Volume of $ 1 e20,000

[wilfulton]

I'm writing a fic that involves 65000 bit encryption (you know like your 128 bit encryption on secure websites, this is more secure, its actually 65,536 bit, but we say 65,000 for short). I go on to say to that this means your chance of correctly guessing the cipher key to decode a coded message is 1 in 1 x 10^20,000 (2 ^65536, is actually 2 x10^19,728)

To give a comparison in layman's terms, I added that if a person had this many 1 dollar bills (same size, weight, and paper type as a US dollar bill), they would fill the known universe. Of course math isn't my strongest point, and I really don't know exactly how thick a dollar bill is (best I can do is stack a few and measure--not very accurate).

Could someone more in the know check my math? And someone more knowledgeable about computers correct me if I'm wrong in how encryption works...

[Chris OFarrell]

Are you talking about current technology with that kind of encryption? Because do you have any idea of the overhead your casualy throwing about?

[phongn]

In addition to the immense overhead you're playing with, even 256-bit symmetrical encryption gives you on the order of 1.16e77 different possibilities. Any breaks against modern cryptosystems are due to weakness of algorithm, implementation or usage and not randomly guessing out the key.

[Durandal]

I'm writing a fic that involves 65000 bit encryption (you know like your 128 bit encryption on secure websites, this is more secure, its actually 65,536 bit, but we say 65,000 for short). I go on to say to that this means your chance of correctly guessing the cipher key to decode a coded message is 1 in 1 x 10^20,000 (2 ^65536, is actually 2 x10^19,728)

To give a comparison in layman's terms, I added that if a person had this many 1 dollar bills (same size, weight, and paper type as a US dollar bill), they would fill the known universe. Of course math isn't my strongest point, and I really don't know exactly how thick a dollar bill is (best I can do is stack a few and measure--not very accurate).

Could someone more in the know check my math? And someone more knowledgeable about computers correct me if I'm wrong in how encryption works...

Do you have any clue how much raw computing power and memory would have to be available to handle encrypting and decrypting with keys of such gigantic size? Seriously, come on. Your key space is 2^65536 bits in size, for Christ's sake. You'd probably end up bloating the message to such enormous size that by the time it was done sending, whatever secret it was hiding would have expired.

[Admiral Valdemar]

Without a quantum computer, you're not going to bypass Blowfish AES at up to 2048 bits encryption. Why would you go for something so massively bloated? A better idea would be using quantum encryption, which is perfect anyway since no amount of computing power will break it unless you have the original key.

[Adrian Laguna]

Valdemar's post reminds me of something that is has me deeply puzzled. I keep hearing two things about quantumn computers: 1) They can break any code. 2) They can make unbreakable codes. Aren't those two things self-contradictory? It's like saying that you can make and unstopable force and an unmovable wall, non-sensical.

[phongn]

Without a quantum computer, you're not going to bypass Blowfish AES at up to 2048 bits encryption. Why would you go for something so massively bloated? A better idea would be using quantum encryption, which is perfect anyway since no amount of computing power will break it unless you have the original key.

From what I've heard, quantum computers will reduce the "effective" bits by a factor of two in decryption - so Blowfish at 2048 may well be secure. And just to be nitpicky, Blowfish isn't AES

[tharkûn]

Valdemar's post reminds me of something that is has me deeply puzzled. I keep hearing two things about quantumn computers: 1) They can break any code. 2) They can make unbreakable codes. Aren't those two things self-contradictory? It's like saying that you can make and unstopable force and an unmovable wall, non-sensical.

QC will be able to "break" any code in that current encryption relies upon the difference between a function and its "inverse". For instance multiplying togethor two numbers is quite quick and easy; factoring back the other way is a royal pain in the ass that takes up exponentially more computing power than multiplication. A QC can use superpositions to do things like factor large numbers 'quickly' so the traditional encrypter no longer has a leg up over the encryption breaker.

QM allows for one to create particles and for measures of various values to be taken. If two people wish to have a secure key one would make a sequence of photons, measure some values and pipe the photons down a cable to the recipient. They would make the some measurements and then call over an open channel to the orginator. Telling each other only what measurements they made (rather than results) they can then build up a unique key based upon their shared results. Anyone who tries to intecept the photon stream and make their own measurements will run afoul of quantum uncertainty and destroy the ability for a key to be made in the first place. One's ability to crack such a code would be nil because you aren't relying upon math, but rather physical uncertainty to get your unique keys.

Everything that is old will be decryptable with QC, new techniques (which are already seeing extremely limited use) will not be effected as much.

[Admiral Valdemar]

From what I've heard, quantum computers will reduce the "effective" bits by a factor of two in decryption - so Blowfish at 2048 may well be secure. And just to be nitpicky, Blowfish isn't AES

My mistake, must've confused it, I swear seeing it saying Blowfish AES on one of my encryption programs.

Valdemar's post reminds me of something that is has me deeply puzzled. I keep hearing two things about quantumn computers: 1) They can break any code. 2) They can make unbreakable codes. Aren't those two things self-contradictory? It's like saying that you can make and unstopable force and an unmovable wall, non-sensical.

