Cryptography, the encoding of messages to render them unreadable by anyone other than their intended recipient(s), is centuries old. The "Caesar Cipher" is so named because it was used by Julius Caesar. With the advent of modern computer technology, many of these older ciphers became trivially crackable using brute-force attacks. Modern cryptography, essential to the security of computer networks, is done with complex algorithms implemented on high speed computer systems. Generally speaking, computer cryptographic tasks can be broken into two general categories: encryption and authentication.
Encryption refers to the scrambling of information so that the original message can not be determined by unauthorized recipients. An encryption algorithm is applied to the message, referred to as the plaintext, and a key to produce ciphertext, which ideally appears to be random bits. A decryption algorithm converts the ciphertext back into plaintext, but only if given the correct key. Conventional, or symmetric, algorithms use the same key for both encryption and decryption. Public key algorithms use paired keys, one for encryption and another for decryption.
Authentication is the verification of a message's sender. Authentication requires protecting a message so it can not be altered, usually by attaching to it a digital signature. Typically, the signature is formed by computing a hash of the message, which is encrypted using a public key cryptosystem, insuring that nobody without the proper key can generate a valid signature. Note that authentication is different from encryption, since the actual message may be completely unencrypted, and cryptography used only to validate the identify of the creator.
Often, much attention is given to the algorithm, and little paid to the key. In fact, just as with login passwords, cryptographic systems are only as secure as their keys, making key management a critical and oft neglected concern. Certificates have emerged as a clever way of managing large scale key distribution.
RSA Laboratory's Cryptography FAQ is an excellent reference source on cryptography.
It's become clear in recent years that strong cryptographic protection is essential to any computer security system. Whether it be protecting login passwords from packet sniffers, defeating trojan horse attacks, or ensuring that a user's files are unreadable even if a hard drive is stolen, cryptography is a critical component in a secure computer architecture. Many of the widely publicized breakins and attacks could have been prevented if stronger cryptographic controls were in place.
For example, Jon Boone's proposal for Integrity Checked Linux would augment the Linux kernel to require every privileged program to pass a cryptographic check before it would be allowed to execute. Since the check would be made using a public key system, and the private key used to sign the programs could be stored off-line, this would immediately defeat any attempt by a hacker to modify system binaries. A similar idea is used by Tripwire, though without kernel support it is both more portable and more vulnerable.
There's been a serious stumbling block in the way of these efforts, though. Adding cryptography to the Linux kernel (or any other piece of software) would make it export-controlled, and that's not a step Linus Torvalds has been willing to take. In fact, the U.S. Federal Government's insistence on restricting the distribution of cryptographic software has probably been one of the biggest barriers to improved computer security.
In recent years, there have been signs of improvement. The U.S. government has relaxed its regulations on exporting cryptographic software. Some cryptographic support has been added to the Linux kernel by the FreeS/WAN project. However, other countries, such as France, continue to impose controls on the use and distribution of strong crypto. I'd be nice to get at least one message across on this point:
Weak cryptography means weak security!