They've contacted the company with the vulnerability and resolved it before publishing the article - search the original article for the substring "now no longer available".
Usually, you demonstrate that an online system is vulnerable by exploiting that vulnerability in good faith, documenting the research, and submitting it for review. It does not matter if you're cracking an encryption scheme, achieving custom code execution for a locked-down game console, proving that you can tamper with data in a voting machine, or proving that you can edit people's comments on a Google Meet Q&A session - the process is the same.
If you say something's vulnerable, people can shrug it off. If you say and prove something's vulnerable, the ability to shrug it off shrinks. If you say and prove something's vulnerable and that you'll publish the vulnerability - again, using the industry standard of disclosure deadlines and making the vulnerability public after 60-or-so days of attempting to contact the author - the ability to shrug it off effectively disappears.
In general, subverting security and privacy controls tends to be illegal in most jurisdictions. Best case is when you have clear permission or consent to do some testing. Absent that there's a general consensus that good faith searching for vulnerabilities is ok, as long as you report findings early and squarely. But if you go on to actually abuse the vulnerability to spy on users, look at data etc ... you've crossed a line. For me, cracking a key is much more like that second case. Now you have a secret that can be used for impersonation and decryption. That's not something I'd want to be in possession of without permission.
Looking at public data, using some other public knowledge to figure out something new does not make it inherently illegal. They didn't crack it on their systems, they didn't subvert it on their systems, they did not use it against their systems. I'd love to see some specific examples under what it could be prosecuted under specifically. Because "that door doesn't actually have a lock" or "the king doesn't actually have clothes" is not practically prosecutable anywhere normal just like that.
Especially in the EU, making such cryptographic blunders might even fall foul of NIS2, should it apply to you.
In general this also quickly boils down to the topic of "illegal numbers" (https://en.wikipedia.org/wiki/Illegal_number) as well.
"Are you aware that this key could be used to decrypt information and impersonate X?"
"Are you aware that this key is commonly called a Private key?"
"Are you aware that this key is commonly called a Secret key?"
"Are you aware that it is common to treat these with high sensitivity? Protecting them from human eyes, using secure key management services and so on?"
"Was it even necessary to target someone else's secret private key to demonstrate that 512-bit keys can be cracked?"
"Knowing all of this, did you still willfully and intentionally use cracking to make a copy of this secret private key?"
I wouldn't want to be in the position of trying to explain to a prosecutor, judge, or jury why it's somehow ok and shouldn't count. The reason I'm posting at all here is because I don't think folks are thinking this risk through.
That key can not be used to decrypt anything. Maybe impersonate, but the researchers haven't done that. It's also difficult to claim something is very sensitive, private or secure if you're publicly broadcasting it, due to the fact that the operation to convert one to an another is so absolutely trivial.
And they did not make a copy of their private key, they did not access their system in a forbidden way. They calculated a new one from publicly accessible information, using publicly known math. It's like visually looking at something and then thinking about it hard.
I wouldn't want to explain these things either, but such a prosecution would be both bullshit and a landmark one at the same time.
If that were true there would be no market for white hat hackers collecting bug bounties. You need to be able to demonstrate cracking the working system for that to be of any use at all. No company will listen to your theoretical bug exploit, but show them that you can actually break their system and they will pay you well for disclosure.
But to pursue data deliberately crosses a bright line, and is not necessary for security research. Secret keys are data that be used to impersonate or decrypt. I would be very very careful.
Also, I don't think DKIM is used for encryption, just signatures.
I see it the other way around. If some hacker contacted me and proved they had cracked my businesses encryption keys and was looking for a reward, I dont think I would be looking to prosecute them and antagonise them further.
Generally, law enforcement and judges don't blame you as long as you use best practices, but you need to adhere to responsible disclosure very strictly in order for this not to be something the police might take an interest in.
