I would say more: encrypted tapes can be decrypted. It's a matter of time and money (how many PC machines do you use for that).
I am not a mathematician (although I played one in college) but I believe there are two basic approaches to decrypting unknown data when you know the encryption algorithm.
1) knowing the algorithm, there may be a mathemical approach to figuring out the key by analyzing patterns of data. AES was adopted because it was resistant to this sort of mathmetical attack, although I saw some recently published papers suggesting that an attack was possible given sufficient CPU power.
2) a brute-force attack, driving some encrypted data through the algorithm using all possible keys (billions and billions of them, Sagen would be proud) but this requirires the ability to recognize valid data when it is successfully decripted. If the data contains printable sequences or other well-known patterns (e.g., packed decimal data) this may be possible, again given sufficient horsepower to try all those keys. So someone trying to get your encrypted data has to be really motivated and have lots of resources available.
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