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Here's the idea: given $w$ and $n$, we find a number $v$ such that $vw \equiv 1 \pmod{n}$. In your case of $w=7$ and $n=173$, we have $v=99$; such a $v$ will always exist if $w$ and $n$ are relatively prime, and can be found by the extended Euclidean algorithm. The value $v$ allows us to map from the "hard values" to the "superincreasing ones". Here's how ...


No, the problem is np-completeness or even np-hardness is a worst case thing. In crypto, we don't want our systems to be unbreakable only in the worst case. We want them to be unbreakable at least in the average case. It would be better if it were unbreakable in the best case (or all cases). Another, related, issue we have is that of generating hard ...

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