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proof format updates using gfm

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Trance-0
2025-08-29 15:51:24 -05:00
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content/CSE442T/CSE442T_L4.md
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@@ -88,7 +88,8 @@ $$
is a strong one-way function.
Proof:
<details>
<summary>Proof</summary>
1. Since $\exist P.P.T.$ that computes $f(x),\forall x$ we use this $q(n)$ polynomial times to compute $g$.
2. (Idea) $a$ has to succeed in inverting $f$ all $q(n)$ times.
@@ -98,7 +99,7 @@ Proof:
Then $P[a$ inverting $g]\sim P[a$ inverts $f$ all $q(n)]$ times. $<(1-\frac{1}{p(n)})^{q(n)}=(1-\frac{1}{p(n)})^{np(n)}<(e^{-\frac{1}{p(n)}})^{np(n)}=e^{-n}$ which is negligible function.
QED
</details>
_we can always force the adversary to invert the weak one-way function for polynomial time to reach the property of strong one-way function_