https://twitter.com/robinhouston/status/1169877007045296128

Its easier to drum up support for your paper when you have a quick way to prove to the community of mathematicians that your results are golden.

EDIT: The original webpage: http://math.mit.edu/~drew/sumsofcubes.html

As you can see, the sum-of-cubes announcements are very terse. Ultimately pointing to the following link: https://share.cocalc.com/share/900eec7e-0710-4e2f-a03a-dba01...

That kind of website / tweet is a "drop the mic" moment. It really makes people pay attention.

https://en.wikipedia.org/wiki/Frank_Nelson_Cole

If you 'destroyed RSA' through better factorization, all you have to do is start publishing factors of RSA challenge numbers.

Matthew Green has a fun thread about other ways to approach this along with an interesting "real talk about factoring" sidebar by Nadia Heninger:

https://twitter.com/matthew_d_green/status/13669500931784990...

This isn't science, it's math. As the article mentions, there is an 862-bit RSA challenge that hasn't been factored yet. Factoring it should be possible on commodity hardware if the claims in the paper are true. So why not just do it? The test of success is simple: either you win the challenge or you don't.

Then why would I trust it? You don't need to write code, you need to write an example

As Linus Torvalds says: talk is cheap, show me the code

Academia is full of "paper scientists" that put out papers but produce nothing of value.

They are also full of postgraduate students as well that would be more than willing to work together and put a proof-of-concept code with the paper.

In particular, I think the right process would be:

1. Give some brief description of the result (eg factoring numbers in O(...)), and some proof (eg a factorisation of the next rsa semiprime, possibly more) that convinces people that your claims are true

2. Wait a while for people to have the chance to not be burned

3. Publish the paper

Instead, the authors seem to be going for:

1. Publish the paper with a provocative abstract.

2. Wait to see who implements the algorithm first.

It doesn’t seem the best idea to me, but what do I know?

Do you believe in "responsible disclosure" [1] of security vulnerabilities? How does your stated philosophy apply or not apply to ethics around disclosure of discovered software security vulnerabilities? Is that different?

[1] https://cheatsheetseries.owasp.org/cheatsheets/Vulnerability...

I mean, I get it, it's not the most straightforward mental leap, but I can understand the sentiment.

And as far as responsible disclosure goes, no, the responsible thing to do is to notify everyone at once. Keep in mind if it is right, this means that nation state actors have just been equipped with a roadmap to potentially cracking a lot of banked ciphertext, probably faster than anyone else.

You don't sit on that kind of thing, even if it does mean some corporate actors get burned.

If the only thing saving your rear was an RSA key... Take notice: the clock may have just been significantly advanced. Be you nation-state, corp, or someone who'd just prefer to remain in the shadows.

Suffer thee not information asymmetry to live lest you carry the blood of those you sacrifice on the altar of your limited disclosure. It also hedges against you getting disappeared and suppressing whatever other people you shared it with that remain to keep something so relied upon from being realistically entertained.

I mean, cmon, how long has everyone been joking they'd hate to be the person who discovered how to break RSA, because we all know it would lead t

<SIGNAL_LOST>

If you found a simple way to kill all of mankind, that could be mitigated by waiting a week to publish while safeguards were implemented, is it wiser to publish immediately and risk someone killing all of mankind or to notify proper groups and then publish later after it won't kill everyone?

Maybe there's some nuance in these things. Ignoring effects of knowledge is not wise.

As it is, if the algorithm presented is valid then this potentially compromises currently operating systems.

Yes, you can replace your SSH keys with elliptic ones, and maybe adjust your TLS accepted algorithms. Even this is not always easy or cheap.

But other things that may rely on RSA (or triple RSA) may have trouble upgrading fast, and upgrading them at all is going to cost a lot.

We know that Quantum computers can break it too, yet nobody really acts on it with any urgency. If suddenly there is a breakthrough and we can reach this state within a year, then there will be no time to adapt as well.

It all boils down to the general corporate attitude of not fixing catastrophic problems without precedence. We see the same with climate change and once it hits hard, it will be too late to adapt.

[For symmetric encryption quantum computers would only matter if they were pretty fast/cheap and we didn't have ready-to-go 256-bit symmetric crypto, but we do]

OpenSSH actually has an implementation of a reasonable contender for SSH. Google have experimented (in Chrome builds) with some of these contenders for TLS too. What you would likely want to do - since by definition these are relatively untried algorithms and so might be unsafe against adversaries with an existing not-at-all-quantum computer - is combine with an existing algorithm, most likely elliptic curve based, but RSA would be possible, under a "swiss cheese" model where you're only dead if an adversary penetrates all the layers.

But like I said, much worse. Given that there aren't any suitably large quantum computers (and it's always possible that we'll eventually figure out we just can't build usefully large quantum computers, just like we eventually found out that while you can travel faster than sound you can't travel faster than light) it would make no sense to deploy this today, even though it continues to make sense to do research Just In Case.

Slower, in a different complexity class from the classical ones (AKA O(n^2) instead of O(n), but I don't know what exact complexities the top candidates have right now, as a function of key length).

