Monday
Sep182006
RSA Signature Forgery Explained (with Nate Lawson) - Part IV
Sep 18, 2006 at 3:16PM Thomas Ptacek
[«Previous: The Attack][p3] | [Top][] | [Next: Eight Other Attacks»][p5]
**Analysis of the patch timeline**
This section works better if we tell it starting from the future and
working backwards. But the future hasn't happened yet. And we don't
know what goes on inside the various software teams. So, like ABC's
Path to 9/11, some of this episode is fictionalized for dramatic
purposes. But the lessons are real.
## Winter 2006
At last, the RSA cleanup work seems complete. The obvious crypto
libraries, commercial applications, and hardware accelerators have
swept their code, in some cases furiously rewriting it to avoid
pernicious variants of the attack.
RSA implementers have a new mantra: "byte-compare against good, don't
parse for bad." It's not sexy, but the simplest approach for checking
a signature is also the best way to eliminate variability, the source
of these security flaws.
It works like this. You're given an RSA signature *S_received*, of modulus size *N*
and hash type *T* over the data *D*. You:
1. Perform an RSA public key operation on *S_received*, turning the
signature into a message block.
2. Match the modulus *N* to a template based on its length (1024,
2048, 4096 bits, etc).
3. Look up the appropriate *algorithm identifier* for your hash
algorithm *T* (SHA1, SHA256).
4. Hash the data *D* using that algorithm
5. Copy the template, algorithm identifier and hash result to a new
buffer *S_expected*
6. Byte-compare *S_received* and *S_expected*.
7. If there is any difference, return "signature verify failed"
There are a few variations. Some RSA code lives in smart cards or
small embedded computers. They only support one modulus size and one
hash type. They skip steps 2 and 3. All they have to do is copy the hash
result directly into a template and compare it against *S_received*.
How did we wind up here? The old approach added checks for bad fields
in signatures. Lots of checks. For every aspect of the padding or the
digest information that could possibly go wrong. It was very hard to
review for correctness. Like a rev1 beta PHP application deployed in
the wild for the first time, no one was sure every bit was validated
for every possible signature an attacker could send.
Since this approach is so simple and obviously correct, projects like
Python's [tlslite][tlslite], [GPG][gpg], and new work from OpenSSL progenitor Eric Young
already used it ([at least for his 2nd time around][eay]). But it took time
for the lesson to sink in for everyone else.
## 2006/9/18
People stopped calling the RSA signature attack the "e=3 problem",
realizing the exponent wasn't really the problem. Calling out one
instance of an implementation problem handling RSA signatures was like
calling all buffers overflows "strcpy() attacks". "e=3" wasn't the
problem. If you did RSA properly, e=3 (and higher exponents) were
closely related to e=2, [and e=2 is provably as secure as factoring][e2]
N. If you did RSA wrong, it [didn't matter what your exponent was][exp].
For example, e=17 was also vulnerable if you used a 4096 bit modulus
and the implementation only checked the SHA1 hash (or also up to 10
other bytes).
However, we have started eliminating the few e=3 root
certificates. That was a good idea. There was no way we were picking
up the millions of pieces of all the broken deployments, and PCs were
plenty fast with e=65537 even 10 years ago. (A 33 MHz machine can do
dozens of verifies per second with a 1024 bit key.)
## 2006/9/15
[Firefox is vulnerable to the same 2 flaws in OpenSSL][firefox], although NSS is
a different codebase. They took the [same approach to fixing][fffix] the
problem as OpenSSL -- check for the number of 0xFF bytes and look for
a bad "parameters" field.
[Opera and Konqueror][opera], both of which used OpenSSL, also turned out to be
vulnerable.
[Did we mention phishing?][phish]
## 2006/9/6
[OpenSSL backed out part of their fix today][change]. They figured they could spot forged
signature results by the way they looked -- the padding would be very
short. In particular, if the hash and its ASN.1 metadata added up to
more than 1/3 the modulus size, then the padding must be less than 2/3
the total, suggesting hash had been shifted to the left by an attacker.
However, with a modulus of 840 bits or less, this check would reject
all valid signatures also. (SHA1 OID + hash = 35 bytes * 3 = 105
bytes or 840 bits.)
A special case was added to handle this as well.
