Re: Should openssl accept weak DSA/DH keys with g = +/- 1 ?

[Georgi Guninski <guninski () guninski com>]

On Tue, Apr 15, 2014 at 09:20:11PM +0200, Hanno Böck wrote:
> On Tue, 15 Apr 2014 17:06:13 +0300
> Georgi Guninski <guninski () guninski com> wrote:
>
> > openssl accepts DSA (and probably DH) keys with
> > g=1 (or g= -1). Both are extremely weak, in
> > practice plaintext.
>
> openssl also accepts 15 as a prime for DH. I recently looked at this:
> http://blog.hboeck.de/archives/841-Diffie-Hellman-and-TLS-with-nonsense-parameters.html

Interesting blog post.

AFAICT weak DH keys can't be recognized
since they can be well formed.

The hardness of the discrete log doesn't
depend on the size of $p$ but on the size
of $q$ which is the largest prime factor
of the multiplicative order of $g$.

State of the art is $O(\sqrt{q})$, naive
is O(q).

Here is a sage program with $p$
1420 bit prime and $q=1021$.
https://j.ludost.net/blog/dh-prime.sage

Session:

sage: load dh-prime.sage
log_2(p) 1419.52213626721
p prime True
G.order() 1021
0 dlog 669
1 dlog 172
2 dlog 683
3 dlog 428
4 dlog 277
5 dlog 914
6 dlog 853
7 dlog 56
8 dlog 774
9 dlog 297
10 dlog 7


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