To put it in perspective, if you have N computers solving a polynomial-time problem, it will be solved in a 1/N of the time that it takes for a single computer - so, the processing time is basically halfed every time you double the amount of computers.
If you have a single computer solving an exponential-time problem, and you add another computer, it'll get solved, say, a second faster. As you add more computers, you'll only shave off single seconds.
If you have a single computer solving an exponential-time problem, and you add another computer, it'll get solved, say, a second faster. As you add more computers, you'll only shave off single seconds.
This is also why P=NP is a big deal - if you can prove that every single problem that can be checked efficiently can also be solved efficiently, you can do stuff like protein folding (that's a cure for cancer!), and solve a lot of currently unsolved math problems. However, you kinda also break encryption completely and forever, so that's kind of a tradeoff..
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All encryption (AES, elliptic-curve, etc.) is based on the fact that while it is possible to decrypt the message without knowing the key, it will take the attacker several lifetimes before cracking it.
All encryption (AES, elliptic-curve, etc.) is based on the fact that while it is possible to decrypt the message without knowing the key, it will take the attacker several lifetimes before cracking it.
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For the last part: not sure if necessarily
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Big enough keys for NP time: 2048-bit.
Big enough keys for P time: several gigabytes.
Big enough keys for NP time: 2048-bit.
Big enough keys for P time: several gigabytes.
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Like, just grab big enough keys, and breaking them will become impossible to do 'easily'
You could argue that by the time we're gonna solve this we'd be juggling petabytes and probably living in fully automated luxury gay space communism, but I'm hoping that actually working out the algorithm would take a long while.
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Did you mean: have a derivative?
All algebraic functions have an derivative; however, they may not have an integral
Did you mean: have a derivative?
All algebraic functions have an derivative; however, they may not have an integral
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And also, proving that P=NP wouldn't necessarily break encryption. Because people would still have to manage to find a way to break it (which has been difficult). And even then: we don't have a warranty the solution is something we *can* do. I'm thinking…
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