What would happen if an alien race gave us a computer capable of 2^256 calculations per second?

Question

The security of public key cryptography relies on computers not being able to generate anywhere near 2²⁵⁶ guesses per any reasonable time length. The obvious implications of a computer this powerful would be that Bitcoin and all other cryptocurrencies would be hacked immediately. But what other less obvious destruction could a computer with this capability provide? What would immediately tumble if the power of this computer were directed at it?

Answer 1

The destructive power of this device would be immense. If you defeated the safeguards on it, it would become the single most powerful bomb ever envisioned.

Doing irreversible calculations, as described here, takes energy. It turns out there's a bare-bones minimum amount of energy required to set 1 bit, based on the entropic content of that data and the temperature. A computer doing irreversible operations will naturally warm up to the temperature of its heatsink, and the coldest heat sink we can get is 3K, the temperature of the background radiation of the universe. You can try to cool it lower than that, but you end up burning more energy than you save.

As a result, there's a minimum of $2.87 \times 10^{-23}$ J/bit of energy wasted every time we flip a bit in an irreversible computer. If we had a reversible computer, this limit would not apply, but in the case of reversible computing, number of calculations is not the unit of measure, so they would not apply to your question.

It turns out that just to run a counter from 0 to $2^{256}$ takes a lot of energy.* A lot of energy. In fact, using that bare bones minimum energy per bit-flip, it will consume 3/4 of the energy in the known galaxy. That's just to run the counter, not even doing any calculations.

So, given a device with 3/4 of the energy of a galaxy, I think we'd want to respect its integrity. The destructive power of this computer would be unimaginable if it were simply disassembled and turned back into usable energy.

* As pointed out in the comments, counting like this is a reversible operation. In this case, I am assuming the counter is implemented using irreversible logic like those we find in a modern ALU. This counter is my surrogate for the general purpose calculations that we could have been doing, such as calculating SHA-1 checksums. This operation is within a factor of a thousand of the most trivial irreversible operation possible (erasure of an unknown bit)

Answer 2

As far as decryption is concerned: The encryption systems currently in use are using key sizes that make it absolutely impossible to crack them using known technology. These key sizes would be cracked if you had 2^256 operations per second available. So what would you do? Increase the key size. RSA with 1024 bit keys is close to uncrackable today. Not completely out there, but very hard. RSA with 4096 bit keys would be uncrackable by the alien computer.

It would be a bit harder to use with our native hardware, but not that hard. The same with symmetric keys; you would have to rearrange your algorithms a bit, but use a 512 bit key where today 256 bits are considered total overkill, and you are fine.

Answer 3

It would make most of our current encryption systems obsolete. However, it would also make new systems possible. These new systems will be unbreakable until the next set of aliens arrive.

Net result: Many old secrets will be revealed. But new secrets would still be secret.

There will be a transition period before we adjust. History shows us that criminals adjust faster than business and law enforcement. That could be chaotic, for a while. But then things will settle down.

Passwords will become a thing of the past. Any password a human can remember, these computers can break.

I think biometric recognition would have to replace it. Today that doesn't work too well, but with better computers we can do a better job of it. You might have to both look into a camera and speak into a microphone to identify yourself. Maybe other sensors can be used too, like smell sensors, signature recognition (with writing speed and pen pressure added to the data) With enough computing power, the possibilities are endless.

However, one thing is certain. Computer programs will be written that are complex enough that even these computers will seem slow to their users.

Answer 4

I not sure we would even understand the limits on what this computer could do.

However, I know one thing, it would not be able to do quickly, simulate a monkey typing out a copy of Shakespeare's Hamlet by random typing. As remarked in Wikipedia

However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed. If there were as many monkeys as there are atoms in the observable universe typing extremely fast for trillions of times the life of the universe, the probability of the monkeys replicating even a single page of Shakespeare is unfathomably minute,

People rarely have an intuitive understanding of the difference between really big numbers and the infinite. 2²⁵⁶ is a really big number (OK, not so much when compared to say Graham's Number). But infinity is completely different.

