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POFinding prime factors to large numbers using specially-crafted CPUs
 

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    <p>My understanding is that many public key cryptographic algorithms these days depend on large prime numbers to make up the keys, and it is the difficulty in factoring the product of two primes that makes the encryption hard to break. It is also my understanding that one of the reasons that factoring such large numbers is so difficult, is that the sheer size of the numbers used means that no CPU can efficiently operate on the numbers, since our minuscule 32 and 64 bit CPUs are no match for 1024, 2048 or even 4096 bit numbers. Specialized Big Integer math libraries must be used in order to process those numbers, and those libraries are inherently slow since a CPU can only hold (and process) small chunks (like 32 or 64 bits) at one time.</p> <p>So...</p> <p>Why can't you build a highly specialized custom chip with 2048 bit registers, and giant arithmetic circuits, much in the same way that we scaled from 8 to 16 to 32 to 64-bit CPUs, just build one a LOT larger? This chip wouldn't need most of the circuitry on conventional CPUs, after all it wouldn't need to handle things like virtual memory, multithreading or I/O. It wouldn't even need to be a general-purpose processor supporting stored instructions. Just the bare minimum to perform the necessary arithmetical calculations on ginormous numbers.</p> <p>I don't know a whole lot about IC design, but I do remember learning about how logic gates work, how to build a half adder, full adder, then link together a bunch of adders to do multi-bit arithmetic. Just scale up. A lot.</p> <p>Now, I'm fairly certain that there is a very good reason (or 17) that the above won't work (since otherwise one of the many people smarter than I am would have already done it) but I am interested in knowing <em>why</em> it won't work.</p> <p>(Note: This question may need some re-working, as I'm not even sure yet if the question makes sense)</p>
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    1. USAdam Batkin
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    1. COWhy did someone vote to close this question?
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      1. USAdam Batkin
    2. COhttp://stackoverflow.com/faq Look under "What kind of question should I not ask here?"
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      1. USMichael Donohue
    3. COSorry, I think stackoverflow started off with a good plan, to be something like experts-exchange, but better, but it's evolved, it needs to grow. These sorts of meta-discussions should be allowed. There are almost NO programming "discussion boards" to talk about programming topics in an open-ended way. I personally think SO needs to evolve with it's users, and the moderators need to stop being like the nazi's over at wikipedia. As an aside, how can you see vote closing meta data, or is that something only the question author sees?
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      1. USChris K
 

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