In this Demonstration, the RSA algorithm is simulated using much smaller randomly chosen prime numbers, and both less than 100. The public key, which is made freely available to Alice and all other users, consists of the two numbers and an exponent , which is an odd integer relatively prime to between 1 and . (Here is Euler's totient function, the number of positive integers less than and relatively prime to .) For simplicity, take and also limit messages to three letters, such as XYZ. This constitutes the plaintext and is converted into an integer using, for example, ASCII codes. The corresponding ciphertext is computed using .

Only the recipient Bob has access to the private key, which is an integer exponent , a modular inverse to such that . To determine , a codebreaker would need to find the prime factors of , which, as noted earlier, is hopefully impossible. The plaintext is recovered using . The method works since (mod ), with application of Fermat's little theorem. The public and private keys can periodically be changed according to some prearranged schedule.

By inputting the public key and the three-part ciphertext , Bob can recover the plaintext message.