change epsilon expression

pages/CSE442T/CSE442T_L12.md

@@ -9,7 +9,7 @@ $$
 $$
 
 - If $\mu(n)\geq \frac{1}{p(n)}\gets poly(n)$ for infinitely many n, then $\{X_n\}$ and $\{Y_n\}$ are distinguishable.
-- Otherwise, indistinguishable ($|diff|<\varepsilon(n)$)
+- Otherwise, indistinguishable ($|diff|<\epsilon(n)$)
 
 Property: Closed under efficient procedures.
 
@@ -58,7 +58,7 @@ $$
 
 ### Next bit test (NBT)
 
-We say $\{X_n\}$ passes the next bit test if $\forall i\in\{0,1,...,l(n)-1\}$ on $\{0,1\}^{l(n)}$ and for all adversaries $\mathcal{A}:P[t\gets X_n:\mathcal{A}(t_1,t_2,...,t_i)=t_{i+1}]\leq \frac{1}{2}+\varepsilon(n)$ (given first $i$ bit, the probability of successfully predicts $i+1$ th bit is almost random $\frac{1}{2}$)
+We say $\{X_n\}$ passes the next bit test if $\forall i\in\{0,1,...,l(n)-1\}$ on $\{0,1\}^{l(n)}$ and for all adversaries $\mathcal{A}:P[t\gets X_n:\mathcal{A}(t_1,t_2,...,t_i)=t_{i+1}]\leq \frac{1}{2}+\epsilon(n)$ (given first $i$ bit, the probability of successfully predicts $i+1$ th bit is almost random $\frac{1}{2}$)
 
 Note that for any $\mathcal{A}$, and any $i$,
 
@@ -71,7 +71,7 @@ If $\{X_n\}\approx\{U_{l(n)}\}$ (pseudorandom), then $X_n$ must pass NBT for all
 Otherwise $\exists \mathcal{A},i$ where for infinitely many $n$,
 
 $$
-P[t\gets X_n:\mathcal{A}(t_1,t_2,...,t_i)=t_{i+1}]\leq \frac{1}{2}+\varepsilon(n)
+P[t\gets X_n:\mathcal{A}(t_1,t_2,...,t_i)=t_{i+1}]\leq \frac{1}{2}+\epsilon(n)
 $$
 
 We can build a distinguisher $D$ from $\mathcal{A}$.
@@ -147,6 +147,6 @@ $f(x)||x$
 
 Not all bits of $x$ would be hard to predict.
 
-**Hard-core bit:** One bit of information about $x$ which is hard to determine from $f(x)$. $P[$ success $]\leq \frac{1}{2}+\varepsilon(n)$
+**Hard-core bit:** One bit of information about $x$ which is hard to determine from $f(x)$. $P[$ success $]\leq \frac{1}{2}+\epsilon(n)$
 
 Depends on $f(x)$