From: mpd@netcom.com (Mike Duvos)

To: cypherpunks@toad.com

Message Hash: 6a922a654c3c403eb4300dd44069a8c075ecf803fe150f383b896e741d67682b

Message ID: <199406170540.WAA13491@netcom.com>

Reply To: <199406170136.SAA28382@mail.netcom.com>

UTC Datetime: 1994-06-17 05:40:27 UTC

Raw Date: Thu, 16 Jun 94 22:40:27 PDT

```
From: mpd@netcom.com (Mike Duvos)
Date: Thu, 16 Jun 94 22:40:27 PDT
To: cypherpunks@toad.com
Subject: Re: Did anyone see...
In-Reply-To: <199406170136.SAA28382@mail.netcom.com>
Message-ID: <199406170540.WAA13491@netcom.com>
MIME-Version: 1.0
Content-Type: text/plain
Eli Brandt writes:
>> Victor S. Miller, [who I suspect is the same Victor S. Miller I
>> knew at UMass Boston many years ago], published a nifty little
>> paper in the mid 1980's on the computation of the function Pi(n)
> Do you have a pointer to this paper? I'd been under the
> impression that this function had no analytic closed form
> (unless you cheat).
I'll also post this to the list since I need to correct a dumb
error in my previous post.
I previously stated that Pi(n) was the Nth prime. It is of
course in reality the Prime Number Counting Function which is
equal to the number of primes <= n. Computing the Nth prime is
trivial given a program which computes Pi(n) since Pi(n) is
asymptotic to a known smooth function and one need only evaluate
it a small number of times to refine an initial estimate of the
Nth prime into the correct value.
Miller's definitive paper on the subject is...
Computing Pi(x): The Meissel-Lehmer method
Mathematics of Computation, 1985, 44, no. 170, 537-560
There is another paper by this gentleman which may be of interest
to Cypherpunks. It is on the use of elliptic curves as a basis
for cryptosystems. He demonstrates how an analogue to the
Diffie-Hellman secure key exchange may be constructed using
groups of points on elliptic curves and conjectures that such a
system may be stronger than one based on the discrete log
problem. Here is the citation.
Use of elliptic curves in cryptography
Advances in cryptology---CRYPTO 85
1986, 417-426 ISBN: 0-387-16463-4
Happy reading.
--
Mike Duvos $ PGP 2.6 Public Key available $
mpd@netcom.com $ via Finger. $
```

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