Can someone randomly guess the key to AES 256 bit encryption?

Question

Is it possible that someone can randomly input a key to AES 256 bit encryption and it is correct? What are the chances of this happening? Is it even possible or not?

Answer 1

There are $2^{256}$ different AES keys, the chance that you hit the one right one on first try is thus $2^{-256}=\frac1{2^{256}}$.

To put this into perspective, here's a list of events that is roughly a billion times more likely to all happen (copied from Thomas Pornin's answer on Information Security SE):

• The computer spontaneously catches fire during the key generation process.
• Great Britain is wiped out by a falling asteroid during the very same second.
• A rogue gorilla escaped from a zoo enters your living room and mauls you.
• You win millions of dollars at the lottery three times in a row.

According to his answer, these events have roughly the chances of happening $2^{-45},2^{-50},2^{-60},2^{-71}$ each, which multiplies to $2^{-226}$ if you want all four to happen which is still roughly a billion times more likely than finding a 256-bit key on first try.

Note that this assumes that the key does indeed contain 256-bit of entropy, ie it can indeed take all the $2^{256}$ different values.

Answer 2

Theoretically, this is possible... but, you have a better chance being hit by a meteor within the next second than seeing that happen as it practically boils down to "getting extremely lucky" with a brute-force attack.

Think about it: 256 bits (32 octets). You can do the math yourself to calculate the chances in both a best case as well as a worst case scenario.

Skipping the details the other answers already provided, you're thinking about someone lucky enough to "guess" that one correct password out of a pool of 1.1579209e+77 possibilities. To put that in perspective… this means that, on average, an attacker would need around and about _{$$57896044618658097711785492504343953926634992332820282019728792003956564819968$$} attempts to guess the correct password (better: key).

That is, assuming an optimal case with both a correct and safe AES implementation as well as cryptographically secure creation and handling of key material. Also, this doesn't look at other potential attack vectors like exploiting a weak block-cipher mode of operation or the likes - as the question specifically asks about the chance of a "randomly input a key" being correct.

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Also see the related question "Probability of guessing random 128-bit AES key" as well as it's accepted answer.

Answer 3

For AES-256 in order for someone to guess a key they would need to guess the sequence of 256 bits. There are $2^{256}$ possible sequences of length 256 bits and only one of them can be the correct key. For comparison the estimated number of atoms in the visible universe is $2^{265}$.

The possibility of randomly guessing 256-bit long sequence is $\frac{1}{2^{256}} = 2^{-256}$.

So while this is theoretically possible, the possibility of actual guessing is incredibly low.