Actually, the Germans were using the scheme you describe for their infamous Enigma machines which they believed were unbreakable. But the Germans let their guard down in several areas. One of these was the fact that every day, German U-boats would send Enigma encrypted weather reports from u-boats back to headquarters which were intercepted by the Brits. This created enough of an opening to allow the Brits to get their foot into because those weather reports contained predictable information that could be (i.e. cloudy, rain, highs, lows) and was used to aid in cracking the cipher.
As for an encryption algorithm being impenetrable, most extreme mathematicians would say there is no such animal. But to understand that concept, you have to understand the difference between “theoretical” cracking and “practical” cracking. Theoretically breaking a cipher is describing in mathematical terms how a cipher could be broken through repetitive iterations of a formula. Once the genius mathematicians agree that the formula for the crack is sound they then have to apply the practical side of things. Using the most powerful computers in the world how long would it take to repeat those iterations until the code is cracked.
AES encryption (used by our government and available to you) has been cracked theoretically by a group of Eastern European Mathematicians. But here’s the practical side of it:
According to the crackers themselves, “On a trillion machines, that each could test a billion keys per second, it would take more than two billion years to recover an AES-128 key. Because of these huge complexities, the attack has no practical implications on the security of user data."
So encrypt your sensitive files and passwords with AES for now and don’t worry too much about it. Of course if you past a sticky note with the key to the AES file, it’s like putting a steel door on a pup tent.
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