Larger messages, in that a signature requires 100's or 10's of Mb instead of a few kb.

Larger public keys, as again 100's of Mb instead of a few kb.

Larger private keys, as in a few to 10's of Mb instead of 1/2 to a few kb.

But I guess the most relevant "much worse" is that people have much less confidence that those algorithms are secure, and they are complex enough to hide huge traps that make implement RSA look like a walk in the park.

Some of the other choices aren't so much slower but are far bigger, for example McEliece systems.

There's lots of opportunities to make different trade-offs - at least if all of them survive a bit more scrutiny by smart motivated opponents - but they're all generally worse than what we have now - except that they resist Shor's algorithm.

I don't think that's a problem for end users, you are not constantly generating keys. It will be a problem for servers handling thousands of connections per second, but I'm sure dedicated HSMs will appear if there is a need for them.

In any case, I'm not an expert in crypto, just a poor sysadmin-by-accident who likes reading about the latest security developments so the bad guys don't pwn my servers. And as you said, engineering is always full of trade-offs, let's see what the NIST PQC standardization process will decide.

larger messages

larger public keys

larger private keys

So there might be DOOMSDAY in the future, where all cryptography will cease to work, because somebody just figures a way to decide NP problems quickly enough.

Interesting. Reference?

If nothing else, quantum computers should break RSA in particular (the algorithm is already known and just waiting for hardware) and the writing has been on the wall there for a long time.

Just like it was generally accepted that god exists. Those claims are of similar strength.

> If nothing else, quantum computers should break RSA in particular

Quantum computers with enough qubits do not exist and it's absolutely not obvious whether they will exist at all.

Yeah, no. 3DES (Triple DES) is/ was a thing, but Triple RSA is not.

The blog post claims that people have been trying to reproduce his results for two years, though.

Seems like we should have figured out a way by now to use one time pad encyption by default for critical paths, even if that requires new industries to distribute pads and guarantee their security.

They're useful in exactly one situation: when you have a temporary secure communication channel, and a long-term insecure channel. Then you can use the temporary channel to pre-share a lot of key material (say, a 1TB micro SD card carried covertly) and then use that for future messages. But that scenario is very rare.

"Our main cargo is a one-time cryptographic pad. The source is Commercial Security at Sjandra Kei; the destination is the certificants' High colony. It was the usual arrangement: We're carrying a one-third xor of the pad. Independent shippers are carrying the others. At the destination, the three parts would be xor'd together. The result could supply a dozen worlds' crypto needs on the Net for ..."

I don't really think the parent comment understands that there are creative ways around the difficulty of sharing secure pads. We don't need it for all data; but I think Vinge does hint at a totally viable means of sharing, and scenario in which it's practical.

Key exchanges would be annoying, but they are even more so for one-time pads.

But it will never come to even that: There are plenty quantum-safe asymmetric cryptosystems around.

If we were serious about it, sharing flash drives and even using couriers could make it work pretty well.

There are so many devices and pieces of software that are stuck on RSA, a headsup of say 5 years would still result in a clossal mess; may as well have the mess now.

I think it is - https://eprint.iacr.org/2021/232.pdf

https://eprint.iacr.org/eprint-bin/getfile.pl?entry=2021/232...

The previous (reportedly wrongly uploaded) version is from 12/5/2019, 9:10:13 AM created with pdfeTeX-1.30.4.

https://eprint.iacr.org/eprint-bin/getfile.pl?entry=2021/232...

The university website version is from 3/5/2020, 12:00:19 PM created with pdfTeX-1.40.15.

These dates & times are MM/DD/YYYY & CET.

A co-editor of the Cryptology ePrint Archive confirmed the submission on twitter:

https://twitter.com/Leptan/status/1367103240228261894

Here is a version in the Google cache, it has an old date on it "work in progress 04.03.2020" and does not contain the "destroys RSA" sentence: https://webcache.googleusercontent.com/search?q=cache:E0L-S3...

But if the author of the paper (or even someone else with a credible reputation) was to public factors and say they used this method then it's useful evidence.

The latter is much more important.

For an algorithm, asking for results is not that weird. It certainly fits within the purview of a paper. Moreover, it would be really strong evidence for the claims made in the paper. It is much easier to check than the proofs.

I wouldn't be surprised if a demonstration that pushes the current publicly known record for largest factored RSA modulus costs hundreds of thousands or millions of dollars even with this new algorithm, and the algorithm is also slower than other methods for, say 384-bit RSA.

It may be difficult even for Peter Schnorr to get that kind of budget for a demonstration before his paper gets traction.

[1]https://en.wikipedia.org/wiki/SHA-1#Attacks

I believe that this breakthrough could be quite a bit bigger because it's changing the costs from exponential to polynomial and so speedup is likely a much bigger change.

That's for previous algorithms, not the one described in the paper.

The paper mentions some gains being possible through parallelism with one of the algorithms their work is based on, but also mentioned most prior art is not effectively parallelizable across discrete machines.

Also, without that sentence nobody would be trying to read the paper, so props to Schnorr who understands how to create the buzz :P