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Earlier quoted context omitted.
Also means it can’t transit the internet. So actually, only on airgapped networks.
If we're going to extremes like that, airgapped networks aren't truly safe either
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…
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…
Earlier quoted context omitted.
> 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…
That NPI wiki link says integer factorization may be in NP-intermediate iff NPI isn't an empty set, which is unknown at the current time. My understanding is the complexity of factorization is also currently an unsolved problem although no polynomial time algorithm is currently known. Eg https://www.connellybarnes.com/documents/factoring.pdf "Finally, in computational complexity theory, it is unknown whether factorin…
Integer factorization is unsolved and it’s decision problem is in NP.
IF’s decision problem’s complexity “may be in NP” because the question of whether P equalling NP is unknown.
Meaning IF is NP, but may well be P if P=NP. If P!=NP then IF is NP.
I’m both a layman and a simpleton, but seeing Guth’s comments, surely it can’t be a new idea that the fundamental interpretation of primes is something to do with waves and harmonics?
"Fundamental interpretation of primes" is a bit much, but this has been understood for a long time. The short version of the story is
- The primes are closely related to the Riemann zeta function, which is more-or-less cobbled out of them;
- The Riemann zeta function has a lot more symmetry than one might initially expect, and harmonic analysis is how you prove this;
- The (still unproved) Riemann Hypothesis is that the zeta function has still more symmetry beyond what we've been able to prove.
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…
Earlier quoted context omitted.
> 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…
> Integer factorization is NP-intermediate 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?…
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…
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.
CS was a software update. RSA is baked into many silicon circuits and firmware ROMs.