diff --git a/06-hash/hash.tex b/06-hash/hash.tex index d5b0eb79c2a0e77287dc7118b0854a36f92c8c4d..7e12db329ecee5b6ebeec0a2313b516f22d449e6 100644 --- a/06-hash/hash.tex +++ b/06-hash/hash.tex @@ -330,7 +330,8 @@ Each term can be handled separately: $$\vbox{\halign{\hfil $\displaystyle{#}$&$\displaystyle{{}#}$\hfil&\quad #\hfil\cr \Pr[M\mid\lnot C] &\le d/m^2 &by $(2,d)$-independence of~${\cal G}$ \cr \Pr[\lnot C] &\le 1 &trivially \cr - \Pr[M\mid C] &\le d/m &because $(2,d)$-independence implies $(1,d)$-independence \cr + \Pr[M\mid C] &\le d/m &for $i_1\ne i_2$: the left-hand side is~0, \cr + {} & {} &for $i_1=i_2$: $(2,d)$-independence implies $(1,d)$-independence \cr \Pr[C] &\le c/r &by $c$-universality of~${\cal F}$ \cr }}$$ So $\Pr[M] \le d/m^2 + cd/mr$. We want to write this as $c' / m^2$, so