The Private Lives of Private Keys Here is what a typical private key looks like, when you come across it:

-----BEGIN RSA PRIVATE KEY-----
MGICAQACEQCxjdTmecltJEz2PLMpS4BXAgMBAAECEDKtuwD17gpagnASq1zQTYEC
CQDVTYVsjjF7IQIJANUYZsIjRsR3AgkAkahDUXL0RSECCB78r2SnsJC9AghaOK3F
sKoELg==
-----END RSA PRIVATE KEY-----

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:

-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

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
 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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::.::
:::::::::::::::::::::::::::.::::::::::::::::::::::::::::::::::::
LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLlL
 
 
 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-----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.

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1. 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.