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Subject: Re: reverse Zero Knowledge
From: Ben Laurie (benalgroup.co.uk)
Date: Wed Aug 02 2000 - 18:21:11 CDT


Ben Laurie wrote:
> As I also said in my evaporated post, now that I've realised my error, I
> see that you can always construct a pair of functions, b and u, s.t.
> u(f(b(x)))=f(x) by setting u(x)=f(b'(f'(x))), where b' really is the
> inverse of b in this case. Then all you have to do is choose b s.t. b'
> is easy for you and hard for everyone else, and you are away. Of course,
> if b' is s.t. it makes b'.f' easy, too, then you have someting useful
> :-)

Arg. I'll get this right one day. Of course, to put this in the original
context, I need to switch f and f', so u(f'(b(x)))=f'(x), and hence
u(x)=f'(b'(f(x))), and what you really want, I guess, is for both b and
f'.b'.f to be easy (for you).

So, to apply this to my original non-counter-example, f(x)=x^2, we
choose b(x)=r^2.x, as suggested by Anonymous. b'(x)=x/r^2 and
f'(x)=x^{1/2}, so u(x) = f'(b'(f(x))) = (x^2/r^2)^{1/2} = x/r, as
expected (but having screwed up already, I'm glad it works out :-).

Cheers,

Ben.

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