# User:TomYu/PKINIT notes

From K5Wiki

## Diffie-Hellman

- Oakley MODP groups (used in PKINIT) have safe primes as moduli
- These primes don't satisfy the OpenSSL DH_check() tests, so there can be some confusion when debugging
- The generator generates the subgroup of order
*q*instead of the whole group. (OpenSSL wants it to generate the whole group -- the test is*p*= 11 mod 24, which includes the test*p*= 3 mod 8, which is false if 2 is a quadratic residue mod*p*.)

### D-H number theory

Safe prime *p* = 2*q* + 1, where *q* is prime. To be cryptographically useful, *p* is a large odd prime, therefore *p* ≡ 1 (mod 2). Also, *p* ≡ 2 (mod 3), as is *q*, because one being congruent to 1 mod 3 implies the other is divisible by 3. (This is only true if *q* ≠ 3.) By Chinese Remainder Theorem, this means *p* ≡ 5 (mod 6). 2 generates the subgroup of size *q* if 2 is a quadratic residue mod *p*. For 2 to be a quadratic residue mod *p*, it must be ±1 mod 8, and it can't be 1 mod 8 because that would mean that *q* is not prime.

### Windows 7 interop

- Windows 7 clients omit the
*q*value in DomainParameters when sending PA-PK-AS-REQ [krbdev.mit.edu #7596] - Even after allowing the omission of the
*q*value, Windows 7 doesn't seem to deal with Diffie-Hellman group negotiation. (The KDC has to accept the 1024-bit modulus, because the counterproposal of the 2048-bit modulus fails on the client somehow.)