Supplement to the cryptocurrency video: How hard is it to find a 256-bit hash just by guessing and checking? What kind of computer would that take?
Cryptocurrency video: https://youtu.be/bBC-nXj3Ng4
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Several people have commented about how 2^256 would be the maximum number of attempts, not the average. This depends on the thing being attempted. If it's guessing a private key, you are correct, but for something like guessing which input to a hash function gives a desired output (as in bitcoin mining, for example), which is the kind of thing I had in mind here, 2^256 would indeed be the average number of attempts needed, at least for a true cryptographic hash function. Think of rolling a die until you get a 6, how many rolls do you need to make, on average?
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Number of tries for the 2 contexts are not the same
1) Verify the message using random signatures and known public key so that we can generate a valid signature without knowing the private key.
Verify (Message, "256 bit signature", pk)
In the worst case this would take 2 to the power of 256 tries, so the explanation is fine for the first context.
2) Find the message whose sha256 is a known hash value (known 256 bits)
Find "Message" such that sha256("Message") = known 256 bits.
Brute force number of tries required for solving this is not 2 to the power of 256. We dont even know the number of characters in the "Message" to begin with.
On 0:36 it is mentioned as 2 to the power of 256 tries. Can you take a look or explain?
"The Enigma machines were a series of electro-mechanical rotor cipher machines developed ..... to be around 3 x 10114 (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around 1023 (76 bits)." from Wikipedia . Yet it was cracked. While I am not saying 256 bit encryption is insecure, I am saying it is much less secure than presented in this video, which practically says it is impossible to break.
Would you please be able to do one or more videos on economics??? So much great content is available online for physics, engineering, etc, but econ seems to be missing. Everyone says that there is a lot of advanced math in economics (game theory, combinatoric optimization, using differential equations to model economic growth, etc), but I've yet to really see it in a context that I felt like I could understand. Could you please give us some applications of fairly advanced math in economics? PS. I'm an undergraduate student. I'm also wondering what math courses would best prepare me for grad school in economics. Will you please make a video on these subjects? Thank you btw for all your wonderful videos. Your linear algebra series has really been helpful for me.
Eye-opening, but it still reminds me of the time when people thought that future computers as powerful as the ones we have today would need to be the size of the earth. That, of course, was before the invention of the microchip. What future invention will turn 256-bit security into something as laughable as a bolt lock?
Assuming the only way to break the cipher is by brute force and there are no known weakness that would weaken the key, it is impossible to brute force a 256 bit key. But it's not the case and often, brute force can be accelerated with known weakness in ciphers. Also, people are sometimes just plain stupid and use common words like someones name and it's much more efficient to crack the key from a dictionary.
tip: don't use sha256,sha512 ... for password hashing, these algorithms were meant to be fast, password hashing should never be done fast, use Bcrpyt, Blowfish or Argon2i.
for php users, check out the php password api : https://secure.php.net/manual/en/ref.password.php
Meh, this video makes the exact same mistake people in the 90's made with computers. "20MBs is all anyone will ever need."
Hint, technology and processing power do NOT stay still. He also doesn't mention quantum computers AT ALL.
Quantum Computing will break the current encryption but at the same time they establish a better and more advanced system. So it's more like a trade.
The main reason (for me) mto say our current encryption is unsecure is that you have a chance to guess right. Even if its incredibly low, it's still there. So it is possible to guess even a SHA 512 at first try ...
When it running square root of 2^256 hashes it would exceed 50% of chance collision. So at around 2^128 of hashes you would finding two input giving a same output, which might reveal some defective aspect of the hash function.
I enjoy expressing this in terms of the absolute theoretical minimum amount of power it would take to run. To "forget" one bit, a computing device has to dissipate Boltzmann's Constant (about 2^-76) * the absolute temperature joules of energy. At liquid helium temperatures (4 degrees), that's 2*10-74 Joules. To check a single hash, the device would have to forget 256 bits. So to brute-force a 256 bit key, we are looking at 2 ^ (256 + 8 - 74), 2^190 Joules. Oh - divided by 2 to get an average. About 10^57, aka 1000^19.
The Sun releases about 3.846×10^26 Watts, so we are talking about 10^31 seconds on average. The universe is about 10^18 seconds old. So if we could harness the *entire* output of the sun to power a computational device running at liquid helium temperatures, we'd expect it to take around 10 trillion times the age of the universe (probably) to crack a single SHA hash.
-- damn: it's not Boltman's constant, it's Boltzman's constant times the natural log of 2. But the natural log of 2 is pretty close to 1, so 10 trillion it is.
You know, regardless how you try to explain it, if a number is bigger than roughly a million it's becoming *incomprehensive* . So people can try all they want, but for our human-sized brains 1000000 = 2^256 = 10^100 = 10^100^100 = pretty big.
I guessed it, it's
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