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Date: Sat, 15 Aug 2015 13:06:23 -0400
From: Daniel Franke <dfoxfranke@...il.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Dumb idea of the day: Public key crypto based on random permutations

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.

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