No, because quantum encryption relies on entangled particle pairs, not sheer mathematical cunning in making a cipher. If you aren't a part of that quantum connection, intercepting the data makes it unreadable gibberish. You need the key to even read the thing. Quantum computers could certainly make normal encryption better too given their speed if anything.

[Beowulf]

Blowfish was one of the canidates for AES. Rjindael was selected over Blowfish, for reasons of speed, IIRC.

[Durandal]

Valdemar's post reminds me of something that is has me deeply puzzled. I keep hearing two things about quantumn computers: 1) They can break any code. 2) They can make unbreakable codes. Aren't those two things self-contradictory? It's like saying that you can make and unstopable force and an unmovable wall, non-sensical.

The transmission in a quantum link relies on particle states. A potential interceptor of that communication would have to impart a force on the particles transmitting in order to intercept them, which changes their momenta and energy. This is simple Heisenberg Uncertainty. If you can't intercept a communication without reducing it to gibberish, there is obviously little point to intercepting it.

[Adrian Laguna]

Okay, so a quantumn computer would be able to break any modern encryption system. Quantumn encryption would be unbreakable by anything, due to the laws of physics.

[J]

This page, used to illustrate the cost of the Iraqi war should help you figure out how large the stack of bills needs to be.

[phongn]

Okay, so a quantumn computer would be able to break any modern encryption system. Quantumn encryption would be unbreakable by anything, due to the laws of physics.

Well, the transmission cannot be eavesdropped on, but some at point you're going to hand off the data to classical computers or hardcopy or whatnot. There are other ways of getting information other than trying to listen in on a bunch of bits.

The transmission in a quantum link relies on particle states. A potential interceptor of that communication would have to impart a force on the particles transmitting in order to intercept them, which changes their momenta and energy. This is simple Heisenberg Uncertainty. If you can't intercept a communication without reducing it to gibberish, there is obviously little point to intercepting it.

Well, intercept it somewhere else? There could also be attacks based on the non-randomness of the pseudorandom number generator for key prediction.

[wilfulton]

I had envisioned a lot of futuristic tech, so their computers would be concievably much faster than ours.

I had also thought 65000 bit encryption would be just that, 65536 bits in length, and I didn't think that would cause a problem as far as transmission goes, considering that 128 bit goes well over a dial up modem. (yes that was maybe not a good way of thinking but that was what was in my mind when I decided to have some 65000 bit encryption files)

Anyway, thanks to J, I did some calcs.

Looks like

4/2 pi r^3 = 1.15 e 31 cubic light years of universe (assuming 14 billion ly across)

9.6e15 ^3, = 8.85 e 47 cubic meters per cubic light year

so there's about 1.02 e 79 cubic meters of universe we live in.

According to J's link, $72,000 fills 70699 cubic centimeters, or 0.071 cubic meters.

1.44 e 80 stacks of 72 G's

the universe can hold $1.04 e 85.

Shit, bad analogy, looks like dumbass me filled the universe 1 e 19,915 times over.

[tharkûn]

Well, the transmission cannot be eavesdropped on, but some at point you're going to hand off the data to classical computers or hardcopy or whatnot. There are other ways of getting information other than trying to listen in on a bunch of bits.

Of course. Humint will never go out of style until humans do. The thing QE allows is for you to transmit perfectly secure data over tappable medium. Essentially nuclear silos could transmit over simple fiber op and the only way to listen in is to have already bugged the interior of a nuclear silo. For submarines this becomes even more fun. Anytime the only way in is to have physical access is a massively GOOD thing (from the security perspective).

Well, intercept it somewhere else? There could also be attacks based on the non-randomness of the pseudorandom number generator for key prediction.

And if that "somewhere else" happens to be solely contained within the most secure facilities in the world you are just screwed.

As far as randomness; with enough money one can make a random number generator looking at QM wave functions and their decay. Take the simplest (if ridiciously impractical) case; you take a lump of radionuclides with exceptionally short half-lives. Make precision counts of alphas coming off at regular intervals and drop all but the last digit. So far as I know there is nothing pseudo about such a RNG.

[Durandal]

Well, intercept it somewhere else? There could also be attacks based on the non-randomness of the pseudorandom number generator for key prediction.

Maybe, but any random number generator used for encryption is generally "good enough" that it won't repeat itself until long after the transmission has ended. For a large N generated numbers, it might as well be random. You can also say that it's a very good approximation of random.

And, wilfulton, where's the 14 billion light-year across figure coming from? There is no evidence that the Universe's expansion rate is at a 1:1 correspondence with its age. If you want to talk about anything useful, you should stick to our visible universe.

Right now, the Universe expands at 72 km/s/mpc. So for every megaparsec away from us a body is, it moves away at 72 km/s. Obviously, when the expansion rate between us and a body reaches c, that will delineate the edge of our universe.

So we have a visible universe with a radius of approximately 4200 mpc, or about 1.3E9 = 1,300,000,000 ly. The total volume of our visible universe would therefore be roughly 7E18 ly^3.

