Question

From what I can see, Microsoft’s RSA CSP always generates identical bitlength pseudo prime numbers. So if the key size is 1024, the P and Q values seem to be (?) guaranteed to be 512 bits each? Does anyone know for sure if this, in fact, is the case?

I’m building an interoperability module between my own RSA implementation and Microsoft’s. In my case I have built in a small random variance between P & Q values so for 1024 bit key I could end up with one value being 506 bits and the other 518. On purely experimental basis, if I lock the variance to 0 (i.e. the P & Q values are equal in size) — Things work the way they should, I soon as I make the size variable Microsoft RSA object responds with “Bad Data” during import process.

I’m looking for a confirmation that Microsoft enforces equal key sizes, so if anyone has any information on it, please post

Before someone has a chance to ask why I had to implement my own RSA provider : CryptoAPI doesn’t play nice in a multithreaded environment, it locks the machine keystore on CryptoServiceProvider calls; which means “File not found” (rather cryptic) errors if accessed from multiple threads

For those that care, take a look here: http://blogs.msdn.com/b/alejacma/archive/2007/12/03/rsacryptoserviceprovider-fails-when-used-with-asp-net.aspx

Answer 1

Microsoft’s RSA CSP generates and uses private keys which it can export and import in the format described on this page, and looks like this:

BLOBHEADER blobheader;
RSAPUBKEY rsapubkey;
BYTE modulus[rsapubkey.bitlen/8];
BYTE prime1[rsapubkey.bitlen/16];
BYTE prime2[rsapubkey.bitlen/16];
BYTE exponent1[rsapubkey.bitlen/16];
BYTE exponent2[rsapubkey.bitlen/16];
BYTE coefficient[rsapubkey.bitlen/16];
BYTE privateExponent[rsapubkey.bitlen/8];

So private keys that the CSP can handle (and in particular generate) must have the following properties:

• The modulus length, in bits, must be a multiple of 16.
• The length of each prime factor must be no more than half the length of the modulus.
• The private exponent must not be longer than the modulus.
• The private exponent, reduced modulo p-1 (resp. q-1) must be no longer than half the modulus.

Technically, there are infinitely many possible values for the private exponent d, and similarly for exponent1 and exponent2 because all that mathematically matters are the value of d modulo p-1 and q-1; it has been suggested to accept slightly longer private exponent parts if they end up with a lower Hamming weight, because this would lead to some performance benefits. Bottom-line: the format described above will not let you do that.

Other characteristics that the key must have to be acceptable to Microsoft’s code (but not directly reported in the description above):

• The numerical value of the first prime (p, aka prime1) must be greater than the numerical value of the second prime (q, aka prime2).
• The public exponent (here encoded within the rsapubkey field) must fit in a 32-bit integer (unsigned).

Therefore there are many RSA key pairs which are nominally valid as per the RSA standard, but which cannot be handled by Microsoft RSA CSP code. Noteworthy is the last constraint, on the public exponent size: this means that the constraint is more general than just the CSP; if you setup a SSL server where the server’s public key (in its certificate) has a public exponent which does not fit in 32 bits, then Internet Explorer will not be able to connect to it.

So, in practice, if you generate RSA key pairs, you will have to make sure that they comply with the rules above. Do not worry: to the best of our knowledge, these rules do not lower security.