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I’m curious as I hadn’t seen it before and it’s gripping: Is the patterns showing in a polar plot of the prime numbers a recent discovery or is it long known and just used as an illustration? What is it called and what is its history?
Earlier quoted context omitted.
I think this is where the move to elliptic curve comes in, and that seems well on its way. Both in signatures and handshakes (Diffie-Hellman). Perhaps it's not a one minute operation to DR, but I doubt everything would be open if RSA/DH was rendered insecure overnight. I know my SSH keys are a mixed bag right now.
does the move to elliptic crypto suggest that the people in the know expect prime factorisation to be broken soon?
Earlier quoted context omitted.
I think this is where the move to elliptic curve comes in, and that seems well on its way. Both in signatures and handshakes (Diffie-Hellman). Perhaps it's not a one minute operation to DR, but I doubt everything would be open if RSA/DH was rendered insecure overnight. I know my SSH keys are a mixed bag right now.
does the move to elliptic crypto suggest that the people in the know expect prime factorisation to be broken soon?
Earlier quoted context omitted.
does the move to elliptic crypto suggest that the people in the know expect prime factorisation to be broken soon?
https://en.wikipedia.org/wiki/Shor%27s_algorithm As soon as quantum computers have enough qbits prime factorisation can be done very quickly. Not sure the timeline on that as there are a lot of challenges in the technology and it is hideously expensive, but a lot of the move away from RSA to elliptic curves is driven by readiness for quantum computing. https://en.wikipedia.org/wiki/Post-quantum_cryptography
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 complexity. Or the logistic map with its parameter above the threshold.
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…
Earlier quoted context omitted.
does the move to elliptic crypto suggest that the people in the know expect prime factorisation to be broken soon?
Since no one mentioned, a major reason to prefer elliptic curves is that you can get equivalent security for much smaller key sizes.
Why is taking methods from other fields an unorthodox move? I come from an engineering background an there it is the common case. The usage of harmonic analysis is a staple in many fields (audio, waves, electrical analysis, statistics) and of course the algorithms are pure math under the hood. If I want to find a reaccuring structure in an underlying system, wouldn't it be normal to try different plotting techniques and choose the one that suits my problem best?
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…
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 push to switch to Elliptic-Curve algorithms has been more down to them being easier for computers to use to encrypt/decrypt data.
Personally if I had to bet on which public key algorithm will still be around in 10 years time then I'd put my money on RSA.