As far as randomness; with enough money one can make a random number generator looking at QM wave functions and their decay. Take the simplest (if ridiciously impractical) case; you take a lump of radionuclides with exceptionally short half-lives. Make precision counts of alphas coming off at regular intervals and drop all but the last digit. So far as I know there is nothing pseudo about such a RNG.

The rounding is not random. Therefore the values produced won't be totally random. Granted, this might be a very good RNG, but it will probably end up repeating itself eventually.

As a rule in computer science, we don't really want computers producing truly random output. That would be ... kinda freaky. They have to remain predictable.

[wilfulton]

Whatever the case may be, the sentiment remains that analogy of being able to fill the universe wasn't as good as I thought at first. Well...anyway...these quantum computers do sound interesting, but as I do try to limit how much time I spend telling how something works, we could just leave it to the imagination that the ship's resident codebreaker is in fact using just such a device.

Of course turning a universe into a giant bank vault might be interesting: You'd either be rich beyond your wildest dreams, or find that your currency is suddenly worth about as much as vacuum.

[Zero]

Of course turning a universe into a giant bank vault might be interesting: You'd either be rich beyond your wildest dreams, or find that your currency is suddenly worth about as much as vacuum.

I imagine the gravitational force of such a large amount of mass would cause it to collapse. Doesn't sound like a great idea.

[tharkûn]

The rounding is not random. Therefore the values produced won't be totally random. Granted, this might be a very good RNG, but it will probably end up repeating itself eventually.

Suppose you expect on average for there to be 10^9 decays during the sample measurement. You record 92,378,920. Your RNG would return 0, the digits 8237892 would be discarded. In reality you'd be more likely to use something like spin decays where you can easily record orders of magnitude more events. Given a binary RNG you could build up RNs simply by measuring if an even or odd number of decays occurred, and for many systems that value HAS to be random (by the laws of physics). The only way to get non-random artifacts would be outside of the QRNG itself.

[phongn]

Maybe, but any random number generator used for encryption is generally "good enough" that it won't repeat itself until long after the transmission has ended. For a large N generated numbers, it might as well be random. You can also say that it's a very good approximation of random.

Bruce Schneier brings up some interesting PRNG attacks and I've read him bring up the point befor that crypto software has not always used appropriate PRNGs.

Of course. Humint will never go out of style until humans do. The thing QE allows is for you to transmit perfectly secure data over tappable medium. Essentially nuclear silos could transmit over simple fiber op and the only way to listen in is to have already bugged the interior of a nuclear silo. For submarines this becomes even more fun. Anytime the only way in is to have physical access is a massively GOOD thing (from the security perspective).

AFAIK, QE has only used the "secure" link for key exchange while everything else goes over more conventional lines. I'd agree that it does improve security, but it is only one aspect of the system and improvements across the entire system is probably a better place to invest the money, IMHO.

[drachefly]

If a Q-bit can be copied, then a listener can get a quantum key. All they need to do is not 'crack' their Q-bit until both the intended sender and receiver have done so.

This assumes of course that they can do this with such efficiency that the difference is undetectable. If they decohere the q-bit stream perceptibly, then this degree of decoherence can be measured and the eavesdropper will be detected by virtue of that change.

What would an eavesdropper do, then?

Gradually increase the noise on the line so the users think it's natural degradation, then swap in his q-bit copier and take out the artificial noise source.

[Durandal]

Suppose you expect on average for there to be 10^9 decays during the sample measurement. You record 92,378,920. Your RNG would return 0, the digits 8237892 would be discarded. In reality you'd be more likely to use something like spin decays where you can easily record orders of magnitude more events. Given a binary RNG you could build up RNs simply by measuring if an even or odd number of decays occurred, and for many systems that value HAS to be random (by the laws of physics). The only way to get non-random artifacts would be outside of the QRNG itself.

It sounds like you're talking about using the measurement of the number of decays as a seed. Even a perfectly random seed will not produce perfectly random numbers. The algorithms which take the seed and produce a number from it are not random themselves.

Now, and interesting thing to try would be to take the idea of measuring the even or odd number of decays and then assigning even to 1 and odd to 0 and using those values to fill in the powers of 2 in a binary number. Of course, you'd have to randomly determine how big you wanted your number to potentially be using ... another RNG.

[Wyrm]

In answering the original post, a stack of eight bills is about 1 mm high. So, a bill is about 1/8 th a mm thick. Call this 0.1 mm, so a stack of 1e20,000 bills would be 1e19,996 m high. In terms of volume, a bill is about 6 1/8 in long and 2 5/8 in (measured with 1/4 in square graph paper ), which is about 16 5/64 sq in, or 0.010372963 m^2, so the volume of this stack is about 1e19,994 m^3 in volume.

The observable universe is 1.5137168756e26 m in radius (16 billion years = 5.049216e17 s; c * 5.049216E17 s = 1.5137168756e26 m), so the volume of the observable universe is on the order of 1e78 m^3 << 1e19,994 m^3 we calculated for the stack of bills.

[Durandal]

Wyrm, did you miss my post or something? The observable universe is related only to the expansion rate of the Universe, not the total age. We cannot observe the whole thing.