Earlier quoted context omitted.
I'm going to read your book, because your book with Mazur on the Riemann Hypothesis was incredible.
Free PDF: https://wstein.org/books/modform/
Thanks.
Factoring may be easier than we think (2016)
71–80 of 174 posts
Re: Factoring may be easier than we think (2016)
#72Earlier quoted context omitted.
Why launder? Plenty of goods and services would accept crypto as payment. No need to launder cryptocurrencies but the wild swings in price will affect your accounting in your business.
I'm not very familiar with cryptocurrencies, but wouldn't you be able to also crack crypto wallets? If so, wouldn't the value of crypto go down to 0 thanks to your service?
Cracking RSA isn't cracking SHA-256. Bitcoin and other coins are based on SHA-256. If someone were able to crack SHA-256, the exploit would be better served (of the hacker) to slowly steal coins, so that value within the network is maintained and the exploit is overlooked and missed by the majority. In addition to stealing national secrets.
But all you'd need to do is steal from one early adopter (it's in their financial interest to be savvy enough) and the adopter could alarm the community that an exploit is in existence.
In addition, there are various cryptographic algorithms used. So, one could accept Litecoin, if SHA-256 was exploited. Or accept Vertcoin if both Script and SHA-256 was exploited. Etc.
So, it's an interesting situation based on game theory of an exploit. There is no hard and fast answer.
Re: Factoring may be easier than we think (2016)
#73Imagine what you would do if you discovered how to factor efficiently? Think carefully. You now how the power to decrypt much of the world's banking and internet traffic and spoof certificates. There are forces in this world that would kill you to have this power. Would you publish your findings for everlasting fame? Would you sell it to the NSA for money (remember you can prove your power without releasing your algo…
I have thought about this before but with even higher stakes - finding a polynomial time algorithm for a NP-hard problem - because this would not only affect encryption algorithms based on factoring.
For any NP hard problem would be ground breaking, but many individual NP hard problems can be approximated with imperfect but extremely effective methods.
Re: Factoring may be easier than we think (2016)
#74Earlier quoted context omitted.
You're going to have to launder a lot of money. What's your strategy there?
No need to launder, this money would not be illegal. Just convert it and pay your taxes. When you will have to justify your revenues, everybody will have migrated to different cryptography anyway and you will not be in danger any more and you will be able to use this money as you want.
Because there will be fifteen nation-states who want to kidnap you and force you to disclose the algorithm?
Re: Factoring may be easier than we think (2016)
#75Earlier quoted context omitted.
I'm not following your story. At the time when 1024-bit numbers used in RSA were 'perfect', it was infeasible to factor the number in a reasonable amount of time. The most straightforward approach is just to iterate over integers from 2 to your target number (call it n ), and see if anything divides evenly. Now, you start looking for shortcuts. First, you can test only half the numbers, because the second half will g…
Even 15 years ago 1024-bit numbers were not secure.
I'm working on RSA4096 and this is secure minimum up to 2040.
Factoring is secure for all times, that's a numeric principle.
You only have to make the key/number greater.
I'm working for 50 years with prime numbers and now I'm
where I was when I was 17. Only a little nearer.
What Fermat didn't find and Euler missed (!)
is the knowledge that there is no super'algorhythm' for factoring.
Re: Factoring may be easier than we think (2016)
#76Imagine what you would do if you discovered how to factor efficiently? Think carefully. You now how the power to decrypt much of the world's banking and internet traffic and spoof certificates. There are forces in this world that would kill you to have this power. Would you publish your findings for everlasting fame? Would you sell it to the NSA for money (remember you can prove your power without releasing your algo…
This is pretty overwrought. There have been numerous times over the last 15-or-so years where people have quietly had the ability to spoof arbitrary certificates due to PKCS1v15 signature verification bugs – there was just this year an NDSS paper published on a whole new raft of them, and it'll be at Black Hat in August as well.
A fundamental class break that takes down RSA would be a big deal, but not a national emergency; the world is already moving somewhat rapidly towards elliptic curve systems anyways.
Re: Factoring may be easier than we think (2016)
#77With a grain of salt > Of course, I have no real evidence for my views: [...]
Might want to include context there: >Of course, I have no real evidence for my views; ... On the other hand, the people who talk about the great difficulty of factoring have equally little evidence.
When we talk about the 'difficulty of factoring' there's an implication. The direct meaning is that there may well be a simple algorithm for factoring that has yet to be discovered. No one disputes this.
The implied idea is that this discovery could happen at any time and all things depending on it are at risk. This is also true but it's unreasonable to think that it is likely given that much effort has been put into this.
Yes we don't know, but two unknowns are not 50:50. Of course regardless of how you estimate its truth consider the cost of being wrong when using anything depending on it.
Re: Factoring may be easier than we think (2016)
#78Imagine what you would do if you discovered how to factor efficiently? Think carefully. You now how the power to decrypt much of the world's banking and internet traffic and spoof certificates. There are forces in this world that would kill you to have this power. Would you publish your findings for everlasting fame? Would you sell it to the NSA for money (remember you can prove your power without releasing your algo…
This is pretty overwrought. There have been numerous times over the last 15-or-so years where people have quietly had the ability to spoof arbitrary certificates due to PKCS1v15 signature verification bugs – there was just this year an NDSS paper published on a whole new raft of them, and it'll be at Black Hat in August as well. A fundamental class break that takes down RSA would be a big deal, but not a national eme…
Spoofing certs is not comparable to breaking RSA. Also, I think for this thought experiment, you should also consider breaking elliptic curve crypto. Neither has been proven hard.
Re: Factoring may be easier than we think (2016)
#79Imagine what you would do if you discovered how to factor efficiently? Think carefully. You now how the power to decrypt much of the world's banking and internet traffic and spoof certificates. There are forces in this world that would kill you to have this power. Would you publish your findings for everlasting fame? Would you sell it to the NSA for money (remember you can prove your power without releasing your algo…
This is the main reason that I don't store any of my sensitive data encrypted on cloud storage. If the encryption eventually gets cracked somehow, my data will be available not only to whoever owns, hacks, or otherwise compromises the cloud storage provider itself, but anyone who happened to have captured the traffic on any of the hops it went through on the way to the provider.
You should be using symmetric encryption, which is likely a lot less breakable.
Re: Factoring may be easier than we think (2016)
#80The reason factoring is hard is because finding very large probably prime numbers is easier making number sieve based methods useless for the purpose of breaking large numbers used in cryptography.