Re: encryption with pi

From: Jeff Williams (frostback_at_canada.com)
Date: 07/30/04 

Date: Thu, 29 Jul 2004 20:23:12 -0500

Tom St Denis wrote:
> vedaal@hush.com wrote:
>
>
>>can the following simple substitution cipher using pi, be made secure
>>?
>>
>>C = P rot [ s(l+n) mod 256 ]
>>
>>where 's' is a substring of pi of length k, beginning at digit 'l',
>>and 'n' is the sequenced character of the plaintext
>
>
> <snip>...
>
> What does "rot" mean anyways?
>
> That aside... finding digits of Pi is **SLOW** and consumes a heck lot of
> memory. That and who says identifying a sequence as part of "Pi" is a hard
> problem? Who knows there may be a sub-exponential algorithm that given L
> digits of pi you can determine where the first one was.
>
> Alternatively who says given L digits of Pi you can't predict the next with
> more than uniform probability?
>
> Quite frankly the idea is a bit short sighted. It's inefficient and has no
> provable properties other than it's not a simple pattern.
>
> Tom
>
>
Rot = rotate. Off-colour posts used to be (haven't seen any recently)
"encrypted" with rot 13 - Caesar cipher with a key of 13.

I've never heard of anyone showing a pattern in the digits of PI (not to
say there are no patterns). Assuming (big assumption) there is no
discernable pattern, using a sequence of the digits of PI as a basis of
(I hate to say it) an OTP MIGHT work.

As Tom noted, very slow generation of digits of PI. Also, the number of
known digits of PI yields a very small (in modern terms) keyspace. Even
worse, the effort to calculate the n+1th digit of PI is greater than the
effort to calculate the nth digit of PI.

It's simple. It's elegant. It may be theoretically secure. But it's
thoroughly impractical.

Don't know how many others though of this concept. It occurred to me
somewhere around 1979 (about the time I got my driver's licence).

Jeff

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