Weak Diffie-Hellman Parameters


Not a long time ago a friend of mine told me that the nginx at duckpond.ch is using 1024 bit standard DH parameters.

ssl lab-weak ciphers SSL-Lab: weak key negotiation because of standard DH parameters

Eww, after being at the 32c3-logjam talk I should have known better. So let’s have some fun with DH before changing the parameters to something (hopefully) more secure.

Openssl is fat and messy and I don’t particularly like their man pages 1. This is why I started reading some blogs. I really like the step by step instructions by steven gordon. Following steven’s blog I defined a plan of action:

  1. Extracting parameters from duckpond.ch.
  2. Generate private random for these parameters.
  3. Perform a DH-key agreement with duckpond.ch using s_client with the just generated private random . Our goal is to agree with duckpond on a pre-master secret with: \begin{equation} k_{0} \equiv g^{r_{c} r_{s}} \pmod{p} \end{equation}
  4. Derive the master secret from the calculated pre-master secret . \begin{equation} k = kdf(k_{0}) \end{equation}
  5. Try to solve in order to get back.

Extracting parameters

Extracting the parameters from duckpond.ch: 2

In : g = 2 
In : p = 0xbbbc2dcad84674907c43fcf580e9cfdbd958a3f568b42d4b08eed4eb0fb3504c6c030276e710800c5ccbbaa8922614c5beeca565a5fdf1d287a2bc049be6778060e91a92a757e3048f68b076f7d36cc8f29ba5df81dc2ca725ece66270cc9a5035d8ceceef9ea0274a63ab1e58fafd4988d0f65d146757da071df045cfe16b9b

checking that I got the whole 1024-bit prime:

In : log(p)/log(2)
Out: 1023.552554397631

Openssl works with a PEM 3 encoded parameters file. Thus we’ve to pack our prime modulo and generator in an ASN.1 encoded representation. I could not find a way using Openssl to generate a arbitrary parameters file. This means I had to “reverse” 4 the PEM data, using Lapo Luchini’s ASN.1 decoder. It’s not rocket science; the following python script generates a PEM 5 for an arbitrary (first argument), (second argument) combination.

#!/usr/bin/env python
import sys
import base64
import textwrap
from math import *

from pyasn1.type import univ
from pyasn1.codec.ber import encoder

def usage():
    """print usage"""
    print(  """Usage: {} prime generator
    NOTE: Numbers in hexadecimal""".format(sys.argv[0]))
    sys.exit(-1)

PEM_LINE_LENGTH = 64 - 1 # -1 because of \n
def pem_lines(m):
    """Yield successive lines of PEM body for bytearray m"""
    m = base64.b64encode(m).decode('ascii')
    for i in range(0, len(m), PEM_LINE_LENGTH):
        yield m[i:i+PEM_LINE_LENGTH]

if len(sys.argv) != 3:
    usage()

(_, prime, generator) = sys.argv
prime = int(prime, 16)
generator = int(generator,16)

m = encoder.encode(
        univ.Sequence().setComponents(
            univ.Integer(prime),
            univ.Integer(generator)
        )
    )

print('-----BEGIN DH PARAMETERS-----')
[print(l) for l in pem_lines(m)]
print('-----END DH PARAMETERS-----')

Using the script:

$ ./pem-dhgen.py 0x2 0xbbbc2dcad84674907c43fcf580e9cfdbd958a3f568b42d4b08eed4eb0fb3504c6c030276e710800c5ccbbaa8922614c5beeca565a5fdf1d287a2bc049be6778060e91a92a757e3048f68b076f7d36cc8f29ba5df81dc2ca725ece66270cc9a5035d8ceceef9ea0274a63ab1e58fafd4988d0f65d146757da071df045cfe16b9b
-----BEGIN DH PARAMETERS-----
MIGHAgECAoGBALu8LcrYRnSQfEP89YDpz9vZWKP1aLQtSwju1OsPs1BMbAMCduc
QgAxcy7qokiYUxb7spWWl/fHSh6K8BJvmd4Bg6RqSp1fjBI9osHb302zI8pul34
HcLKcl7OZicMyaUDXYzs7vnqAnSmOrHlj6/UmI0PZdFGdX2gcd8EXP4Wub
-----END DH PARAMETERS-----

Generate

The generated PEM can be used for Openssl’s genpkey command 6.

