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User:TomYu/PKINIT notes

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(New page: == 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 debug...)
 
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** These primes don't satisfy the OpenSSL DH_check() tests, so there can be some confusion when debugging
 
** 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''.)
 
** 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''.)
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=== D-H number theory ===
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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.
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=== Windows 7 interop ===
   
 
* Windows 7 clients omit the ''q'' value in DomainParameters when sending PA-PK-AS-REQ {{bug|7596}}
 
* Windows 7 clients omit the ''q'' value in DomainParameters when sending PA-PK-AS-REQ {{bug|7596}}

Revision as of 21:10, 10 April 2013

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 = 2q + 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.)
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