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With AES (128-bit) encryption there are approximately 3.4 x 1038 possible 128-bit keys or 340,000,000,000,000,000,000,000,000,000,000,000,000. In comparison, DES keys are 56 bits long, which means there are approximately 7.2 x 1016 possible DES keys. Thus, there are on the order of 1021 times more AES 128-bit keys than DES 56-bit keys.
