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<p>[QUOTE="InfleXion, post: 2662598, member: 29012"]I apologize for not having better post restraint, but this PBS link literally admits that MIT is using quauntum computers to crack PGP keys. If they can do that, is BitCoin really so bulletproof?</p><p><br /></p><p><i>The normal way of doing public key cryptography was developed by [Ron] Rivest, [Adi] Shamir, and [Len] Adleman here at MIT. The idea is that you have a very long number, hundreds of digits long, and this number is the product of two smaller numbers. The long number is the public key, and the numbers that make up the product are the private key. So in order to get the private key from the public key, you have to figure out what the two smaller numbers are. This is called factoring, right? Like the factors of 15 are three and five. Well, factoring 15 ain't too hard, but factoring a number that's 500 digits long is hard. Quantum computers can factor large numbers easily, and this is what Peter Shore told us.</i></p><p><i><br /></i></p><p><i>A conventional, classical digital computer could, indeed, factor a 500-digit number, but the only known methods are basically, well, let's try these two numbers and multiply them together and see if it's this big number. Let's try these other two numbers. The problem is that there are gagillions—that's a technical term—there are gagillions of numbers that could be multiplied together, and to explore all those numbers would essentially take the age of the universe on a conventional digital computer, even the biggest supercomputers.</i></p><p><i><br /></i></p><p><i>On a quantum computer, you can actually factor these numbers very, very rapidly. The way it works is, well, it's very sneaky and tricky, but it boils down to the following:</i></p><p><i><br /></i></p><p><i>In this factoring problem, there's a kind of a hidden periodicity. So you can rephrase the factoring problem as, oh, I've got this wave, and it wiggles up and down over some very long time. Intuitively, quantum mechanics is about waves. And zero and one have a wave that's associated with them, and this gigantic number that's hundreds and hundreds of digits long also has waves associated with it. Now, waves are famously, you know, wavy, and quantum computers are darn good at figuring out how fast waves wiggle up and down.</i></p><p><i><br /></i></p><p><i>Peter Shore showed that you can set up this factoring problem so that if you're given the wave for this 500-digit number, then you can find the hidden waves for the two 250-digit numbers which, when multiplied together, give you the 500-digit number. It's very sneaky, and it involves more stuff than that, but at its quantum heart, the guts of the quantum problem, that's what it is, finding out the periodicity of waves.</i>[/QUOTE]</p><p><br /></p>
[QUOTE="InfleXion, post: 2662598, member: 29012"]I apologize for not having better post restraint, but this PBS link literally admits that MIT is using quauntum computers to crack PGP keys. If they can do that, is BitCoin really so bulletproof? [I]The normal way of doing public key cryptography was developed by [Ron] Rivest, [Adi] Shamir, and [Len] Adleman here at MIT. The idea is that you have a very long number, hundreds of digits long, and this number is the product of two smaller numbers. The long number is the public key, and the numbers that make up the product are the private key. So in order to get the private key from the public key, you have to figure out what the two smaller numbers are. This is called factoring, right? Like the factors of 15 are three and five. Well, factoring 15 ain't too hard, but factoring a number that's 500 digits long is hard. Quantum computers can factor large numbers easily, and this is what Peter Shore told us. A conventional, classical digital computer could, indeed, factor a 500-digit number, but the only known methods are basically, well, let's try these two numbers and multiply them together and see if it's this big number. Let's try these other two numbers. The problem is that there are gagillions—that's a technical term—there are gagillions of numbers that could be multiplied together, and to explore all those numbers would essentially take the age of the universe on a conventional digital computer, even the biggest supercomputers. On a quantum computer, you can actually factor these numbers very, very rapidly. The way it works is, well, it's very sneaky and tricky, but it boils down to the following: In this factoring problem, there's a kind of a hidden periodicity. So you can rephrase the factoring problem as, oh, I've got this wave, and it wiggles up and down over some very long time. Intuitively, quantum mechanics is about waves. And zero and one have a wave that's associated with them, and this gigantic number that's hundreds and hundreds of digits long also has waves associated with it. Now, waves are famously, you know, wavy, and quantum computers are darn good at figuring out how fast waves wiggle up and down. Peter Shore showed that you can set up this factoring problem so that if you're given the wave for this 500-digit number, then you can find the hidden waves for the two 250-digit numbers which, when multiplied together, give you the 500-digit number. It's very sneaky, and it involves more stuff than that, but at its quantum heart, the guts of the quantum problem, that's what it is, finding out the periodicity of waves.[/I][/QUOTE]
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