$ openssl genpkey -paramfile dhp.pem -text
-----BEGIN PRIVATE KEY-----
MIIBIQIBADCBlQYJKoZIhvcNAQMBMIGHAoGBALu8LcrYRnSQfEP89YDpz9vZWKP1
aLQtSwju1OsPs1BMbAMCducQgAxcy7qokiYUxb7spWWl/fHSh6K8BJvmd4Bg6RqS
p1fjBI9osHb302zI8pul34HcLKcl7OZicMyaUDXYzs7vnqAnSmOrHlj6/UmI0PZd
FGdX2gcd8EXP4WubAgECBIGDAoGAfDxqaNChsZaQuJ9W/o/Jh0J6HmaOOrrHl4d9
W5rRR4XsT8IVIeuD3fQo6TXWn5y8ULngmVs+WiKLZRtO35N4Uu1z45bFutdTcuu/
rMbm5WVknaHH/6K5ygBRQD4d0FW9KxywwFnPGyD3lBlyGpqUgA/EDF+02Il+Y5ho
Qpi8VHA=
-----END PRIVATE KEY-----
DH Private-Key: (1024 bit)
    private-key:
        7c:3c:6a:68:d0:a1:b1:96:90:b8:9f:56:fe:8f:c9:
        87:42:7a:1e:66:8e:3a:ba:c7:97:87:7d:5b:9a:d1:
        47:85:ec:4f:c2:15:21:eb:83:dd:f4:28:e9:35:d6:
        9f:9c:bc:50:b9:e0:99:5b:3e:5a:22:8b:65:1b:4e:
        df:93:78:52:ed:73:e3:96:c5:ba:d7:53:72:eb:bf:
        ac:c6:e6:e5:65:64:9d:a1:c7:ff:a2:b9:ca:00:51:
        40:3e:1d:d0:55:bd:2b:1c:b0:c0:59:cf:1b:20:f7:
        94:19:72:1a:9a:94:80:0f:c4:0c:5f:b4:d8:89:7e:
        63:98:68:42:98:bc:54:70
    public-key:
        5c:59:23:8c:0b:09:78:f3:8f:db:f0:15:c1:2d:da:
        e1:f7:ca:a5:8c:42:e0:ff:29:da:33:ae:89:6d:cb:
        78:d4:3e:0d:11:79:5c:82:f2:8d:27:bb:ca:12:fb:
        22:ef:de:48:c3:00:0d:e7:a3:0d:3e:61:3d:0d:d8:
        82:bb:16:d7:73:94:f3:1c:54:39:de:cd:d9:c9:38:
        55:95:d3:d0:b5:aa:9f:66:01:56:29:00:6b:04:bb:
        22:a6:66:16:51:d1:44:32:60:04:5a:2b:7b:c5:a8:
        70:25:2d:40:07:d3:46:fe:62:1f:5d:2c:bb:24:c9:
        50:7a:54:d3:a9:e2:62:18
    prime:
        00:bb:bc:2d:ca:d8:46:74:90:7c:43:fc:f5:80:e9:
        cf:db:d9:58:a3:f5:68:b4:2d:4b:08:ee:d4:eb:0f:
        b3:50:4c:6c:03:02:76:e7:10:80:0c:5c:cb:ba:a8:
        92:26:14:c5:be:ec:a5:65:a5:fd:f1:d2:87:a2:bc:
        04:9b:e6:77:80:60:e9:1a:92:a7:57:e3:04:8f:68:
        b0:76:f7:d3:6c:c8:f2:9b:a5:df:81:dc:2c:a7:25:
        ec:e6:62:70:cc:9a:50:35:d8:ce:ce:ef:9e:a0:27:
        4a:63:ab:1e:58:fa:fd:49:88:d0:f6:5d:14:67:57:
        da:07:1d:f0:45:cf:e1:6b:9b
    generator: 2 (0x2)

Well, that was easy…

Key agreement

The I used s_client with the just generated private key and recorded the ssl-handshake: 7

$ openssl s_client -connect duckpond.ch:443 -cipher DHE-RSA-AES256-SHA256 -key dhkey.pem 

[...]

---
New, TLSv1/SSLv3, Cipher is DHE-RSA-AES256-SHA256
Server public key is 4096 bit
Secure Renegotiation IS supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
    Protocol  : TLSv1.2
    Cipher    : DHE-RSA-AES256-SHA256
    Session-ID: A137EBD4BC7E0407C9EE1C2C3DFAEF372B582F6434B6ED5A18C5121293F14484
    Session-ID-ctx: 
    Master-Key: DABAC095DD28532DF643F4BA7476D194851E64F75BCE4C5EADA2906B702B1F758BB15FED4A37DB2682791D9ACA629DDA
    Key-Arg   : None
    PSK identity: None
    PSK identity hint: None

[...]

