Hanno's blog

Lately, some attention was drawn to a widespread problem with TLS certificates. Many people are accidentally publishing their private keys. Sometimes they are released as part of applications, in Github repositories or with common filenames on web servers.

If a private key is compromised, a certificate authority is obliged to revoke it. The Baseline Requirements – a set of rules that browsers and certificate authorities agreed upon – regulate this and say that in such a case a certificate authority shall revoke the key within 24 hours (Section 4.9.1.1 in the current Baseline Requirements 1.4.8). These rules exist despite the fact that revocation has various problems and doesn’t work very well, but that’s another topic.

I reported various key compromises to certificate authorities recently and while not all of them reacted in time, they eventually revoked all certificates belonging to the private keys. I wondered however how thorough they actually check the key compromises. Obviously one would expect that they cryptographically verify that an exposed private key really is the private key belonging to a certificate.

I registered two test domains at a provider that would allow me to hide my identity and not show up in the whois information. I then ordered test certificates from Symantec (via their brand RapidSSL) and Comodo. These are the biggest certificate authorities and they both offer short term test certificates for free. I then tried to trick them into revoking those certificates with a fake private key.

Forging a private key

To understand this we need to get a bit into the details of RSA keys. In essence a cryptographic key is just a set of numbers. For RSA a public key consists of a modulus (usually named N) and a public exponent (usually called e). You don’t have to understand their mathematical meaning, just keep in mind: They’re nothing more than numbers.

An RSA private key is also just numbers, but more of them. If you have heard any introductory RSA descriptions you may know that a private key consists of a private exponent (called d), but in practice it’s a bit more. Private keys usually contain the full public key (N, e), the private exponent (d) and several other values that are redundant, but they are useful to speed up certain things. But just keep in mind that a public key consists of two numbers and a private key is a public key plus some additional numbers. A certificate ultimately is just a public key with some additional information (like the host name that says for which web page it’s valid) signed by a certificate authority.

A naive check whether a private key belongs to a certificate could be done by extracting the public key parts of both the certificate and the private key for comparison. However it is quite obvious that this isn’t secure. An attacker could construct a private key that contains the public key of an existing certificate and the private key parts of some other, bogus key. Obviously such a fake key couldn’t be used and would only produce errors, but it would survive such a naive check.

I created such fake keys for both domains and uploaded them to Pastebin. If you want to create such fake keys on your own here’s a script. To make my report less suspicious I searched Pastebin for real, compromised private keys belonging to certificates. This again shows how problematic the leakage of private keys is: I easily found seven private keys for Comodo certificates and three for Symantec certificates, plus several more for other certificate authorities, which I also reported. These additional keys allowed me to make my report to Symantec and Comodo less suspicious: I could hide my fake key report within other legitimate reports about a key compromise.

Symantec revoked a certificate based on a forged private key

Comodo didn’t fall for it. They answered me that there is something wrong with this key. Symantec however answered me that they revoked all certificates – including the one with the fake private key.

No harm was done here, because the certificate was only issued for my own test domain. But I could’ve also fake private keys of other peoples' certificates. Very likely Symantec would have revoked them as well, causing downtimes for those sites. I even could’ve easily created a fake key belonging to Symantec’s own certificate.

The communication by Symantec with the domain owner was far from ideal. I first got a mail that they were unable to process my order. Then I got another mail about a “cancellation request”. They didn’t explain what really happened and that the revocation happened due to a key uploaded on Pastebin.

I then informed Symantec about the invalid key (from my “real” identity), claiming that I just noted there’s something wrong with it. At that point they should’ve been aware that they revoked the certificate in error. Then I contacted the support with my “domain owner” identity and asked why the certificate was revoked. The answer: “I wanted to inform you that your FreeSSL certificate was cancelled as during a log check it was determined that the private key was compromised.”

To summarize: Symantec never told the domain owner that the certificate was revoked due to a key leaked on Pastebin. I assume in all the other cases they also didn’t inform their customers. Thus they may have experienced a certificate revocation, but don’t know why. So they can’t learn and can’t improve their processes to make sure this doesn’t happen again. Also, Symantec still insisted to the domain owner that the key was compromised even after I already had informed them that the key was faulty.

How to check if a private key belongs to a certificate?

In case you wonder how you properly check whether a private key belongs to a certificate you may of course resort to a Google search. And this was fascinating – and scary – to me: I searched Google for “check if private key matches certificate”. I got plenty of instructions. Almost all of them were wrong. The first result is a page from SSLShopper. They recommend to compare the MD5 hash of the modulus. That they use MD5 is not the problem here, the problem is that this is a naive check only comparing parts of the public key. They even provide a form to check this. (That they ask you to put your private key into a form is a different issue on its own, but at least they have a warning about this and recommend to check locally.)

Furthermore we get the same wrong instructions from the University of Wisconsin, Comodo (good that their engineers were smart enough not to rely on their own documentation), tbs internet (“SSL expert since 1996”), ShellHacks, IBM and RapidSSL (aka Symantec). A post on Stackexchange is the only result that actually mentions a proper check for RSA keys. Two more Stackexchange posts are not related to RSA, I haven’t checked their solutions in detail.

Going to Google results page two among some unrelated links we find more wrong instructions and tools from Symantec (Update 2020: Link offline), SSL247 (“Symantec Specialist Partner Website Security” - they learned from the best) and some private blog. A documentation by Aspera (belonging to IBM) at least mentions that you can check the private key, but in an unrelated section of the document. Also we get more tools that ask you to upload your private key and then not properly check it from SSLChecker.com, the SSL Store (Symantec “Website Security Platinum Partner”), GlobeSSL (“in SSL we trust”) and - well - RapidSSL.

Documented Security Vulnerability in OpenSSL

So if people google for instructions they’ll almost inevitably end up with non-working instructions or tools. But what about other options? Let’s say we want to automate this and have a tool that verifies whether a certificate matches a private key using OpenSSL. We may end up finding that OpenSSL has a function x509_check_private_key() that can be used to “check the consistency of a private key with the public key in an X509 certificate or certificate request”. Sounds like exactly what we need, right?

Well, until you read the full docs and find out that it has a BUGS section: “The check_private_key functions don't check if k itself is indeed a private key or not. It merely compares the public materials (e.g. exponent and modulus of an RSA key) and/or key parameters (e.g. EC params of an EC key) of a key pair.”

I think this is a security vulnerability in OpenSSL (discussion with OpenSSL here). And that doesn’t change just because it’s a documented security vulnerability. Notably there are downstream consumers of this function that failed to copy that part of the documentation, see for example the corresponding PHP function (the limitation is however mentioned in a comment by a user).

So how do you really check whether a private key matches a certificate?

Ultimately there are two reliable ways to check whether a private key belongs to a certificate. One way is to check whether the various values of the private key are consistent and then check whether the public key matches. For example a private key contains values p and q that are the prime factors of the public modulus N. If you multiply them and compare them to N you can be sure that you have a legitimate private key. It’s one of the core properties of RSA that it’s secure based on the assumption that it’s not feasible to calculate p and q from N.

You can use OpenSSL to check the consistency of a private key:
openssl rsa -in [privatekey] -check

For my forged keys it will tell you:
RSA key error: n does not equal p q

You can then compare the public key, for example by calculating the so-called SPKI SHA256 hash:
openssl pkey -in [privatekey] -pubout -outform der | sha256sum
openssl x509 -in [certificate] -pubkey |openssl pkey -pubin -pubout -outform der | sha256sum

Another way is to sign a message with the private key and then verify it with the public key. You could do it like this:
openssl x509 -in [certificate] -noout -pubkey > pubkey.pem
dd if=/dev/urandom of=rnd bs=32 count=1
openssl rsautl -sign -pkcs -inkey [privatekey] -in rnd -out sig
openssl rsautl -verify -pkcs -pubin -inkey pubkey.pem -in sig -out check
cmp rnd check
rm rnd check sig pubkey.pem

If cmp produces no output then the signature matches.

As this is all quite complex due to OpenSSLs arcane command line interface I have put this all together in a script. You can pass a certificate and a private key, both in ASCII/PEM format, and it will do both checks.

Summary

Symantec did a major blunder by revoking a certificate based on completely forged evidence. There’s hardly any excuse for this and it indicates that they operate a certificate authority without a proper understanding of the cryptographic background.

Apart from that the problem of checking whether a private key and certificate match seems to be largely documented wrong. Plenty of erroneous guides and tools may cause others to fall for the same trap.

Update: Symantec answered with a blog post.