Back in January I posed a question "to the Internet": What the heck is RFC 5114?

It looks like a lot happened since then around it. I would like to use this post to recollect some of the stuff around RFC5114 .

RFC5114 draft was submitted to the IETF .

Longer answer: FIPS 186-3 was written about generating values for DSA,

not DH. Now, for DSA, there is a known weakness if the exponents you

use are biased; these algorithms used in FIPS 186-3 were designed to

make sure that the exponents are unbiased (or close enough not to

matter). DH doesn't have similar issues, and so these steps aren't

required (although they wouldn't hurt either).

[...]

For these new groups, (p-1)/q is quite large, and in all three cases,

has a number of small factors (now, NIST could have defined groups where

(p-1)/q has 2 as the only small factor; they declined to do so).

you don't validate the peer value) to effective cut your exponent size

by about 137 bits with using only O(2**42) time);

acceptable.

All this happened toward the first half of the year and the situation was kind of quiet until really recently when Fried et al. released "A kilobit hidden SNFS discrete logarithm computation" that made some people wake up. What is so special about this paper you might ask? An easy explanation can be found in this article. In a nutshell the authors of the paper were able to reuse some theory from the '90s and introduce a backdoor into a 1024 prime such that:

The paper contains a detailed usage of RFC5114 in various protocols: HTTPS, POP3S, IKE. etc and analyzes over 20 open-source cryptographic libraries. For the sake of correctness the paper doesn't focus only on RFC5114 but includes also analysis of non-safe primes usage in the wild. For example

Another thing present in the paper is a complete factorization of group 22 and improved factorization for the other groups:

#
Funnily enough one of the author of RFC5114 was invited to express his point of view

It looks like a lot happened since then around it. I would like to use this post to recollect some of the stuff around RFC5114 .

# Chapter 0: October 2007

RFC5114 draft was submitted to the IETF .

# Chapter I: January 2016

In short RFC5114 is an IETF

**Informational**RTC that "*describes eight Diffie-Hellman groups that can be used in conjunction with IETF protocols to provide security for Internet communications.*" .
One of the thing about this RTC that attracted the attention of many (and also mine) is that violates the Nothing up my sleeve principle.

The other peculiar thing about this RTC (that caught my attention) was that the P

*s*specified for groups 22/23/24 were not safe primes but were indeed DSA primes adapted to Diffie Hellman. So far so good. Except that all the p-1 specified for those groups factored in a really nice way! So I decided to intensify a bit my research and found something here (emphasis mine):

**...a semi-mysterious RFC 5114**– Additional Diffie-Hellman Groups document. It introduces new MODP groups not with higher sizes, but just with different primes.

and

*the odd thing is that when I talked to people in the IPsec community, no one really knew why this document was started. Nothing triggered this document, no one really wanted these, but no one really objected to it either, so the document (originating from Defense contractor BBN) made it to RFC status.*

It was than that I
posted this question in my blog post and other places in the web
(including randombit) hoping for an answer. Well it turned out I got a
pretty decent one (thanks again Paul Wouters BTW!!). This answer was pointing to an old IETF mailing thread that contained a really interesting part (emphasis mine) :

Longer answer: FIPS 186-3 was written about generating values for DSA,

not DH. Now, for DSA, there is a known weakness if the exponents you

use are biased; these algorithms used in FIPS 186-3 were designed to

make sure that the exponents are unbiased (or close enough not to

matter). DH doesn't have similar issues, and so these steps aren't

required (although they wouldn't hurt either).

[...]

For these new groups, (p-1)/q is quite large, and in all three cases,

has a number of small factors (now, NIST could have defined groups where

(p-1)/q has 2 as the only small factor; they declined to do so).

**For**

example, for group 23 (which is the worse of the three), (p-1)/q == 2 *

3 * 3 * 5 * 43 * 73 * 157 * 387493 * 605921 * 5213881177 * 3528910760717

* 83501807020473429349 * C489 (where C489 is a 489 digit composite

number with no small factors).The attacker could use this (again, ifexample, for group 23 (which is the worse of the three), (p-1)/q == 2 *

3 * 3 * 5 * 43 * 73 * 157 * 387493 * 605921 * 5213881177 * 3528910760717

* 83501807020473429349 * C489 (where C489 is a 489 digit composite

number with no small factors).

you don't validate the peer value) to effective cut your exponent size

by about 137 bits with using only O(2**42) time);

**if you used 224 bit**

exponents, then the attacker would cut the work used to find the rest

of the exponent to about O(2**44) time.Obviously, this is notexponents, then the attacker would cut the work used to find the rest

of the exponent to about O(2**44) time.

acceptable.

**NOTE:**it turned out that this factorization listed here is actually wrong (more about it below).

At this point we started to look for some usage of the specification in the wild and with surprisingly we found was kind of commonly used!! In turn it was:

- the default choice for Bouncy Castle and Exim
- OpenSSL has built-in support for RFC5114 in OpenSSL 1.0.2
- and much more...

One of the outcome of this analysis was OpenSSL Key Recovery Attack on DH small subgroups (CVE-2016-0701) (easy explanation in this ArsTechnica article). In turn we had:

- OpenSSL fixing the vulnerability by adding validation of the DH parameters
- While BoringSSL was not affected by it (due the deprecation of SSL_OP_SINGLE_DH_USE done many months in advance) they decided to also add validation of the DH parameters
- Amazon also added validation of the DH parameters

# Interlude: February 2016- June 2016

In the meantime another news came into the game. It was indeed discovered that Socat (a versatile command line utility that builds bi-directional communication) contained an hard-coded Diffie-Hellman 1024-bit prime number that was NOT prime!! This story is covered here. All this brought David Wong to write "How to Backdoor Diffie-Hellman"

# Chapter II: October 2016

All this happened toward the first half of the year and the situation was kind of quiet until really recently when Fried et al. released "A kilobit hidden SNFS discrete logarithm computation" that made some people wake up. What is so special about this paper you might ask? An easy explanation can be found in this article. In a nutshell the authors of the paper were able to reuse some theory from the '90s and introduce a backdoor into a 1024 prime such that:

- it would be
*feasible*for the creator of the backdoor to calculate discrete log - it would be impossible for anybody else to prove that this particular number was actually backdoored!

- Exim moved away from RFC5114
- ...same for LibreSwan
- Watson Ladd started wondering if is the case to write an rfc5114-die-die-die

The paper contains a detailed usage of RFC5114 in various protocols: HTTPS, POP3S, IKE. etc and analyzes over 20 open-source cryptographic libraries. For the sake of correctness the paper doesn't focus only on RFC5114 but includes also analysis of non-safe primes usage in the wild. For example

**Amazon ELB**was also found to be partially vulnerable while it was not using RFC5114 :

*"...We were able to use a small-subgroup key recovery attack to compute 17 bits of our load balancer’s private Diffie-Hellman exponent..." .*

Another thing present in the paper is a complete factorization of group 22 and improved factorization for the other groups:

## Comments

https://www.bouncycastle.org/devmailarchive/msg14882.html

Gruss

Bernd