[900] in Cypherpunks
Re: Dig. Cash Question.
daemon@ATHENA.MIT.EDU (J. Michael Diehl)
Sun Jun 6 02:48:32 1993
From: J. Michael Diehl <mdiehl@triton.unm.edu>
To: smb@research.att.com
Date: Sun, 6 Jun 1993 00:30:01 -0600 (MDT)
Cc: cypherpunks@toad.com
In-Reply-To: <9306052306.AA05980@triton.unm.edu> from "smb@research.att.com" at Jun 5, 93 07:05:14 pm
According to smb@research.att.com:
>
> If I understand this correctly, if p is not a prime, then n may not be
> unique.
>
> Well, n isn't unique even if p is prime. Consider a=10,p=11.
> 10^2=10^4=10^6=10^8=10^10=1 mod 11. You only get a maximum-length
> cycle if ``a'' is a primitive root, hence the restriction I stated
> in the part I deleted...
That is, if a is a generator of G, or as close to one as possible.
My thinking was obviously clowded... Not that I have a beer in me, I remember
that for any element, a of group G, a will have order n, such that n|ord(G).
This implies that there are n different (positive) powers of a which yield a
particular number, b in our case. Each of which would qualify as a log. I
think I understand.
> It doesn't matter that n isn't unique, though you do want a good
> distribution. Primitive roots have a maximal distribution, which is
Then which root are we to use in discussion?
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