update notations and fix typos
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@@ -98,7 +98,7 @@ $x_1\equiv x_2\mod N$
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So it's one-to-one.
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EOP
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QED
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Let $y\in \mathbb{Z}_N^*$, letting $x=y^d\mod N$, where $d\equiv e^{-1}\mod \phi(N)$
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@@ -130,7 +130,7 @@ By RSA assumption
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The second equality follows because for any finite $D$ and bijection $f:D\to D$, sampling $y\in D$ directly is equivalent to sampling $x\gets D$, then computing $y=f(x)$.
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EOP
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QED
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#### Theorem If inverting RSA is hard, then factoring is hard.
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