71–80 of 161 posts
Something inspiring about this: "In dedicated Friday afternoon thinking sessions, he returned to the problem again and again over the past decade, to no avail."
Earlier quoted context omitted.
The industry couldn’t even prepare for a bad Crowdstrike update. And yet, it figured things out in a few days or so. The ability to prepare for catastrophic scenarios is overestimated. The ability to survive them is underestimated.
This would be a lot worse than that. Crowdstrike was bad because everyone lets relatively untested code straight into the Windows kernel - i.e. known incompetence of approach. This would be bad despite massive care taken to have the right approach.
Earlier quoted context omitted.
A generator of "all primes" is pretty simple and deterministic. But you cannot simply generate next prime given only prime n without recomputing its non-trivial remainders. That means just a binary representation of a number n doesn't provide enough information to make quick answer what is the next prime. You have to pre-compute some 'pivots' first. Basically, more complexity, but it's still simple and trivial, not e…
> not even in NP This is incorrect. Integer factorization is NP-intermediate. Very much “in NP”. https://en.m.wikipedia.org/wiki/NP-intermediate Also, saying factorization lacks “complexity” because sieves exist misunderstands both concepts. > In order to talk about complexity classes such as P, NP, and co-NP, the problem has to be stated as a decision problem. > Decision problem (Integer factorization) — For every n…
People backing up math with wikipedia links is never a good look. Particularly when those references contradict the points they seemed they were trying to make: Since it is also true that if NPI problems exist, then P ≠ NP, it follows that P = NP if and only if NPI is empty.[your NPI reference]
So... if you've shown FACTORING is NPI then you've proven P ≠ NP, I guess, too? Hahaha! :)
This got me thinking. Imagine this discovery led to a larger breakthrough on prime numbers that allowed easy factorization of large integers and effectively rendered public key cryptography such as RSA ineffective overnight, by allowing anyone with a consumer-grade CPU to crack any production-size key. Does the industry have DR plans for this scenario? Can the big players quickly switch to a different, unbroken encry…
If someone found a way to easily factorize large integers easily on consumer grade hardware then it would be very painful as RSA is one of the big public key algorithms. Before you start worrying about it though consider that RSA has held up for 47 years of active cryptanalysis so far - during which time many alternative algorithms have been suggested as being superior, only to be broken a short time later. Also the…
(Basically your data is not encrypted with RSA, you encrypt a secondary key, send it with RSA but the main encryption is AES see https://en.wikipedia.org/wiki/Transport_Layer_Security#Key_e... )
This got me thinking. Imagine this discovery led to a larger breakthrough on prime numbers that allowed easy factorization of large integers and effectively rendered public key cryptography such as RSA ineffective overnight, by allowing anyone with a consumer-grade CPU to crack any production-size key. Does the industry have DR plans for this scenario? Can the big players quickly switch to a different, unbroken encry…
The industry couldn’t even prepare for a bad Crowdstrike update. And yet, it figured things out in a few days or so. The ability to prepare for catastrophic scenarios is overestimated. The ability to survive them is underestimated.
Earlier quoted context omitted.
And the key consituents don't have to be prime. That use of heuristics has always scared me a bit.
Nit-pic: the key constituents only need to be co-prime rather than absolutely prime, though in practise this makes little or no difference.
Earlier quoted context omitted.
Still, plenty of old stuff was scraped/sniffed under the "store now, decrypt later" methodology.
True. The only solution is to keep your data outside cloud(aka someone else's computer) no matter what encryption you use.
People always think the structure of primes is complex, but it's not really, it's just a recursive structure of the magnitude gaps not landed on by multiples of previous gaps. It doesn't make it easier to "predict" without tracking all prior gaps, but it's not essentially a complex structure. Kind of funny that like such a simple structure is so elusive. Sorta like how the 3n + 1 sequence gives rise to such complexit…
https://en.wikipedia.org/wiki/Information_theory
Earlier quoted context omitted.
If someone found a way to easily factorize large integers easily on consumer grade hardware then it would be very painful as RSA is one of the big public key algorithms. Before you start worrying about it though consider that RSA has held up for 47 years of active cryptanalysis so far - during which time many alternative algorithms have been suggested as being superior, only to be broken a short time later. Also the…
Actually RSA has several "gotchas", so it is not that it has held up but people have managed to work around those gotchas into a working encryption system (Basically your data is not encrypted with RSA, you encrypt a secondary key, send it with RSA but the main encryption is AES see https://en.wikipedia.org/wiki/Transport_Layer_Security#Key_e... )
Earlier quoted context omitted.
If someone found a way to easily factorize large integers easily on consumer grade hardware then it would be very painful as RSA is one of the big public key algorithms. Before you start worrying about it though consider that RSA has held up for 47 years of active cryptanalysis so far - during which time many alternative algorithms have been suggested as being superior, only to be broken a short time later. Also the…
Actually RSA has several "gotchas", so it is not that it has held up but people have managed to work around those gotchas into a working encryption system (Basically your data is not encrypted with RSA, you encrypt a secondary key, send it with RSA but the main encryption is AES see https://en.wikipedia.org/wiki/Transport_Layer_Security#Key_e... )