Brute-force attacks practical limit 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.
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 of symmetric algorithms 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 (normal sized) Sudoku - still seems some way off.