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The reason for the comparison to the infinite is that this example is often phrased in terms of an infinite number of monkeys. With infinite monkeys you get Hamlet, Mabeth, etc. including translations into every language, as well as else everything else that can be typed in the time it take to type it in without without mistakes.

Really big as in 26^130000 for Shakespeare is so far beyond 2^256 that the computer will not dent the problem before the heat death of the universe. There are many computer algorithms that act more like the Shakespeare problem in terms of needed computation time that you might expect intuitively. Just because an algorithm is known, does not always make the problem solvable.

Answer 5

Most of the existing answers are completely ignoring physics. Assuming you want to compute anything, you need data, and the Bekenstein bound puts a lower bound on the physical size of the device that has any hope of representing a given amount of data. Combined with whatever size you get, the speed of light then gives an upper bound on propagation of data within the system. 2²⁵⁶ is such a huge number that even if your data size were just a few bits, you could not reach anywhere near that computation speed. So your computer simply does not exist.

Answer 6

New physics. Attempting a 2^256 calculation with terrestrial timescales and energies is utterly impossible. Cort Ammon's answer is spot on with what happens attempting it given trying to build the computer with current physical understanding.

Whatever befalls in the finding of such a computer to our current internet is nothing compared to the power that would be unlocked by dissecting it to learn the new physics and rip the secret out of it. I see no non-magical cases where a contained computer such as can be delivered to the earth that can do this does not unlock for us one of warp drive or time travel.

Answer 7

Practically: It would make any sort of super computer superfluous and it would break all and every encryption currently employed. It would NOT allow password guessing or breaking into a remote computer (not a mathematical problem - you can block access after x attempts and there is no way around this) but forget any sort of digital signature. Forget HTTPS.

Answer 8

It would mean that WPA2 wouldn't be safe anymore. Keys could be bruteforced in no time. Router manufacturers would be required to develop and deploy new, secure WiFi encryption schemes into their new models, and until their wide adoption (could take years), everyone and their dog would use their neighbours WiFi.

Answer 9

This would allow the aliens to simulate other possible Worlds, simulate life appearing, intelligent life forms appearing, and eventually a civilization appearing. They can then build a real world copy of that civilization for their own use.

A potential problem for us is then that the outcome of such a simulation might be that they happen to generate our civilization by chance. If they happen to generate a virtual copy of you and decide to copy you as well, you may wake up in an alien World instead of your own bed.

Answer 10

Assuming the physics actually worked(see Cort Ammon answer about the amount of energy)

Nearly every single mathematical problem would be able to be solved by brute force. And for the ones that don't the numbers would get extremely high very quickly.

Chess for instance only has 2^155 positions. So it could evaluate a board to the finish faster then you could decide a move.

Answer 11

In terms of cryptography it would indeed mean the end to all current forms of crypto and the mechanisms which rely on them (I've seen RSA, WPA2 and others mentioned in the other answers here but really all of our current algorithms rely on the same fundamental theory). However, we are already looking at post-quantum cryptography and designing theoretical algorithms to be 'quantum-hard', in anticipation of our research into quantum computers turning up serious results in the foreseeable future. A quantum computer would have a similar effect to one capable of vast numbers of computations as by nature it is able to check every value simultaneously (in theory - I believe the prototypes have to limit the range of possible states but the idea holds). It is believed to be possible to create an algorithm which doesn't rely on a computationally expensive problem (in current crypto, this being the basic mathematical problem of the generation of large primes).

I'm no mathematician but my field is IT security. If you're interested in how we might alter our systems to deal with an issue like this then check out the New Hope algorithm. You can find a paper about it here

Answer 12

Connectapocalypse

we could now create server to host mind diving and connect the whole human race to it via their spinal cord (sound familiar?)

unlock human potential

that many calculations per second would only be beneficial on running multiple calculation at once like the brain. it could help us understand the brain if at least not emulate the brain.