The check returned a distinct error value ("signature too small") as
opposed to a general "signature verify failed". Believe it or not,
even the specificity of your error messages can be used to break your
crypto. [Bleichenbacher used distinguishing error messages in 1998][oracle] as
an oracle to attack Netscape's RSA encryption. Fortunately, since this
was signature verification, and not decryption, the data being handled
was ostensibly "public"; nothing would be gained by an attacker
knowing what part of a signature was found corrupt.
However, in embedded cryptosystems, attackers can often
[glitch a private key operation][glitch] and from it, recover the private key. One of the
defenses against this is to always check the signature with the public
key before exposing it (this discards faulty results before they're
revealed to an attacker). By leaking small bits of information about
that faulty computation via the signature library's error codes, this approach may have been problematic in such embedded environments.
Since the other half of the original patch was essential and this
approach of looking for bad data was fundamentally flawed, this code
was backed out.
## 2006/9/5
In response to Bleichenbacher's attack, [OpenSSL just checked in a fix][ossl].
It actually patches 2 flaws. The first is already being discussed to
death on mailing lists and blogs (varying the number of 0xFF bytes).
The second is just starting to be discussed as
[it also applied to gnutls][gnutls] (varying the bytes in the encoded hash algorithm type).
The patch is simple. It adds 2 more checks of the padding format:
Unfortunately, it's not clear that this covers all the possible
variability that a future attacker might exploit. **Any amount of
unchecked or variable data in the signature can potentially be
leveraged by an attacker**, especially as the underlying cryptanalytic
attacks evolve. Also, because these patches are implemented as
point-checks for specific bad cases, it's very hard to verify that
they are correct and complete.
Instead of trying to parse the potentially malicious signature, why
doesn't everyone just generate a template of what the signature should
look like and byte-compare it?
[Next: Eight Other Attacks»][p5]
[p7]:/log/531/rsa-signature-forgery-explained-with-nate-lawson-wrapup/
[p6]:/log/528/rsa-signature-forgery-explained-with-nate-lawson-part-vi/
[p5]:/log/513/rsa-signature-forgery-explained-with-nate-lawson-part-v/
[p4]:/log/501/rsa-signature-forgery-explained-with-nate-lawson-part-iv/
[p3]:/log/489/rsa-signature-forgery-explained-with-nate-lawson-part-iii/
[p2]:/log/487/rsa-signature-forgery-explained-with-nate-lawson-part-ii/
[p1]:/log/486/rsa-signature-forgery-explained-with-nate-lawson-part-i/
[change]: http://cvs.openssl.org/chngview?cn=15536
[opera]: http://marc.theaimsgroup.com/?l=cryptography&m=115836115228365&w=2
[gnutls]: http://lists.gnupg.org/pipermail/gnutls-dev/2006-September/001205.html
[ossl]: http://cvs.openssl.org/chngview?cn=15513
[glitch]: http://citeseer.ist.psu.edu/491209.html
[oracle]: http://citeseer.ist.psu.edu/bleichenbacher98chosen.html
[fffix]: http://lxr.mozilla.org/security/source/security/nss/lib/cryptohi/secvfy.c
[firefox]: http://www.mozilla.org/security/announce/2006/mfsa2006-60.html
[tlslite]: http://sourceforge.net/projects/tlslite/
[e2]: http://www.cacr.math.uwaterloo.ca/hac/about/chap8.pdf
[exp]: http://marc.theaimsgroup.com/?l=cryptography&m=115850665318184&w=2
[gpg]: http://marc.theaimsgroup.com/?l=cryptography&m=115834040518036
[eay]: http://marc.theaimsgroup.com/?l=cryptography&m=115806018302825&w=2
[phish]:
/log/489/rsa-signature-forgery-explained-with-nate-lawson-part-iii/
[top]: /log/558/public-key-signature-forgery-collected/
**Analysis of the patch timeline**
This section works better if we tell it starting from the future and
working backwards. But the future hasn't happened yet. And we don't
know what goes on inside the various software teams. So, like ABC's
Path to 9/11, some of this episode is fictionalized for dramatic
purposes. But the lessons are real.
