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  1. What are the three possible values (in bits) for the length of the AES algorithm keys?

  2. Approximately how big is the AES key space?

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    $\begingroup$ a) is literally answered by typing "AES key lengths" into your favourite internet search engine, and b) is an easy computation using those values. What have you tried? Where are you stuck? This is not an online homework service. $\endgroup$ – yyyyyyy Nov 13 '16 at 20:39
  • $\begingroup$ The key space of an n-bit AES key is precisely $2^n$. What is the point of the second question? $\endgroup$ – CodesInChaos Nov 13 '16 at 20:41
  • $\begingroup$ first I'm new in this field and I searched but I wanted to make sure by asking the people here since they know better about cryptography than anyone else.. anyway thank you for your effort $\endgroup$ – F.Moe Nov 14 '16 at 6:07
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AES key sizes are 128, 192 and 256 bits. Note that Rijndael has more possible key sizes, so this is not a limitation of the algorithm; it's just what the AES competition had as requirements. Note that the number of rounds and the key schedule is adjusted to the key size.

AES keys don't have any redundancies; each bit directly influences the key space. So therefore the key size is $2^{128}$, $2^{192}$ or $2^{256}$ for the respective key sizes. This is somewhat different from the old DES cipher that also contains parity bits in the full key. More modern symmetric ciphers simply use all bits and try to avoid weak keys.

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