Cryptography tries to solve a common problem. The problem of secure communication using a unsecured transport. In this series we will use three Persons in our examples. Jack wants to communicate with Jones without Jane being able to read.
The definition of a Cryptosystem is (P,C,K,E,D): P is a finite set of plan text C is a finite set of cipher text K is a finite set of keys E stands for the encryption rule D stands for the decryption rule
$encrypted = encrypt("the #care is awesome","mysecretkey"); echo decrypt($encrypted,"mysecretkey"); //prints "the #care is awesome"
In short: If you encrypt plain text with your secret key and afterwards decrypt it again with your secret key, you will get back your plain text. One can say that the representation is injective.
A special variant of crypto systems are storm based ones. They encrypt each variable with a different key. They provide a encryption and decryption key generator. The simplest solution is to have a very long secret key, in order to have a crypto system that is not vulnerable to most common attacks.