Oakley Groups 2 and 14 with OpenSSL (eighty-twenty news)

Yesterday, while experimenting with Diffie-Hellman key exchange as done by the SSH protocol, I discovered (after quite a bit of confusion) that the 1024-bit and 2048-bit parameter groups included with OpenSSL’s Diffie-Hellman implementation are not the same as the 1024-bit “group 2” from RFC 2409 and the 2048-bit “group 14” from RFC 3526! They’re completely unrelated.

Once I discovered this, I spent some time figuring out how to construct PEM files containing the right values formatted appropriately for use with OpenSSL.

If you need to use the “Second Oakley Group” (1024-bit MODP group) from RFC 2409 with OpenSSL, you should load the following parameter file, oakley-group-2.pem, using OpenSSL’s PEM_read_DHparams function:

-----BEGIN DH PARAMETERS-----
MIGHAoGBAP//////////yQ/aoiFowjTExmKLgNwc0SkCTgiKZ8x0Agu+pjsTmyJRSgh5jjQE
3e+VGbPNOkMbMCsKbfJfFDdP4TVtbVHCReSFtXZiXn7G9ExC6aY37WsL/1y29Aa37e44a/ta
iZ+lrp8kEXxLH+ZJKGZR7OZTgf//////////AgEC
-----END DH PARAMETERS-----

If you need to use the 2048-bit MODP group from RFC 3526 with OpenSSL, load the following parameter file, oakley-group-14.pem:

-----BEGIN DH PARAMETERS-----
MIIBCAKCAQEA///////////JD9qiIWjCNMTGYouA3BzRKQJOCIpnzHQCC76mOxObIlFKCHmO
NATd75UZs806QxswKwpt8l8UN0/hNW1tUcJF5IW1dmJefsb0TELppjftawv/XLb0Brft7jhr
+1qJn6WunyQRfEsf5kkoZlHs5Fs9wgB8uKFjvwWY2kg2HFXTmmkWP6j9JM9fg2VdI9yjrZYc
YvNWIIVSu57VKQdwlpZtZww1Tkq8mATxdGwIyhghfDKQXkYuNs474553LBgOhgObJ4Oi7Aei
j7XFXfBvTFLJ3ivL9pVYFxg5lUl86pVq5RXSJhiY+gUQFXKOWoqsqmj//////////wIBAg==
-----END DH PARAMETERS-----

Running the files through openssl asn1parse shows that the contents are the same as the numbers given in the RFCs:

$ openssl asn1parse < oakley-group-2.pem 
0:d=0  hl=3 l= 135 cons: SEQUENCE          
3:d=1  hl=3 l= 129 prim: INTEGER           :FFFFFFFFFFFFFFFFC90FDAA22168C234
C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B
302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED
EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF
  135:d=1  hl=2 l=   1 prim: INTEGER           :02

$ openssl asn1parse < oakley-group-14.pem 
0:d=0  hl=4 l= 264 cons: SEQUENCE          
--------------------------------------------------------------------------------
4:d=1  hl=4 l= 257 prim: INTEGER           :FFFFFFFFFFFFFFFFC90FDAA22168C234
C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B
302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED
EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A
69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D670C354E4ABC9804
F1746C08CA18217C32905E462E36CE3BE39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9
DE2BCBF6955817183995497CEA956AE515D2261898FA051015728E5A8AACAA68FFFFFFFFFFFFFFFF
  265:d=1  hl=2 l=   1 prim: INTEGER           :02