ArsTechnica is reporting on a “new” attack against RSA, one that bypasses factoring.

First, this attack isn’t new. The original research is from 2007. What is new is the implementation.

Second, it is a forgery attack. It allows an attacker to forge digital signatures. It does not recover the private key from the public key.

Third, the attack only works against pure signatures. That is, signatures without any formatting or padding. This is not generally how we use RSA in practice.

Fourth, speed is all relative. This is not a polynomial-time algorithm; it’s a subexponential-time algorithm. But it is somewhat faster than factoring. The authors were able to forge messages for 1024-bit RSA with 1380 CPU core-years (over five real-world months).

The authors have a webpage that explains the context much better than the article. And here’s the paper.

EDITED TO ADD: Slashdot thread.

Interesting research on a new class of weak RSA keys: keys with lots of zeros. It turns out that these keys are out in the wild.

The badkeys project is an open-source service that checks public keys for known vulnerabilities. While developing this tool, Hanno collected a massive number of real-world keys from public sources, including Certificate Transparency logs, internet-wide TLS and SSH scans, PGP keys, and many others. By searching this dataset for unexpectedly sparse RSA moduli, we uncovered a large number of keys in the wild with the patterns in Figure 1.

Both patterns include several regularly spaced blocks of all zeros interleaved with seemingly random data. Pattern 1 appears in CT logs for certificates issued to several large organizations, including Yahoo and Verizon, and on some devices running NetApp software. Fortunately, these certificates have already expired, but we still shared our findings with these companies. We wanted to learn more about which product could be responsible for generating these keys, but we did not hear back. Pattern 2 appears on SSH hosts running the CompleteFTP software from EnterpriseDT. The underlying vulnerability affects RSA keys generated using versions 10.0.0­12.0.0 (Dec 2016­Mar 2019) and DSA keys generated with v10.0.0­23.0.4 (Dec 2016­Dec 2023).

These vulnerabilities affect a small minority of hosts on the internet, but the more interesting takeaway is that independent cryptographic implementations failed in similar ways. More implementations may include the same bugs, and so it’s worth tailoring cryptanalytic algorithms for this particular type of failure.

The article doesn’t speculate, but I will. This could be a deliberately designed backdoor, of the sort I wrote about back in 2013. I could imagine some government agency figuring out how to break this class of RSA keys, and then convincing different providers to hand them out to users.

I’m skeptical about—and not qualified to review—this new result in factorization with a quantum computer, but if it’s true it’s a theoretical improvement in the speed of factoring large numbers with a quantum computer.