For centuries the cryptographic process applied a single and same key for encryption and decryption. Only a few decades ago did Rivest, Shamir, and Adelman (RSA) ask: Why So?.
It was easy to define a crypto system where the encryption key, K_{e}is different from the decryption key K_{d}. See illustration below.
But this had little consequence as long as one could deduce one from the other. The genius behind the RSA innovation was to find a pair of encryption and decryption keys that are not mutually deducible in an easy way. This simple added attribute enables a wealth of practical cryptographic services: confidentiality between strangers, message authentication, writer authentication, contract signing, etc.
RSA is quite slow. The computational burden is of the order of O(k^{3}), where k is the size of the key.

