Breakthrough a step toward revealing hidden structure of prime numbers
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Re: Breakthrough a step toward revealing hidden structure of prime numbers
#2This 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 encryption system? While it would probably be a heavenly day for jailbreakers, console modders and other "device freedom" types generally, the overall impact would be disastrous and incalculable.
Does the industry simply not consider "sudden number theory breakthrough" a possible event?
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#3This 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…
From what I remember in my math class where we made those cryptography calculations by hand, the teacher many years ago said that the day we could guess prime numbers it will be a disaster because many cryptographic calculations are based on the premise that we can’t guess prime numbers. I don’t know if that changed ?
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#4This is from May and there was a better article in Quanta already discussed here.
https://www.quantamagazine.org/sensational-proof-delivers-ne...
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#5This 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…
We could always switch to symmeric keys (but key exchange would be somewhat problematic). Also elliptic curves crypto doesn't use primes, so even public key/private key crypto would still be around and secure.
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#6This 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 world has moved away from RSA etc to elliptic curves. Not everybody did, through. RSA is no longer the standard, and has not been for many years.
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#7This 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…
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.
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#8This 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…
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?
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#9I’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?
Re: Breakthrough a step toward revealing hidden structure of prime numbers
#10I’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?