After this I extracted the transmitted from the ssl-handshake:

In : gr_c = 0xac5b13ac2d295e8779d1beca26c06f54071d804dd82914160941732f6252875ac61704b925f2e540fead8ef29cc678604cf060f49ca9b5008aa5763ffcf0cced3271000c3ecf7b089e05dd506a9ca9e438c75db80da2a93c6081a5412

and realized that I fucked up. Ephemeral DH (DHE) uses a new for every connection. Which is a good thing to do, but for now very annoying. DHE makes it hard to reproduce results. Attaching a debugger quickly revealed that Openssl does load the provided DH-parameters but is not using them once the Client Key Exchange-message is generated. So I patched Openssl’s crypto/dh/dh_key.c:generate_key() and made it always return the first loaded key 8. The first loaded key is the one we provide via the ‘-key’ parameter:

diff --git a/crypto/dh/dh_key.c b/crypto/dh/dh_key.c
index 9b79f39..2c22b46 100644
--- a/crypto/dh/dh_key.c
+++ b/crypto/dh/dh_key.c
@@ -70,6 +70,7 @@ static int generate_key(DH *dh)
     BN_CTX *ctx;
     BN_MONT_CTX *mont = NULL;
     BIGNUM *pub_key = NULL, *priv_key = NULL;
+    static DH *static_dh;
 
     ctx = BN_CTX_new();
     if (ctx == NULL)
@@ -145,6 +146,12 @@ static int generate_key(DH *dh)
     if (priv_key != dh->priv_key)
         BN_free(priv_key);
     BN_CTX_free(ctx);
+    // hack: always reuse same dh parameters
+    if(static_dh == NULL){
+        static_dh = dh;
+    }else{
+        (*dh) = (*static_dh);
+    }
     return (ok);
 }

Re-running the ssl-handshake2 using the patched Openssl version:

$ openssl s_client -connect duckpond.ch:443 -cipher DHE-RSA-AES256-SHA256 -key dhkey.pem 

[...]

---
New, TLSv1.2, Cipher is DHE-RSA-AES256-SHA256
Server public key is 4096 bit
Secure Renegotiation IS supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
    Protocol  : TLSv1.2
    Cipher    : DHE-RSA-AES256-SHA256
    Session-ID: 2D9161954D7998884AC496BE16085C7200D36773B83C97746D50B756FF7F3F2B
    Session-ID-ctx: 
    Master-Key: 403247E9625BE70E2AC4076297B48A18178696404FC7FFCD924ECAA5628FDBA049DFBD4170F65ACBC6A84AA18696144A
    PSK identity: None
    PSK identity hint: None

[...]

And extracting the from the new ssl-handshake2:

g_rc = 0x5c59238c0b0978f38fdbf015c12ddae1f7caa58c42e0ff29da33ae896dcb78d43e0d11795c82f28d27bbca12fb22efde48c3000de7a30d3e613d0dd882bb16d77394f31c5439decdd9c9385595d3d0b5aa9f66015629006b04bb22a6661651d1443260045a2b7bc5a870252d4007d346fe621f5d2cbb24c9507a54d3a9e26218

Finally the is the same as the just generated public-key. Which means the we should be able to compute the using the known private key :

In : r_c = 0x7c3c6a68d0a1b19690b89f56fe8fc987427a1e668e3abac797877d5b9ad14785ec4fc21521eb83ddf428e935d69f9cbc50b9e0995b3e5a228b651b4edf937852ed73e396c5bad75372ebbfacc6e6e565649da1c7ffa2b9ca0051403e1dd055bd2b1cb0c059cf1b20f79419721a9a94800fc40c5fb4d8897e6398684298bc5470
In : pow(g, r_c, p) == g_rc
Out: True

Yayy! From here it should be straight forward to calculate the pre-master secret .

\begin{equation} k_{0} \equiv g^{r_{c} r_{s}} \equiv g^{r_{s}^{r_{c}}} \pmod{p} \end{equation}

The only thing we need for this is the server public key which is easy to extract from the ssl-handshake2:

In : g_rs = 0x3f2be9298aa84d6889dcfbd1a0bb0788a440b81f5b5b5d948174c6a1daf729d8f760ecf5363cdbee460ceee8f8b64d8a1710c61a9a8b9f043570e6a17ce0846f1af6a215dd4c5dd2e567547345cd9b9ef24af8791060f2e7451f11735f64d3b80d1d2253587ca3c5676ed3f1c84e96d32d9766607811a9996e802cacc4b97f05
In : k0 = pow(g_rs, r_c, p)

Now I’m in perfect shape for step 4 and 5 which I’ll do in a follow-up.

  1. If somebody can point out a good cheat-sheet I’d be soooo happy. 

  2. By capturing an ssl-handshake

  3. I’ve no idea what this has to do with mail. 

  4. The ASN.1 standard is even more cumbersome than Openssl manpages. 

  5. Append it to all the MAIL! 

  6. So that you can send it to your friends via mail. 

  7. Yes, I restarted the web server and client after doing this. 

  8. Don’t do this at home.