Can AES-256 be decrypted if after the encryption process you destroy the key that must be used to decrypt the data, is it possible?
In theory, you could try to brute force the key and recover the data. In practice, that's extraordinarily unlikely to be successful as it would be expected to take a very, very long time.
AES permits the use of 256-bit keys. Breaking a symmetric 256-bit key by brute force requires 2128 times more computational power than a 128-bit key. Fifty supercomputers that could check a billion billion (1018) AES keys per second (if such a device could ever be made) would, in theory, require about 3×1051 years to exhaust the 256-bit key space.
Keep in mind, the universe has existed for about 1.38×1010 years. Supposedly, a quantum computer could reduce this substantially, but it would still be expected to take longer than the universe has existed.
Of course, you could get really lucky (like win the lottery every week for the next decade lucky) and brute force it in a year or two, but if I were you I wouldn't waste the time or effort.
You cannot decrypt the data without knowledge of the key. However, that does not guarantee that destroying the key prevents decryption of the data:
- You may have destroyed one copy of the key, but other copies of the key may exist.
- The key could have been generated with a weak random number generator, reducing the number of possible keys so much that you can try them all.
- The key may have been derived from other data, and an attacker may be able to repeat this process.
If the key was securely and randomly generated, and all copies of the key have been destroyed, it is considered impossible to decrypt the data based on what we know. Brute-force attacks on a 256-bit key are impossible (physically impossible, actually).
However, mathematical weaknesses in AES could be discovered in the future (or could already have been discovered and kept secret) that would make it feasible to decrypt AES-encrypted data without the key. That said, symmetric crypto algorithms (like AES) tend to hold up pretty well. DES is now over 40 years old, and no practical attacks faster than brute-force have been publicly discovered so far.