Ah, the math-magic of semantic encryption... :) (re: random zeta)
We can certainly walk through the proof of the semantic encryption (the
random zeta) as it is quite mathematically beautiful, but it will take us
even further down the algebraic path.

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On Wed, Sep 21, 2016 at 8:19 AM, Tim Ellison <t.p.elli...@gmail.com> wrote:
> On 19/09/16 18:36, Walter Ray-Dulany wrote:
> <snip/>
> > Let's see what we've got.
> >
> > ( (16**12)*(7**15) ) mod 225 = 208.
> >
> > I will leave it as an exercise to check that the decryption of 208 is in
> > fact 12.
>
> I like a challenge :-)
>
> So we got to p=3, q=5, and my encrypted value c=208.
>
> Following the Wideskies Pallier decryption algorithm,
> Step (2):
> N = p * q
> = 15
>
> lambda(N) = lcm(p-1,q-1)
> = 4
>
> Step (3):
> mu = lambda(N) modinverse N
> = 4
>
> Step (4):
> c' = c^lambda(N) mod N^2
> = 208^4 mod 225
> = 46
>
> Step(5):
> m' = L(c')
> = ((c' - 1) / N) mod N
> = (45 / 15) mod 15
> = 3
>
> Step(6):
> m = (m' * mu) mod N
> = 12
>
> yay!
>
> The fog is slowly clearing, though I'm totally baffled about how I can
> pick a random zeta during encryption, and it plays no part in the
> decryption.
>
> Regards,
> Tim
>