Of course, the government may have a cryptanalytic service we do not know of. The general name for a method of attacking product ciphers is called differential cryptanalysis. Cryptography A cryptosystem of 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.
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 to plaintext. A cryptosystem is usually a whole collection of algorithms.