# RSA Algorithm Javascript Page

Welcome to the cryptography home (designed by Cary Sullivan and Rummy Makmur.) We have designed a model of RSA public-key cryptosystem. Following a brief background and description, you can ask another person to encrypt a "message"( actually a letter) and let you decrypt it, using your computer-generated private key. Enjoy. If you have any comments, do not hesitate to contact us.

## INTRODUCTION TO RSA

RSA is a public-key cryptosystem developed by MIT professors: Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman in 1977 in an effort to help ensure internet security. As Steve Burnett of RSA Data Security, Inc. described it, a cryptosystem is simply an algorithm that can convert input data into something unrecognizable (encryption), and convert the unrecognizable data back to its original form (decryption).

To encrypt data, enter the data ("plaintext") and an encryption key to the encryption portion of the algorithm. To decrypt the "ciphertext," a proper decryption key is used at the decryption portion of the algorithm. Those keys, which contains simply a string of numbers, are called public key and private key, respectively. For example, suppose Alice intends to send e-mail to Bob. Through a public-key directory, she finds his public key. Then, she encrypts her message using the key and send it to Bob. This public key, however, will not decrypt the ciphertext. Knowledge of Bob's public key will not help an eavesdropper. In order for Bob to decrypt his ciphertext, he must use his private key. If Bob wants to respond to Alice, he encrypts his message using her public key.

The challenge of public-key cryptography is developing a system in which it is impossible to determine the private key. This is accomplished through the use of a one-way function. With a one-way function, it is relatively easy to compute a result given some input values. However, it is extremely difficult, nearly impossible, to determine the original values if you start with the result. In mathematical terms, given x, computing f(x) is easy, but given f(x), computing x is nearly impossible. The one-way function used in RSA is multiplication of prime numbers. It is easy to multiply two big prime numbers, but for most very large primes, it is exremely time-consuming to factor them. Public-key cryptography uses this function by building a cryptosystem which uses two large primes to build the private key and the product of those primes to build the public key.

## The Model

RSA uses modular arithmatic and elementary number theory to do certain computation. Before you start, please make sure you understand how it works. And, also remember, our model is nothing compared to the REAL RSA algorithm which involves two LARGE primes and messages of unconditional length. In our model, VERY small primes are used and only one letter will be encrypted.

Instructions:

• This model is best carried out by two persons. Name them Alice and Bob.
• Alice will pick two available primes. Public and private keys will be generated by computer.
• Record the public key containing the exponent value, E and the product of the primes, N. And, record the private key, D.
• Give E and N to Bob (your partner).
• Bob will go to another page to pick a letter to encrypt. Enter E and N. The encrypted message / number will be generated.
• Bob will send or give the encrypted message to Alice.
• Alice will go to decryption page. Enter the message, D and N. The message will be decrypted to the original letter. Later, Alice can check with Bob to see if it is the right letter.

Remember, the main purpose of this model is understanding the RSA algorithm, not necessarily for encryption purpose. A lot of simplification has been made, while the mathematics and algorithm stay the same. So, ENJOY !

Now, proceed to: key generation page, encryption page, or decryption page.