RSA Public Key Encryption Algorithm

This section describes the RSA public key encryption algorithm. Generating public and private keys used in RSA encryption requires two large prime numbers.

RSA public key encryption algorithm was invented in 1976 by three MIT mathematicians, Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman. The name of the algorithm "RSA" represents the initials of their surnames.

The first part of the RSA algorithm is the public key and private key generation, which can be described as:

• Choose two distinct prime numbers p and q. For security purposes, the integers p and q should be chosen at random, and should be of similar bit-length of 1024 bits or higher
• Compute n = p*q. n is used as the modulus for both public and private keys. Its length, usually expressed in bits, is the key length.
• Compute m = (p-1)*(q-1). m is actually the Euler's totient function value of n.
• Choose an integer e such that 1 < e < n and greatest common divisor gcd(e, m) = 1; i.e., e and m are coprime numbers.
• Compute d such that d*e mod m = 1. d is also called the modular multiplicative inverse of e with modulo m.
• Package the public key as {n,e}.
• Package the private key as {n,d}.

The second part of the RSA algorithm is the message encryption and decryption, which can be described as:

To encrypt a message, the sender can follow these steps:

• Divide the original message into blocks so that each block can be converted to a number, M < n.
• Compute the encrypted block with the public key as C = M**e mod n.
• Deliver encrypted blocks as the encrypted message to the owner of the private key.

To decrypt a message, the owner of the private key can follow these steps:

• Divide the encrypted message back into blocks of the same block size used in the encryption process.
• Decrypt the block with the private key as M = C**d mod n.
• Put decrypted block together to get the original message.