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change epsilon expression

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Zheyuan Wu
2024-12-05 21:23:34 -06:00
parent d18e86852c
commit 75ef366b1c
10 changed files with 37 additions and 37 deletions
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pages/CSE442T/CSE442T_L5.md
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@@ -2,10 +2,10 @@
Proving that there are one-way functions relies on assumptions.
Factoring Assumption: $\forall a, \exist \varepsilon (n)$, let $p,q\in prime,p,q<2^n$
Factoring Assumption: $\forall a, \exist \epsilon (n)$, let $p,q\in prime,p,q<2^n$
$$
P[p\gets \Pi_n;q\gets \Pi_n;N=p\cdot q:a(N)\in \{p,q\}]<\varepsilon(n)
P[p\gets \Pi_n;q\gets \Pi_n;N=p\cdot q:a(N)\in \{p,q\}]<\epsilon(n)
$$
Evidence: To this point, best known procedure to always factor has run time $O(2^{\sqrt{n}\sqrt{log(n)}})$