cryptography:
The art or science encompassing the principles and methods of transforming an intelligible message into one that is unintelligible, and then retransforming that message back to its original form.

plaintext:
The original intelligible message

ciphertext:
The transformed message

cipher:
An algorithm for transforming an intelligible message into one that is unintelligible by transposition and/or substitution methods

key:
Some critical information used by the cipher, known only to the sender and receiver

encipher (encode):

Encryption is the transformation of data into a form unreadable by anyone without a secret decryption key. Its purpose is to ensure privacy by keeping the information hidden from anyone for whom it is not intended, even those who can see the encrypted data. For example, one may wish to encrypt files on a hard disk to prevent an intruder from reading them.

Authentication in a digital setting is a process whereby the receiver of a digital message can be confident of the identity of the sender and/or the integrity of the message. Authentication protocols can be based on either conventional secret-key cryptosystems like DES or on public-key systems like RSA; authentication in public-key systems uses digital signatures.

Traditional cryptography is based on the sender and receiver of a message knowing and using the same secret key: the sender uses the secret key to encrypt the message, and the receiver uses the same secret key to decrypt the message. This method is known as secret-key cryptography. The main problem is getting the sender and receiver to agree on the secret key without anyone else finding out. If they are in separate physical locations, they must trust a courier, or a phone system, or some other transmission system to not disclose the secret key being communicated.

The primary advantage of public-key cryptography is increased security: the private keys do not ever need to be transmitted or revealed to anyone. In a secret-key system, by contrast, there is always a chance that an enemy could discover the secret key while it is being transmitted.