change epsilon expression

This commit is contained in:
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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@@ -87,8 +87,8 @@ $F=\{f_i:D_i\to R_i\},i\in I$, $I$ is the index set.
1. We can effectively choose $i\gets I$ using $Gen$.
2. $\forall i$ we ca efficiently sample $x\gets D_i$.
3. $\forall i\forall x\in D_i,f_i(x)$ is efficiently computable
4. For any n.u.p.p.t $a$, $\exists$ negligible function $\varepsilon (n)$.
$P[i\gets Gen(1^n);x\gets D_i;y=f_i(x):f(a(y,i,1^n))=y]\leq \varepsilon(n)$
4. For any n.u.p.p.t $a$, $\exists$ negligible function $\epsilon (n)$.
$P[i\gets Gen(1^n);x\gets D_i;y=f_i(x):f(a(y,i,1^n))=y]\leq \epsilon(n)$
#### Theorem
@@ -107,7 +107,7 @@ Algorithm for sampling a random prime $p\gets \Pi_n$
- Deterministic poly-time procedure
- In practice, a much faster randomized procedure (Miller-Rabin) used
$P[x\cancel{\in} prime|test\ said\ x\ prime]<\varepsilon(n)$
$P[x\cancel{\in} prime|test\ said\ x\ prime]<\epsilon(n)$
3. If not, repeat. Do this for polynomial number of times