RE: Issue in DH Algorithm Keys Generation in OpenSSL 3.3.0

Hi Viktor,

Is there any way to make this prime number work by doing some modifications in the openssl source code.

Like bypassing the OpenSSL DH prime check?

Regards,
Vishal


General
-----Original Message-----
From: openssl-users <[email protected]> On Behalf Of Viktor Dukhovni
Sent: Friday, May 31, 2024 03:01 PM
To: [email protected]
Subject: Re: Issue in DH Algorithm Keys Generation in OpenSSL 3.3.0

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On Fri, May 31, 2024 at 07:47:40AM 퍍 Vishal Kevat via openssl-users wrote:

> I am using OpenSSL source version 3.3.0 and facing an issue in key
> generation part of Diffie Hellman (DH) Algorithm. Below are the APIs I
> am using for generating Public and Private Keys:
>
> static unsigned char DH_PRIME_128[] = { /* 128 bit prime */
>       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
>       0xc9, 0x0f, 0xda, 0xa2, 0x21, 0x68, 0xc2, 0x34 };
>
> static unsigned char dh_g[] = {
>       0x02,
> };

That number is clearly not prime, it is, for a start obviously divisible by 4!  And of course "2" is then clearly not a generator of the multiplicative group of residues that are coprime to it, indeed the group is not cyclic:

    https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n#Cyclic_case

so it has no generator.

FWIW, the factors of your "prime" are:

    4, 31, 2347, 439409, 1327715723, 2004151850481839419

As can be confirmed via:

    $ echo '4 31 * 2347 * 439409 * 1327715723 * 2004151850481839419 * 16o p' | dc
    FFFFFFFFFFFFFFFFC90FDAA22168C234

Bottom line you should not expect this "prime" to yield a viable DH group.

--
    Viktor.