It is nearly impossible to decrypt passwords, but it is easy to generate some possible passwords, encrypt them, and compare the result with your encrypted password. If the two match, they know your password. So you should never use passwords that occur in a dictionary. E.g. use an unlogic combination of words, or make a sentence and take the first letter of each word. Your password should be kept secret, you can be responsible for the damage done by others with your userid.
Encryption can be a solution.
Digital signatures can be a solution for E-mail users, or encryption can be used to secure and authenticate web transactions. They do not connect at all, or they only connect a few separate computers to the Internet. CERT s, Computer Emergency Response Teams, are organizations which try to handle security accidents. They will notify their users of newly discovered security holes, and they will help in solving network crimes. First is an organization coordinating CERTs.