phc-discussions - Re: [PHC] Dumb idea of the day: Public key crypto based on random permutations

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Message-ID: <CAOLP8p56WzgZw=UdyKaSkwDX89Cp3bCA6EysfOJK+8HCUMbEtQ@mail.gmail.com>
Date: Sat, 15 Aug 2015 10:09:00 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Dumb idea of the day: Public key crypto based on random permutations

On Sat, Aug 15, 2015 at 10:06 AM, Daniel Franke <dfoxfranke@...il.com>
wrote:

> Adding an efficiently-invertible group automorphism doesn't make the
> system any more secure than the system based on the underlying group
> operation. Here that group operation is modular addition, for which
> the discrete log problem is easy. If I have your public key X =
> Finv(F(x)*F(g)) where x is your private key, then I compute F(X) =
> F(Finv(F(x)*F(g))) = F(x)*F(g), use Euclid's algorithm to solve for
> F(x), then recover your private key by computing Finv(F(x)) = x.
>

You are 100% right.  Making the automorphism impractical or impossible to
compute seems to be the key.

Bill

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