Fast Unencryption through brute force

There are supposedly many black sites out there that have the encrypted form of passwords that were obtained through scrupulous means and having this machine would allow these black sites to get a likely password more re-actively instead of brute force attempting the password for months at a time. usually its quicker to run a few computed guesses based on other information such as the location the data was obtained from, when information was obtained, how much information there is etc..

Answer 13

Unfortunately 2^256 is a very big number; for all practical purposes it's close to infinite. Remember that 1 googol, 10^100, is literally more than everything, for example more than all photons and atoms in the observable universe. 2^256, or roughly 1e77, is almost nothing compared to a googol, but still close enough to be over the top. It is for example more than the number of atoms in the galaxy (perhaps 4e11 stars * 1e57 atoms/star). This makes the question less interesting than, say, 2^100 flops. But ok, let's suppose that we have essentially unlimited computing power, adequate storage with it and that it is 100% reliable:

Update: The first thing to note would be that it's likely that this computer would be a post-singularity super intelligence of its own. It will not only be alive but it will be the equivalent of a god to us; all speculation about it is futile because its ways will be unfathomable. Still, in human terms it'd be an interesting question what its motivation would be to talk to us or even help us, and in which ways it would choose to help us. These are similar questions as people around the world ask about their respective gods. I'm tempted to say that this machine is — next to the spaghetti monster — a candidate for the god of the SE crowd (except perhaps the Judaism SE), in as far as it is a surface for the projection of our speculations and hopes of redemption. (This paragraph was inspired by my Marvin quote in the comments section.)

The rest of the discussion is based on the however incongruent assumption that the computer will behave like a contemporary computer, just faster.

Not only cryptography but all computationally intensive tasks would be almost infinitely accelerated, if the device is (remotely) accessible to the general public.

• Essentially all cloud storage will be transferred to this machine. The only reason to have local or regional computers is speed of access: akamai won't go out of business.

• All simulations which today are performed on supercomputers or expensive work station clusters will be performed on it. The interesting thing is that with better simulations less true insight is necessary (take chess as an example).

  • Weather: One can simply brute-force simulate the whole atmosphere, by the molecule. Don't get me wrong -- weather is a chaotic system and simply is not deterministic. But forecasts will improve dramatically. I suppose that the computational complexity of weather forecasts is exponential; every doubling of the computing power may buy the forecasters perhaps 6 hours more prediction time. But we probably talk 20 or 40 or 80 doublings, depending on how much of the computing power we want to devote to weather forecasts.
  • Brain: A human brain apparently has < 10e11 neurons. We could not only brute-force simulate a brain but all brains. (I'm not sure whether we'll have consciousness; that may need some qualitative insights. But the progress will be immense.)
  • Physics: One could, for example, simply brute-force simulate a whole star; the sun has apparently only 1e57 atoms in it. Which gives you an idea of the size of the machine, by the way, if it has storage to match its computational power and each bit is an atom: as big as 1e20 suns, or 1e9 galaxies.

  It is clear that the machine's capacity is sufficient to simulate all of the physical reality in our galaxy to a degree of precision (the atomic level) which will make it very close to the actual thing. My guess is that we would start uploading simulations of ourselves fairly soon (some decades or at most a couple hundred years). Elon Musk's simulacrum would run around in it and speculate about being in a simulation.--

That we'll be immediately able to have CGI look like real life is just a foot note; but one which will change the entertainment business and may have implications in the court room because true evidence could not be told from falsifications.

Answer 14

Nothing will really happen.

Most secure system have a 2 party login, your bank have a token, where you need the token and the password to get in. Every time the token changes so you have to make the right guess at the first try.

Lets say you could make a qualified guess with the right algorithm, you still would only have a limited amount of attempts before the account is closed down, because the intrusion counter measures kicks in.

Then the next step would be to try and kick in the door. Well, unless you are able to pick out the data and move it physically to your device, then the bandwidth of the unit stored on it (High end PCI harddrive makes about 250.000 operations per second) would make it a major slow down. Doing this over the internet would be even worse, asuming you had the bandwidth you would just make one HUGE DDOS attack on the world.

