Even with the various advances in safe cracking and decryption techniques, there are still means of keeping information safe.
Firstly, you don't call attention to yourself or your information. Hillary Clinton's email server stood out like a beacon because its ID on the internet unambiguously called attention to itself and who owned it. If you skulked down the street with a large aluminum briefcase chained to your wrist, most observers would note something interesting is in there. If you walk down the street from a grocery store with a paper bag, who would suspect that you actually have $1,000,000 in hundred dollar bills inside?
Secondly, information needs to have controlled distribution. You might have a Top Secret clearance, but that does not mean you are entitled to every piece of Top Secret intelligence. Information is compartmentalized and distributed on a "need to know" basis. Information also needs to have a clear paper trail. To use the Clinton email server example again, information was obviously lifted from secure servers and transferred to the unsecured server. There should be a record of every individual who had access to this information on the secure server, and logs of when they accessed the information. Potentially, quite a lot of people could be charged with various violations of securities laws for making and distributing unauthorized copies of information (although realistically this does not appear to be in the cards)
In the internet age, information also needs to be isolated from the "public" Internet. The so called "Dark Web" simply means this part of the web is only accessible by special permissions, passwords etc. and/or physically separate from the internet by "air gaps".
Information which is stored or transmitted should be encrypted with the highest possible level of encryption, and techniques which should be extremely difficult to break, such as "one time pads" or book codes.
In the future, the best form of security might well be straight pen and paper; which isn't accessible by remote means. Teams of agents might still be able to break into a room and go through a filing cabinet, but this is far more difficult and time consuming than the Chinese hack which took the information and security clearance forms of an estimated 4 million US government employees. Imagine how long it would take to go through vaults full of filing cabinets to do the same thing.