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From: billp@azure.UUCP (Bill Pfeifer)
Newsgroups: net.crypt
Subject: Re: One-time pads
Message-ID: <2550@azure.UUCP>
Date: Wed, 22-Feb-84 13:05:40 EST
Article-I.D.: azure.2550
Posted: Wed Feb 22 13:05:40 1984
Date-Received: Fri, 24-Feb-84 00:09:15 EST
Organization: Tektronix, Beaverton OR
Lines: 46

Gene Spafford writes:

>	However, suppose you are the person reading the encrypted message.  If
>	you see text which happened to be readable and described a recipe for
>	Aunt Pat's oatmeal cookies, you probably would ascribe to the
>	randomness of the encryption. (You might also decide to see if it was a
>	code of some sort (as opposed to cypher)).  On the other hand, if you
>	saw something like the formula for a new nerve gas, you'd definitely
>	try to have your chemists put it together and give it a try.  Your
>	chances might not be good that it was actually a formula for nerve gas,
>	but if it was, you'd have it.

Horsepuckey!

I suppose Gene does not appreciate the magnitude of the numbers involved!
To get a feel for the numbers, consider the famous "Problem of a Printed Line",
as described by George Gamow in his book "One Two Three ... Infinity"
(Bantam Books, New York).
He describes the attempt of continuously printing one line after the other,
each line having a different combination of letters, numbers and punctuations,
until all possible combinations have been printed.  There are 26 letters, 10
numbers and 14 common punctuations, 50 symbols altogether.  George Gamow
limits the length of the line to 65 characters, that of an average printed
line.  That is 50^65 or 10^110 combinations!
Not impressed yet?
Assume that every atom in the entire universe (3*10^74 of them) represents a
separate printer, working simultaneously.  Assume further that these printers
are printing at the rate of atomic vibrations, 10^15 lines per second
(that's a quadrillion lines, 16 2/3 trillion pages, or about 5 billion boxes
of paper per second EACH), and that they have been printing uninterrupted
since the beginning of the universe (3*10^9 years, or 10^17 seconds).
By now they would have printed 3*10^106 lines, which is one thirtieth of
1 percent of the total required.

The probability of text left unencrypted by a string of zeroes in a truly
random bitstream is similar to that of finding the real nerve gas formula
in this output.  Besides, how much of a formula could you pack into a
65 characters?  Remember, each added character multiplies the output volume
by 50.
Along with the real formula, there will also be 10^xxx phony formulas, some
of which will actually yield Aunt Pat's oatmeal cookies.  There aren't enough
molecules on this planet to put together all formulas that might look like
nerve gas, even if you tried.

	Bill Pfeifer
{cbosgd,decvax,harpo,ihnss,ogcvax,pur-ee,ucbvax,zehntel} !tektronix!tekmdp!billp