## Winter 2006
At last, the RSA cleanup work seems complete. The obvious crypto
libraries, commercial applications, and hardware accelerators have
swept their code, in some cases furiously rewriting it to avoid
pernicious variants of the attack.
RSA implementers have a new mantra: "byte-compare against good, don't
parse for bad." It's not sexy, but the simplest approach for checking
a signature is also the best way to eliminate variability, the source
of these security flaws.
It works like this. You're given an RSA signature *S_received*, of modulus size *N*
and hash type *T* over the data *D*. You:
1. Perform an RSA public key operation on *S_received*, turning the
signature into a message block.
2. Match the modulus *N* to a template based on its length (1024,
2048, 4096 bits, etc).
3. Look up the appropriate *algorithm identifier* for your hash
algorithm *T* (SHA1, SHA256).
4. Hash the data *D* using that algorithm
5. Copy the template, algorithm identifier and hash result to a new
buffer *S_expected*
6. Byte-compare *S_received* and *S_expected*.
7. If there is any difference, return "signature verify failed"
There are a few variations. Some RSA code lives in smart cards or
small embedded computers. They only support one modulus size and one
hash type. They skip steps 2 and 3. All they have to do is copy the hash
result directly into a template and compare it against *S_received*.
How did we wind up here? The old approach added checks for bad fields
in signatures. Lots of checks. For every aspect of the padding or the
digest information that could possibly go wrong. It was very hard to
review for correctness. Like a rev1 beta PHP application deployed in
the wild for the first time, no one was sure every bit was validated
for every possible signature an attacker could send.
Since this approach is so simple and obviously correct, projects like
Python's [tlslite][tlslite], [GPG][gpg], and new work from OpenSSL progenitor Eric Young
already used it ([at least for his 2nd time around][eay]). But it took time
for the lesson to sink in for everyone else.
## 2006/9/18
People stopped calling the RSA signature attack the "e=3 problem",
realizing the exponent wasn't really the problem. Calling out one
instance of an implementation problem handling RSA signatures was like
calling all buffers overflows "strcpy() attacks". "e=3" wasn't the
problem. If you did RSA properly, e=3 (and higher exponents) were
closely related to e=2, [and e=2 is provably as secure as factoring][e2]
N. If you did RSA wrong, it [didn't matter what your exponent was][exp].
For example, e=17 was also vulnerable if you used a 4096 bit modulus
and the implementation only checked the SHA1 hash (or also up to 10
other bytes).
However, we have started eliminating the few e=3 root
certificates. That was a good idea. There was no way we were picking
up the millions of pieces of all the broken deployments, and PCs were
plenty fast with e=65537 even 10 years ago. (A 33 MHz machine can do
dozens of verifies per second with a 1024 bit key.)
## 2006/9/15
[Firefox is vulnerable to the same 2 flaws in OpenSSL][firefox], although NSS is
a different codebase. They took the [same approach to fixing][fffix] the
problem as OpenSSL -- check for the number of 0xFF bytes and look for
a bad "parameters" field.
[Opera and Konqueror][opera], both of which used OpenSSL, also turned out to be
vulnerable.
[Did we mention phishing?][phish]
## 2006/9/6
[OpenSSL backed out part of their fix today][change]. They figured they could spot forged
signature results by the way they looked -- the padding would be very
short. In particular, if the hash and its ASN.1 metadata added up to
more than 1/3 the modulus size, then the padding must be less than 2/3
the total, suggesting hash had been shifted to the left by an attacker.
However, with a modulus of 840 bits or less, this check would reject
all valid signatures also. (SHA1 OID + hash = 35 bytes * 3 = 105
bytes or 840 bits.)
A special case was added to handle this as well.
The check returned a distinct error value ("signature too small") as
opposed to a general "signature verify failed". Believe it or not,
even the specificity of your error messages can be used to break your
crypto. [Bleichenbacher used distinguishing error messages in 1998][oracle] as
an oracle to attack Netscape's RSA encryption. Fortunately, since this
was signature verification, and not decryption, the data being handled
was ostensibly "public"; nothing would be gained by an attacker
knowing what part of a signature was found corrupt.
However, in embedded cryptosystems, attackers can often
[glitch a private key operation][glitch] and from it, recover the private key. One of the
defenses against this is to always check the signature with the public
key before exposing it (this discards faulty results before they're
revealed to an attacker). By leaking small bits of information about
that faulty computation via the signature library's error codes, this approach may have been problematic in such embedded environments.
