# Sumcheck

x_1
x_2
x_3
b
\text{bits}
f(b)
0
1
2
3
4
5
6
7
\textcolor{lightgreen}{0}00
\textcolor{lightgreen}{0}01
\textcolor{lightgreen}{0}10
\textcolor{lightgreen}{0}11
\textcolor{red}{1}00
\textcolor{red}{1}01
\textcolor{red}{1}10
\textcolor{red}{1}11
f_0
f_1
f_2
f_3
f_4
f_5
f_6
f_7
\vec{f}_{\textsf{lo}}
\vec{f}_{\textsf{hi}}
\underbrace{\hspace{3.55cm}}{}
\underbrace{\hspace{3.55cm}}{}
\sum
\sum
(\textcolor{lightgreen}{0},\textcolor{red}{1})
(\textcolor{lightgreen}{1},\textcolor{red}{0})
(\textcolor{lightgreen}{-1},\textcolor{red}{2})
H(.)
\big((\textcolor{lightgreen}{1-r}),(\textcolor{red}{r})\big)
\vec{f}_{\textsf{next}}

# Sumcheck

x_1
x_2
x_3
b
\text{bits}
f(b)
0
1
2
3
4
5
6
7
\textcolor{lightgreen}{0}00
\textcolor{lightgreen}{0}01
\textcolor{lightgreen}{0}10
\textcolor{lightgreen}{0}11
\textcolor{red}{1}00
\textcolor{red}{1}01
\textcolor{red}{1}10
\textcolor{red}{1}11
f_0
f_1
f_2
f_3
f_4
f_5
f_6
f_7
\vec{f}_{\textsf{lo}}
\vec{f}_{\textsf{hi}}
\underbrace{\hspace{3.55cm}}{}
\underbrace{\hspace{3.55cm}}{}
\sum
\sum
(\textcolor{lightgreen}{0},\textcolor{red}{1})
(\textcolor{lightgreen}{1},\textcolor{red}{0})
(\textcolor{lightgreen}{-1},\textcolor{red}{2})
H(.)
\big((\textcolor{lightgreen}{1-r}),(\textcolor{red}{r})\big)
\vec{f}_{\textsf{next}}
C

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