A public-key cryptosystem for both encryption and authentication, invented in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman. Its name comes from their initials.

The RSA algorithm works as follows: take two large prime numbers, p and q, and find their product n = pq; n is called the modulus. Choose a number, e, less than n and relatively prime to (p-1)(q-1), and find its inverse, d, mod (p-1)(q-1), which means that ed = 1 mod (p-1)(q-1); e and d are called the public and private exponents, respectively. The public key is the pair (n,e); the private key is d. The factors p and q must be kept secret, or destroyed. It is difficult (presumably) to obtain the private key d from the public key (n,e). If one could factor n into p and q, however, then one could obtain the private key d. Thus the entire security of RSA depends on the difficulty of factoring; an easy method for factoring products of large prime numbers would break RSA.

RSA FAQ.