Since the other half of the original patch was essential and this
approach of looking for bad data was fundamentally flawed, this code
was backed out.
## 2006/9/5
In response to Bleichenbacher's attack, [OpenSSL just checked in a fix][ossl].
It actually patches 2 flaws. The first is already being discussed to
death on mailing lists and blogs (varying the number of 0xFF bytes).
The second is just starting to be discussed as
[it also applied to gnutls][gnutls] (varying the bytes in the encoded hash algorithm type).
The patch is simple. It adds 2 more checks of the padding format:
- Verify the number of 0xFF bytes is correct
- Check that the optional "parameters" ASN.1 extension is either:
- Not present
- Set to the special value V_ASN1_NULL
Unfortunately, it's not clear that this covers all the possible
variability that a future attacker might exploit. **Any amount of
unchecked or variable data in the signature can potentially be
leveraged by an attacker**, especially as the underlying cryptanalytic
attacks evolve. Also, because these patches are implemented as
point-checks for specific bad cases, it's very hard to verify that
they are correct and complete.
Instead of trying to parse the potentially malicious signature, why
doesn't everyone just generate a template of what the signature should
look like and byte-compare it?
[Next: Eight Other Attacks»][p5]
[p7]:/log/531/rsa-signature-forgery-explained-with-nate-lawson-wrapup/
[p6]:/log/528/rsa-signature-forgery-explained-with-nate-lawson-part-vi/
[p5]:/log/513/rsa-signature-forgery-explained-with-nate-lawson-part-v/
[p4]:/log/501/rsa-signature-forgery-explained-with-nate-lawson-part-iv/
[p3]:/log/489/rsa-signature-forgery-explained-with-nate-lawson-part-iii/
[p2]:/log/487/rsa-signature-forgery-explained-with-nate-lawson-part-ii/
[p1]:/log/486/rsa-signature-forgery-explained-with-nate-lawson-part-i/
[change]: http://cvs.openssl.org/chngview?cn=15536
[opera]: http://marc.theaimsgroup.com/?l=cryptography&m=115836115228365&w=2
[gnutls]: http://lists.gnupg.org/pipermail/gnutls-dev/2006-September/001205.html
[ossl]: http://cvs.openssl.org/chngview?cn=15513
[glitch]: http://citeseer.ist.psu.edu/491209.html
[oracle]: http://citeseer.ist.psu.edu/bleichenbacher98chosen.html
[fffix]: http://lxr.mozilla.org/security/source/security/nss/lib/cryptohi/secvfy.c
[firefox]: http://www.mozilla.org/security/announce/2006/mfsa2006-60.html
[tlslite]: http://sourceforge.net/projects/tlslite/
[e2]: http://www.cacr.math.uwaterloo.ca/hac/about/chap8.pdf
[exp]: http://marc.theaimsgroup.com/?l=cryptography&m=115850665318184&w=2
[gpg]: http://marc.theaimsgroup.com/?l=cryptography&m=115834040518036
[eay]: http://marc.theaimsgroup.com/?l=cryptography&m=115806018302825&w=2
[phish]:
/log/489/rsa-signature-forgery-explained-with-nate-lawson-part-iii/
[top]: /log/558/public-key-signature-forgery-collected/
Reader Comments (14)
Are the commercial CAs which deployed e=3 root certs (Entrust,
Digital Signature Trust Co.IdenTrust, others?) known to be doing anything about this snafu?Interesting Finds: September 18, 2006
Great summary Thomas, thanks for taking the time to fill in the blanks.
nice. :-)
I am by no means a security specialist, but I love your blog and find it VERY interesting. Keep up the excelent work.
-Emmanuel
Matt:
I'm unaware of any changes in the root certs. We won't know for another 3-6 months, my guess. It takes a while for them to make a CRL, get it into IE and Firefox, etc.
The tone we used was more one of wishful thinking than future certainty. :)
[...] «Previous: Why Public Key Is Hard | [Top][] | Next: Bad Patches» [...]
[...] How to fix the problem properly and a wishful analysis of how the repair process might have been [...]
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