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Wrote up sat

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Joshua-Gordon 2 years ago
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      proj.tex

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proj.tex

@ -72,5 +72,11 @@ Furthermore, we can define relations such as \begin{verbatim}ADD(x,y,z),MULT(x,y
The second bit of machinery we need is, given a string $w$, a relation \begin{verbatim}
LexicographicallyAfterW(b1,b2,...,bk)
\end{verbatim}
which is true when the string $b$ is lexicographically after $w$. This can be implemented by a lookup table
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.
At last, consider, given some pivot string $w$ in the $2^k$ space of strings, the formula:
\begin{verbatim}
EncryptsToC(X) && LexicographicallyAfterW(X)
\end{verbatim}
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.
\end{document}
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