Methods of deliberately distorting a message so that the legitimate receiver can recover it easily while being nearly impossible for an eavesdropper to do the same.
In symmetric encryption, a personal encryption key cipher known only to the sender and its intended receiver is used to control the encryption of the data. Manual encryption has been used since Roman times (such as Caesar cipher, used by Julius Caesar in his private correspondence). Mechanical systems improved on this, and were used during the world wars. With digital hardware, the most commonly used algorithm is Data Encryption Standard (DES), now phased out for Advanced Encryption Standard (AES).
These schemes allow for cryptographic communications among people who have made prior preparation for cryptographic security. However, it is unviable for large telecommunications systems, where users would have to wait for a key to be sent over secure, physical means.
Asymmetric encryption, or public-key cryptography, requires a pair of keys: one for encryption and one for decryption. Public-key cryptography is a modern breakthrough designed by Whitfield Diffie and Martin Hellman, two academics who disrupted the government monopoly on encryption. It uses trapdoor one-way functions so that encryption may be done by anyone with access to the "public key" but decryption may be done only by the holder of the "private key." A public key may be freely published in directories, while the corresponding private key is closely guarded.
The RSA algorithm (developed by Rivest, Shamir, and Adleman) is the most widely used form of public key encryption. Pretty Good Privacy (PGP) was written by Phillip Zimmerman as an open implementation of RSA which empowered people to take their privacy into their own hands. As EFF co-founder John Perry Barlow put it: "You can have my encryption algorithm... when you pry my cold dead fingers from my private key."
For performance reasons, a popular scheme is to use RSA to transmit session keys and then a high-speed cipher like DES for the actual message text. Public-key cryptography enabled private communication and financial transactions over the internet.
Elliptic Curve Cryptography (ECC) is a modern system and very efficient in computational time and space. It is slated to replace RSA. Based on the trap-door properties of points on elliptic curves. Unlike prime factoring, there doesn’t appear to be any mathematical shortcuts. As such, its security is exponentially stronger than RSA.