Nth digit of PI

[Robert Israel]

In article <394a5ed7.83928743 at 10.1.1.28>,
Tim Dixon <tdixon.no at spam.fwi.com> wrote:
>On Fri, 16 Jun 2000 16:33:59 GMT, Courageous <jkraska1 at san.rr.com>
>wrote:


>>> Suppose, however, that you could get digit 'n' of pi directly (or e,
>>> or any other inifinte, nonrepeating sequence).  All I have to do is
>>> communicate which digit of pi the message key starts at, and I can
>>> generate the rest of the key.
>>
>>This is a collosally bad idea, IMO.

>Just for curiosity, why?

Because the real key is the number of the digit that you start at, and
that's pitifully small by cryptographic standards.  The time to generate
the n'th digit is not much less than the time to generate all the digits
up to the n'th, given that you have lots of memory available.  So the
cryptanalyst with a computer somewhat bigger than yours could try all
the keys you could be using.  

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            
Vancouver, BC, Canada V6T 1Z2