Transcendentals and Encryption (was Re: Nth digit of PI)

[James Graves]

Tim Dixon <tdixon.no at spam.fwi.com> wrote:
>On 16 Jun 2000 17:36:32 GMT, israel at math.ubc.ca (Robert Israel) wrote:
>
>>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.  
>>
>
>Right, but in the hypothetical example where I can get *any* digit of
>pi, that could be any of an infinite number of starting points.

Using transcendentals for encryption is an interesting idea, one that's
been banging around in my head for a while.

I am under the impression that there are an infinite number of
transcendental numbers.  If there was some way to arbitrarily pick one
and the starting point, that might be harder to crack.  Then again, if
the black hats have your encryption algorithm (which is good to assume)
it wouldn't be any more secure than spending all the key bits on the
starting position inside of Pi.

This scheme still has the weaknesses of conventional stream
cyphers, in that it can be brute-forced.  A cypher can give you N years
of protection for your data (based on estimations of future computing
power).  But a one-time-pad is _forever_ if the pad was generated
correctly and used only once.

James Graves
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