Cypher-decyphering, as you call it, is a secure method. For instance, when you submit a credit card number or a social security number over an SSL connection (https), encryption is what keeps that information safe. Or when you use SFTP (secure FTP), you're relying on encryption. Even when you password protect your browser-saved passwords, you're relying on encryption then too.
These are all open algorithms. Anyone may examine them, even math teachers. But not even the world's best cryptographers can break them. That's why they're used to protect the most sensitive information sent through the Internet.
You may distrust them if you wish, but it's wrong to say they aren't secure.