My conclusion is: Unless you have the data directly on your device (and it could take months to transfer, because of this google even fedexed nasas website to them self), it would be useless, and if you have access to the raw data, well you don't need a fast computer to break in to it.

It would be like have a F1 car on the Faroe Islands.

(More about fast cracking computers and its problems here)

Answer 15

It would be the end of RSA. Some evil genius would make a boatload of money and we go back to the age of trading goods in stead of electronic currency.

Answer 16

For, this answer, I am assuming the aliens tech make us look like cavemen and discussion of laws of physics are all moot because we don't understand anything.

If the computer was practical (similar to a regular PC), not the size of a galaxy, nor using a solar system worth of energy to power it.

If we could duplicate it, we could make it bigger better stronger, and defeat most encryption for a long time.

If it were general purpose enough like a PC, it would end all illness as the human genome would be fully sequenced instantly. All drugs would run all permutation basically instantly, and instead of trial and error we would just brute force every molecule combination against every genome of every illness.

If you could keep it a secret, you could get a large set of all the secrets and use them for good or evil. Blackmail people into whatever you want, or your secrets will be revealed.

As soon as people knew, all encryption would be increased by orders of magnitude nullifying your advantage. 512 bits = 2^256 seconds to crack, not in many lifetimes. 256 bits to 1024 or 2048 or whatever. 4096 bits encryption to maybe 65536 bit encryption, and it is impossible to crack again. It will take several weeks for critical systems to be updated, but after that your device is worthless for this purpose. Login to all vulnerable systems would probably just be disabled until the new bits lengths were deployed. There are devices that won't be updated, and you can get their data until people buy version 2 of the product that is no longer vulnerable.

The additional bits will slow things down for awhile, but the hardware will catch up and everything will be fine.

If the device is like one of our ASIC dedicated to only brute forcing passwords, it will quickly become useless, and all system are updated to longer more complex encryption.

Answer 17

Late to the party here.

But a lot of people talked about the physics challenges of a computer like this. People have already brought up that you would need antigravity to prevent the energy contained from destroying the planet, and that you would need a very good system for dealing with excess heat. I'd also like to explore for a moment the spatial requirements of a computer that can do 2^256 operations per second.

To my knowledge, the current most powerful supercomputer is Sunway TaihuLight, which can hit speeds around 100 PFLOPS (about 2^53 operations a second). That is probably a decent order-of-magnitude estimate for the maximum density of FLOPS that can be achieved by transistor-based computing.

For anything resembling transistor-based computation, a computer capable of 2^256 operations per second would be a lot bigger than the planet.

Even if you just gave humans a client to this massive computer and kept the actual computer somewhere up in space... Such a large computer would be unable to function. Because it would be so big that to send data from one part of the computer to another in a timely fashion, you'd need to send signals at speeds faster than the speed of light.

And you could only get the computer back to a manageable size by making something 2^203 times more compact than a transistor. For reference, a quark is only somewhere in the ballpark of 2^32 times smaller than a transistor.

Probably the only way to get around this to use more than 3 dimensions of space to build your computer. That allows all of the bits to be closer together, so that data transfer is no longer impossible.

In N dimensions, for a computer made of transistors that are close enough to reasonably communicate data, we can estimate that it's computing power would be very roughly (2^(cuberoot(53)))^N operations per second.

If we want that number to equal 2^256, N=14.4633, but since you can't exactly have a fraction of a dimension, we round up to 15.

So basically, you would want about 15 spatial dimensions to house a computer capable of 2^256 operations per second.

I figure it is probably hard to put an upper limit on the capabities of any technology that can leverage 15 spatial dimensions.

Answer 18

Brute force any tech. Want some nanotech? just tell this computer to simulate possibilities using an evolutionary algorithm ( + quantum theory) until perfect nanobots are developed. The computer could design almost any tech that fitted our understanding of physics in an instant.