What is cryptology? Cryptography? Plaintext? Ciphertext? Encryption? Key?

  The story begins: When Julius Caesar sent messages to his trusted
  acquaintances, he didn't trust the messengers. So he replaced every A
  by a D, every B by a E, and so on through the alphabet. Only someone
  who knew the ``shift by 3'' rule could decipher his messages.

  A cryptosystem or cipher system is a method of disguising messages so
  that only certain people can see through the disguise. Cryptography is
  the art of creating and using cryptosystems. Cryptanalysis is the art
  of breaking cryptosystems---seeing through the disguise even when
  you're not supposed to be able to. Cryptology is the study of both
  cryptography and cryptanalysis.

  The original message is called a plaintext. The disguised message is
  called a ciphertext. Encryption means any procedure to convert
  plaintext into ciphertext. Decryption means any procedure to convert
  ciphertext into plaintext.

  A key is usually a number which is used to easily encrypt or decrypt 
  a message.

What is public-key cryptography?

  In a classic cryptosystem, we have encryption we have two functions
  E and F, where E encrypts a message, and F decrypts an encrypted
  message.  A user has two keys, a private key, K which only the user knows,
  and a public key X, which is computed from K, and which the user makes
  available to the public.  Anyone wishing to send the user an encrypted
  message encrypts the message using the public key X.  So once X is
  published, anyone can encrypt messages.  Once encrypted, however, the
  message is very difficult to decrypt without knowledge of the private key
  K.  With knowledge of the private key K, however, the message can be 
  easily decrypted, however.  If decryption D_K cannot be easily 
  computed from public key X without knowledge of private key K, but 
  readily with knowledge of K, then only the person who generated K can 
  decrypt messages. That's the essence of public-key cryptography, 
  introduced by Diffie and Hellman in 1976. 
  
How does public-key cryptography solve cryptography's Catch-22?

  In a classic cryptosystem, knowledge of the private key is required both to
  encrypt and decrypt a message.  If you want your friends to be able to
  send secret messages to you, you need to give your friends the public key K,
  so that they can encrypt the message, and you have to make sure 
  nobody other than them sees the private key K, since K is also used to
  decrypt the message. The problem with classic cryptosystems, then, is how
  to communicate the private key K to your friends.
  
  In a public-key cryptosystem, however, you just publish 
  a public key X, and you don't have to worry about spies. Hence public key 
  cryptography `solves' one of the most vexing problems of all prior 
  cryptography: the necessity of establishing a secure channel for the 
  exchange of the key. To establish a secure channel one uses 
  cryptography, but private key cryptography requires a secure channel! 
  In resolving the dilemma, public key cryptography has been considered 
  by many to be a `revolutionary technology,' representing a 
  breakthrough that makes routine communication encryption practical 
  and potentially ubiquitous.


What is the National Security Agency (NSA)?

  The NSA is the official communications security body of the U.S.
  government. It was given its charter by President Truman in the early
  50's, and has continued research in cryptology till the present. The 
  NSA is known to be the largest employer of mathematicians in the world,
  and is also the largest purchaser of computer hardware in the
  world. Governments in general have always been prime employers of
  cryptologists. The NSA probably possesses cryptographic expertise many
  years ahead of the public state of the art, and can undoubtedly break
  many of the systems used in practice; but for reasons of national
  security almost all information about the NSA is classified.

  Bamford's book [BAMFD] gives a history of the people and operations of
  the NSA. The following quote from Massey [MAS88] highlights the
  difference between public and private research in cryptography:

  ``... if one regards cryptology as the prerogative of government,
  one accepts that most cryptologic research will be conducted
  behind closed doors. Without doubt, the number of workers engaged
  today in such secret research in cryptology far exceeds that of
  those engaged in open research in cryptology. For only about 10
  years has there in fact been widespread open research in
  cryptology. There have been, and will continue to be, conflicts
  between these two research communities. Open research is common
  quest for knowledge that depends for its vitality on the open
  exchange of ideas via conference presentations and publications in
  scholarly journals. But can a government agency, charged with
  responsibilities of breaking the ciphers of other nations,
  countenance the publication of a cipher that it cannot break? Can
  a researcher in good conscience publish such a cipher that might
  undermine the effectiveness of his own government's code-breakers?
  One might argue that publication of a provably-secure cipher would
  force all governments to behave like Stimson's `gentlemen', but one
  must be aware that open research in cryptography is fraught with
  political and ethical considerations of a severity than in most
  scientific fields. The wonder is not that some conflicts have
  occurred between government agencies and open researchers in
  cryptology, but rather that these conflicts (at least those of which
  we are aware) have been so few and so mild.''