On Jul 21, 2009, at 3:11 PM, Hal Finney wrote:
The first is equivalent to: knowing g^(xy) is it impossible to
deduce g^x,
where y = H(g^x). Define Y = g^x, then y = H(Y) and g^(xy) = Y^H(Y).
The
question is then:
Given Y^H(Y) can we deduce Y?
To make a simple observation: H matters. If

Zooko's proposal for semi-private keys is worthy of discussion here
I think. The full idea is in http://allmydata.org/~zooko/lafs.pdf but I
will present it here for your enjoyment (I should emphasize that I played
no part in any of the development of this idea, I just read his PDF).
Apologies in