Demonstrating the insecurity of a 512 bit key is easy to do without cracking a real life key someone else owns; just generate your own to show it can be done, then use that as proof when reporting these issues to other companies. The best legal method may be to only start cracking real keys if they ignore you or deny the vulnerability, or simply report on the fact you can do it and that the company/companies you've reached out to deny the security risk.
Companies that pay for disclosure won't get you into trouble either way, but companies that are run by incompetent people will panic and turn to law enforcement quickly. White-hat hackers get sued and arrested all the time. You may be able to prove you're right in the court room, but at that point you've already spent a ton of money on lawyers and court fees.
In this case, the risk is increased by not only cracking the key (which can be argued is enough proof already, just send them their own private key as proof), but also using it to impersonate them to several mail providers to check which ones accept the cracked key. That last step could've easily been done by using one's own domains, and with impersonation being a last resort to prove an issue is valid if the company you're reporting the issue to denies the risk.
As I said in my post, no company will listen to your hypothetical exploit. Show them youve hacked their system and they listen.
Pointing out that someone is doing something stupid is also not illegal, though they make try to make your life painful for doing so.
Just as if you made a copy of the physical key for a business's real-world premises, you could well find yourself in trouble. Even if you never "use" it.
They _did_ call out the 3 of 10 tested major email providers that don't follow the DKIM RFC properly: Yahoo, Tuta, Mailfence (after having notified them).
Matthias, co-founder of Tuta Mail
Actually making a clone of the key, and then showing "hey it fits" will get you more traction more quickly ... but there's also plenty of Police Departments who might well arrest you for that.
That's exactly what I meant in terms of not actually doing anything with the result. That said, it's obviously somewhat different with a physical key than a cryptographic key.
But I think many others, and many in law enforcement, will see cracking a key as "actually exploiting it". You've exploited the cracking vulnerability to target a particular key, is how they'll see it. Law enforcement also have a natural incentive to want possession of harm-adjacent paraphernalia to carry substantial liability.
I think they have a point; that key is private data, and there's a reason people lock keys up in KMSs and HSMs; they can have a large blast radius, and be hard for companies to revoke and rotate. Importantly, a compromise of a key will often trigger notification requirements and so now it is a breach or an incident, in a way that a good faith security vulnerability report is not.
To make an extreme example; if you were to crack an important key for a government agency, good luck with that is all I'll say. I sure wouldn't.
The CFAA has a clause about "trafficing in passwords or similar information" (18 USC 1030(a)(6)), but the mental state requirements are very high: that trafficking has to be knowing and with intent to defraud (that intent will be something prosecutors will have to prove at trial).
There might be some state law somewhere that makes this risky, but virtually every hacking prosecution in the US anyone has heard of happens under CFAA. I'm not a lawyer, but I've spent a lot of time with CFAA, and I think cracking DKIM keys is pretty safe.
My understanding, and IANAL, is that decrypting things that aren't yours is a bad idea and is covered mainly by electronic communications and wire acts, e.g. U.S. Code § 2511 and others.
Worth remembering: when CFAA was originally passed, an objection to it was "we already have laws that proscribe hacking computers"; the fraud statutes encompass most of this activity. CFAA's original motivation was literally WarGames: attacks with no financial motivation, just to mess things up. So even without statutory issues, breaking an encryption key and using it to steal stuff (or to gain information and ferry it to others who will use it for crimes) is still illegal.
Your guess is as good as mine about whether ECPA covers wifi sniffing. But: presuming you obtain an encryption key through lawful means, ECPA can't (by any obvious reading) make cracking that key unlawful; it's what you'd do with the key afterwards that would be problematic.
Private keys are not "generally accessible" and my concern is that the authorities will see cracking the key itself as issue enough, and unlawful. If a security researcher triggers painful breach notifications, which could well happen for a compromised private key, I don't think it's unthinkable at all that an upset target will find a DA who is happy to take this interpretation.
I don't think this specific DKIM case is particularly high-risk, but I still wouldn't do it without permission from the key holder.