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My question is about practical limit for brute force attacks. As I know 3DES with 56 bits key length can be broken via brute force. I also heard the same news about 64 bit key length (correct me if I am wrong).

My question is about the minimal length of the key that can be considered as a non breakable by classical computers (not quantum ones). I have 90 bits in my mind but unfortunately don't remember the reasons for the number. I.e. it's impossible to perform $2^{90}$ operations on a classical computer in a reasonable time. Is it correct? Could somebody provide me explanations for the number (90) or provide another answer.

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    $\begingroup$ The current hash rate of Bitcoin network is 2^73 hashes per second, which is approximately 2^89 hashes per day, can it be assumed that such effort for brute forcing an AES key is also possible? $\endgroup$ – khan Sep 12 '17 at 7:47
  • $\begingroup$ @Resa I think that it can be considered as a possible effort for a brute forcing an AES key. As result the suggested number $90$ is incorrect. But I know that 128 bits length is considered as safe (if we don't take into consideration quantum computers). I.e. the requested number is between 90 and 128 $\endgroup$ – Ivan Sep 12 '17 at 7:55
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    $\begingroup$ @Raza: you're off by a thousand; bitcoin is currently 8e18 ~ 2^63 /sec. If an AES-128 trial costs about the same as a bitcoin hash, then the resources used for bitcoin (thus demonstrated to be feasible) would brute-force AES-128 in about 500 billion years on average, except our Earth and Sun won't last nearly that long. $\endgroup$ – dave_thompson_085 Sep 13 '17 at 0:12
  • $\begingroup$ yeah you are right bitcoin hashrate is ~ 2^63/sec. I calculated it wrongly and took Tera as 2^50 instead of 2^40 which led the calculation to a difference of 2^10. $\endgroup$ – khan Sep 13 '17 at 10:14
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Obviously the answer is about the attack potential by adversaries, such as large governments or organisations. And the truth is: we don't know. The attack on SHA-1 shows that the NSA is certainly not the only large organisation to worry about. Anybody with enough money to rent a server farm could be your adversary.

In the end, we don't really know. But there are the Lenstra equations and the site keylength.com which can be used to put in the right numbers. Entering a symmetric key size of 90 will show that 2033 is about the time that this key may be cracked using ga 50M machine, given that Moore's law holds. That's not that far away anymore. Note that single processor speed is not what Moore's law is about; it doesn't seem to be slowing down yet.

To protect against quantum computing you'd have to double the key size in the end. But how fast quantum computers evolve is anybody's guess. Currently there have been some break-throughs with e.g. the Dutch government spending heavily on research at Delft. However a machine that could attack large keys - or anything heavier than a Sudoku - still seems some way off.

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