Re: [CFRG] Using Diffie-Hellman With a Non-prime Modulus

Michael D'Errico <> Fri, 30 October 2020 02:28 UTC

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From: Michael D'Errico <>
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Date: Thu, 29 Oct 2020 22:28:46 -0400
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Subject: Re: [CFRG] Using Diffie-Hellman With a Non-prime Modulus
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> It's not true in general that exponentiation modulo M is cyclic with period M-1.  It is true if M is prime; however you are considering composite M, hence Fermat does not apply.

My point exactly.  All the current published groups
have a prime modulus M, which might be problematic
due to Fermat.  This leads me to consider non-prime
moduli as a possible improvement.

> Mike Hamburg already outlined the issues for M with public factorization. For M with a secret factorization, there are a number of ways for us to hide a backdoor in the DH operation, for example, (not the best, IMHO, just the first reference I found) - hence, good luck in getting anyone to trust that you didn't...

I'm not doing anything in secret.  It's all here on
this mailing list.  Sure, one part of the threat
model of the Internet is that the standards writers
are sabotaging the very standards we're relying on.
I've no doubt that this has occurred and is occurring
now.  If I can't figure out a way to objectively show
that my results are better than the current groups
then I won't pursue it further.  I've no stake in
this other than trying to make the Internet better.

Thank you for providing a reference.