Headlines:

* In (rare) vulnerable targets, this allows you to recover the host's key, and thus impersonate a host. You can't compromise client credentials with this attack, since client credentials are exchanged after the (active) secure channel is established. If you can impersonate a host, as this attack would allow you to do, you could capture client password credentials, and you can drive a forwarded agent.

* OpenSSH --- really, SSH servers on any Unix host you've been using in the last 20 years --- isn't vulnerable to this attack. The vulnerability is publishing a signature that is validly signed under RSA p and not under RSA q. Solution: just never do that; when you generate the signature, check it yourself before publishing. This is one of the better-known attacks on RSA, so this is a standard implementation countermeasure.

* The things that are vulnerable are crappy middleboxes from Zyxel, Mocana, apparently a rare subset of Cisco devices, and whatever "SSH-2.0-SSHD" is (the authors don't know either).

* This is a Nadia Heninger paper, and Heninger is, like, the modern master of the Coppersmith RSA attack, which transforms an RSA problem into a series of polynomials and then transforms those into a linear algebra problem set in a lattice (roughly: a vector space with exclusively integer components; really, when we say "lattice" we mean "some generated basis for that lattice"). You then use the LLL algorithm to reduce the basis, which gives you small vectors that, when reframed back into polynomials or whatever, can tractably solved for their roots. Get the intuition? Yeah, I mean, me neither. Lattice attacks on PQ crypto have a simpler intuition! But the lattices bases here are just R^3 matrices, so, that's pretty simple.

* You can get the intuition for the underlying vulnerability much more simply. From the paper: Boneh, DeMillo, and Lipton noted that if an attacker had a correct signature s and an incorrect signature s_hat of this form then the attacker could compute gcd(N, s_hat − s) = p. The complicated math comes from the fact that while we have the incorrect signature we're hoping for, we don't have the correct signature over the same message, or a fully known message.

* This attack is made possible by our old friend PKCSv1.5, this time in a signing setting. It works because a P1v1.5 RSA signature has regular format: 00 01 FF ... FF 00 aa .. aa hh .. hh, where aa are the (known) bits of the ASN.1 identifier of the hash, and hh are the (unknown) bits of the hash. Everything but the bit values of hh is known to the attacker.

* Amusing detail: the attack relies on a condition of the unknown bits being less than 1/4 of the RSA message (modulus) size, so the attack actually gets harder for RSA-1024 with better hashes, and is impossible for RSA-1024 with SHA2-512, which blows that budget.

* Another thing that uses PKCSv1.5-RSA signatures is DNSSEC. You could scan the Internet collecting DNSSEC signatures hoping to find some that don't validate (I think it's RIPE that periodically does surveys looking for invalid DNSSEC records, and routinely finding them?), and because all RSA DNSSEC is in viable parameters for this attack I guess recover keys from it? Or you could just not use DNSSEC. I guess maybe this is particularly problematic for "online-signers"; most DNSSEC signatures are computed offline, so you can't just repeatedly ask for new signatures waiting for a fault, but you could with an online signer.