrypted message (cipher):


Message decrypted to ASCII code:

Decrypted Message: encrypted_message^D % N      (PowerMod can be used to calculate this very fast. Formula is applied on ASCII code of each character.)

Decrypted Message: