Private Key Redaction: UR DOIN IT RONG

Posted: Sun, 17 May 2020 | permalink | No comments

Because posting private keys on the Internet is a bad idea, some people like to “redact” their private keys, so that it looks kinda-sorta like a private key, but it isn’t actually giving away anything secret. Unfortunately, due to the way that private keys are represented, it is easy to “redact” a key in such a way that it doesn’t actually redact anything at all. RSA private keys are particularly bad at this, but the problem can (potentially) apply to other keys as well.

I’ll show you a bit of “Inside Baseball” with key formats, and then demonstrate the practical implications. Finally, we’ll go through a practical worked example from an actual not-really-redacted key I recently stumbled across in my travels.

The Private Lives of Private Keys

Here is what a typical private key looks like, when you come across it:

Obviously, there’s some hidden meaning in there – computers don’t encrypt things by shouting “BEGIN RSA PRIVATE KEY!”, after all. What is between the BEGIN/END lines above is, in fact, a base64-encoded DER format ASN.1 structure representing a PKCS#1 private key.

In simple terms, it’s a list of numbers – very important numbers. The list of numbers is, in order:

A version number (0);
The “public modulus”, commonly referred to as “n”;
The “public exponent”, or “e” (which is almost always 65,537, for various unimportant reasons);
The “private exponent”, or “d”;
The two “private primes”, or “p” and “q”;
Two exponents, which are known as “dmp1” and “dmq1”; and
A coefficient, known as “iqmp”.

Why Is This a Problem?

The thing is, only three of those numbers are actually required in a private key. The rest, whilst useful to allow the RSA encryption and decryption to be more efficient, aren’t necessary. The three absolutely required values are e, p, and q.

Of the other numbers, most of them are at least about the same size as each of p and q. So of the total data in an RSA key, less than a quarter of the data is required. Let me show you with the above “toy” key, by breaking it down piece by piece¹:

MGI – DER for “this is a sequence”
CAQ – version (0)
CxjdTmecltJEz2PLMpS4BX – n
AgMBAA – e
ECEDKtuwD17gpagnASq1zQTY – d
ECCQDVTYVsjjF7IQ – p
IJANUYZsIjRsR3 – q
AgkAkahDUXL0RS – dmp1
ECCB78r2SnsJC9 – dmq1
AghaOK3FsKoELg== – iqmp

Remember that in order to reconstruct all of these values, all I need are e, p, and q – and e is pretty much always 65,537. So I could “redact” almost all of this key, and still give all the important, private bits of this key. Let me show you:

-----BEGIN RSA PRIVATE KEY-----
..............................................................EC
CQDVTYVsjjF7IQIJANUYZsIjRsR3....................................
........
-----END RSA PRIVATE KEY-----

Now, I doubt that anyone is going to redact a key precisely like this… but then again, this isn’t a “typical” RSA key. They usually look a lot more like this:

People typically redact keys by deleting whole lines, and usually replacing them with [...] and the like. But only about 345 of those 1588 characters (excluding the header and footer) are required to construct the entire key. You can redact about 4/5ths of that giant blob of stuff, and your private parts (or at least, those of your key) are still left uncomfortably exposed.

But Wait! There’s More!

Remember how I said that everything in the key other than e, p, and q could be derived from those three numbers? Let’s talk about one of those numbers: n.

This is known as the “public modulus” (because, along with e, it is also present in the public key). It is very easy to calculate: n = p * q. It is also very early in the key (the second number, in fact).

Since n = p * q, it follows that q = n / p. Thus, as long as the key is intact up to p, you can derive q by simple division.

Real World Redaction

At this point, I’d like to introduce an acquaintance of mine: Mr. Johan Finn. He is the proud owner of the GitHub repo johanfinn/scripts. For a while, his repo contained a script that contained a poorly-redacted private key. He since deleted it, by making a new commit, but of course because git never really deletes anything, it’s still available.

Of course, Mr. Finn may delete the repo, or force-push a new history without that commit, so here is the redacted private key, with a bit of the surrounding shell script, for our illustrative pleasure:

#Add private key to .ssh folder
cd /home/johan/.ssh/
echo  "-----BEGIN RSA PRIVATE KEY-----
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
ÄÄÄÄÄÄÄÄÄÄÄÄÄÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::.::
:::::::::::::::::::::::::::.::::::::::::::::::::::::::::::::::::
LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLlL
ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ
YYYYYYYYYYYYYYYYYYYYYyYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
gff0GJCOMZ65pMSy3A3cSAtjlKnb4fWzuHD5CFbusN4WhCT/tNxGNSpzvxd8GIDs
nY7exs9L230oCCpedVgcbayHCbkChEfoPzL1e1jXjgCwCTgt8GjeEFqc1gXNEaUn
O8AJ4VlR8fRszHm6yR0ZUBdY7UJddxQiYOzt0S1RLlECggEAbdcs4mZdqf3OjejJ
06oTPs9NRtAJVZlppSi7pmmAyaNpOuKWMoLPElDAQ3Q7VX26LlExLCZoPOVpdqDH
KbdmBEfTR4e11Pn9vYdu9/i6o10U4hpmf4TYKlqk10g1Sj21l8JATj/7Diey8scO
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AvMzXk5OXrUEALUvt84u6m6XZZ0pq5XZxq74s8p/x1JvTwcpJ3jDKNEixlHfdHEZ
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PvJxssLdaWILyp3Ws8Q4RAoC5c0ZP0W2j+5NSbi3jsDFi0Y6/2GRdY1HAZX4twem
Q0NCedq1JNatP1gsb6bcnVHFDEGsj/35oQKCAQEAgmWMuSrojR/fjJzvke6Wvbox
FRnPk+6YRzuYhAP/YPxSRYyB5at++5Q1qr7QWn7NFozFIVFFT8CBU36ktWQ39MGm
cJ5SGyN9nAbbuWA6e+/u059R7QL+6f64xHRAGyLT3gOb1G0N6h7VqFT25q5Tq0rc
Lf/CvLKoudjv+sQ5GKBPT18+zxmwJ8YUWAsXUyrqoFWY/Tvo5yLxaC0W2gh3+Ppi
EDqe4RRJ3VKuKfZxHn5VLxgtBFN96Gy0+Htm5tiMKOZMYAkHiL+vrVZAX0hIEuRZ
JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
-----END RSA PRIVATE KEY-----" >> id_rsa

Now, if you try to reconstruct this key by removing the “obvious” garbage lines (the ones that are all repeated characters, some of which aren’t even valid base64 characters), it still isn’t a key – at least, openssl pkey doesn’t want anything to do with it. The key is very much still in there, though, as we shall soon see.

Using a gem I wrote and a quick bit of Ruby, we can extract a complete private key. The irb session looks something like this:

>> require "derparse"
>> b64 = <<EOF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>> b64 += <<EOF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>> der = b64.unpack("m").first
>> c = DerParse.new(der).first_node.first_child
>> version = c.value
=> 0
>> c = c.next_node
>> n = c.value
=> 80071596234464993385068908004931... # (etc)
>> c = c.next_node
>> e = c.value
=> 65537
>> c = c.next_node
>> d = c.value
=> 58438813486895877116761996105770... # (etc)
>> c = c.next_node
>> p = c.value
=> 29635449580247160226960937109864... # (etc)
>> c = c.next_node
>> q = c.value
=> 27018856595256414771163410576410... # (etc)

What I’ve done, in case you don’t speak Ruby, is take the two “chunks” of plausible-looking base64 data, chuck them together into a variable named b64, unbase64 it into a variable named der, pass that into a new DerParse instance, and then walk the DER value tree until I got all the values I need.

Interestingly, the q value actually traverses the “split” in the two chunks, which means that there’s always the possibility that there are lines missing from the key. However, since p and q are supposed to be prime, we can “sanity check” them to see if corruption is likely to have occurred:

>> require "openssl"
>> OpenSSL::BN.new(p).prime?
=> true
>> OpenSSL::BN.new(q).prime?
=> true

Excellent! The chances of a corrupted file producing valid-but-incorrect prime numbers isn’t huge, so we can be fairly confident that we’ve got the “real” p and q. Now, with the help of another one of my creations we can use e, p, and q to create a fully-operational battle key:

>> require "openssl/pkey/rsa"
>> k = OpenSSL::PKey::RSA.from_factors(p, q, e)
=> #<OpenSSL::PKey::RSA:0x0000559d5903cd38>
>> k.valid?
=> true
>> k.verify(OpenSSL::Digest::SHA256.new, k.sign(OpenSSL::Digest::SHA256.new, "bob"), "bob")
=> true

… and there you have it. One fairly redacted-looking private key brought back to life by maths and far too much free time.

Sorry Mr. Finn, I hope you’re not still using that key on anything Internet-facing.

What About Other Key Types?

EC keys are very different beasts, but they have much the same problems as RSA keys. A typical EC key contains both private and public data, and the public portion is twice the size – so only about 1/3 of the data in the key is private material. It is quite plausible that you can “redact” an EC key and leave all the actually private bits exposed.

What Do We Do About It?

In short: don’t ever try and redact real private keys. For documentation purposes, just put “KEY GOES HERE” in the appropriate spot, or something like that. Store your secrets somewhere that isn’t a public (or even private!) git repo.

Generating a “dummy” private key and sticking it in there isn’t a great idea, for different reasons: people have this odd habit of reusing “demo” keys in real life. There’s no need to encourage that sort of thing.

Technically the pieces aren’t 100% aligned with the underlying DER, because of how base64 works. I felt it was easier to understand if I stuck to chopping up the base64, rather than decoding into DER and then chopping up the DER. ↩

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