\font\largerbold = cmbx10 scaled \magstep1
\font\largerrm =cmr10 scaled \magstep1
\nopagenumbers
\font\sc=cmcsc10.tfm
\font\show = cmdunh10.tfm
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%\parindent=0pt
\rightline{April 9, 2000}
\smallskip
\centerline{\largerbold Authentication my way ...\footnote*{\rm \underbar{Not}
recommended for the real world!}}

\bigskip

The {\bf G}reenfield {\bf A}uthentication {\bf G}roup will
authenticate documents and make me a multimillionaire. The foundation
of my {\sc business plan} is an authenticating and compressing
algorithm. The algorithm uses an easy technique to produce a number
from a document. The public will not be able to reconstruct the
information in the document, but the algorithm's output will be unique
enough so that people will not be able to repudiate the document or
forge another document in its place. I'll make a vast \raise
-.14em\hbox{\show FORTUNE}\thinspace .

\medskip
\centerline{\bf The GAG algorithm}

{\narrower
\smallskip

\item{\bf Step 1} Discard any punctuation, any numbers, and any other
characters which are not letters. Do, however, preserve spaces
between words. Also, do {\it not}\/ distinguish between lower and
upper case (so ``A'' and ``a'' are considered the same letter).

\smallskip

\item{\bf Step 2} Count the number of vowels in the document (a vowel
is one of the letters 
``a'', ``e'', ``i'', ``o'' or ``u''). Count the number of consonants
in the document (a consonant here is any letter that's not a
vowel). Count the number of spaces in the document. Note that a
document {\it must}\/ begin and end with a letter -- spaces before the
beginning and after the end don't count. Also, any succession of
consecutive spaces will count as just one space.

\smallskip

\item{\bf Step 3} Multiply the number of vowels by 7, subtract 3 times
the number of consonants, and add the {\it square} of the number of
spaces. Find the mod 17 remainder of this number and output this
number. This is the GAG number!

}

\bigskip

\noindent {\bf Example} I'll apply the famous GAG algorithm to the
following ``document'':

\smallskip

\def\start{\noindent \tt \frenchspacing }
%\obeylines \obeyspaces}
\smallskip
\centerline{
\start I will pay Thomas \$50 next Wednesday, or else \$75 on the Friday following.
}

\smallskip
\noindent 
Step 1 yields the following:
\smallskip
\centerline{
\start i will pay thomas next wednesday or else on the friday following
}
\smallskip

\noindent 
\def\u{\underbar}
\noindent 
We count the vowels:
\smallskip
\centerline{
\start \u{i} w\u{i}ll p\u{a}y th\u{o}m\u{a}s n\u{e}xt w\u{e}dn\u{e}sd\u{a}y \u{o}r \u{e}ls\u{e} \u{o}n th\u{e} fr\u{i}d\u{a}y f\u{o}ll\u{o}w\u{i}ng
}

\smallskip

\noindent There seem to be 19 vowels. 
\def\sp{\underbar{\ }}
\smallskip
\centerline{
\start i\sp will\sp pay\sp thomas\sp next\sp wednesday\sp or\sp else\sp on\sp the\sp friday\sp following
}

\smallskip

\noindent There are 11 spaces. Heroic further work enumerates 
34 consonants. Now we compute
$$7(19)-3(34)+(11)^2=133-102+121=152$$
but 152 mod 17 is 16: the GAG number of this document is {\bf 16}.

\vfil
\rightline{\bf OVER}\eject

\centerline{\largerbold Homework \hskip-.98in //////////\  Some questions}
\bigskip


\noindent {\bf Problem 1} Compute the GAG number of 

\smallskip

\centerline{
\start Good morning! I am here to help you. (He smiles and grabs the
money.)
}

\medskip

\noindent {\bf Problem 2} Ted and I agree that

\smallskip

\centerline{
\start We jointly and equally own the gravel pit at Loon Lake.
}

\smallskip

\noindent but we've only published the GAG number of this document. It
is known the document deals with the ownership of the Loon Lake gravel
pit. First, compute the GAG number of this document. Then create a
relevant document which will enable one of us to disavow the agreement
published above. The document must have the same GAG number and deal
with Loon Lake and its gravel pit, but it must assign ownership in
some other manner. It should also be written in grammatical English!
\underbar{Show the details of your computations.}

\bigskip

\noindent {\bf Some possible answers}\footnote{**}{with remarks on how
I got them!}

\smallskip

The algorithm creating the GAG number is not too good. It would assign
the same GAG number to {\tt frog jumping} and to {\tt gorf jumping}
and to {\tt jumping frog}. There are lots of collisions using this
algorithm! Also, the algorithm only has 17 possible outputs, so of
{\it any}\/ 18 ``documents'' at least 2 of them will have the same GAG
number. 

Here are a few answers I concocted to the problem above:

\smallskip

\line{\noindent {\bf Example 1} \tt \frenchspacing
Ted owns the whole Loon Lake gravel pit and I own none of it.\hfil
}

\smallskip

\line{\noindent {\bf Example 2} \tt \frenchspacing
Ted has one third interest in the Loon Lake gravel pit.\hfil
}

\smallskip

\line{\noindent {\bf Example 3} \tt \frenchspacing
Ted has nineteen percent of the Loon Lake gravel pit.\hfil
}

\overfullrule=0pt
\smallskip

\line{\noindent {\bf Example 4} \tt \frenchspacing
Ted owns none of the Loon Lake gravel pit. I own all the gravel
pit.\hfil
}

%\centerline{
%\start Ted owns two thirds of the whole Loon Lake gravel pit.
%}

\smallskip

I recommend starting with some sentences and computing the GAG number
of what you've written. Make small modifications until you get the
``correct'' GAG number, and until the sense of the document is what
you want.

\vfil\eject\end

forgery
7#vowels -3#consonants + (#spaces)^2 mod 131


