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Wrote up sat

Joshua-Gordon 11 months ago
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@@ -72,5 +72,11 @@ Furthermore, we can define relations such as \begin{verbatim}ADD(x,y,z),MULT(x,y
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 The second bit of machinery we need is, given a string $w$, a relation \begin{verbatim}
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 LexicographicallyAfterW(b1,b2,...,bk)
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 \end{verbatim}
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-which is true when the string $b$ is lexicographically after $w$. This can be implemented by a lookup table 
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+which is true when the string $b$ is lexicographically after $w$. This can be implemented by a lookup table as well; runtime is the oracle's problem.
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+
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+At last, consider, given some pivot string $w$ in the $2^k$ space of strings, the formula:
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+\begin{verbatim}
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+EncryptsToC(X) && LexicographicallyAfterW(X)
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+\end{verbatim}
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+Applying the SAT oracle to this sentence will tell us if there is a bitstring in the upper half of the search space that is the desired plaintext string. We can run binary search using this, and acquire the desired plaintext in linear time.
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 \end{document}

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