Sumcheck
Sumcheck
x1
x_1
x2
x_2
x3
x_3
b
b
bits
\text{bits}
f(b)
f(b)
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
000
\textcolor{lightgreen}{0}00
001
\textcolor{lightgreen}{0}01
010
\textcolor{lightgreen}{0}10
011
\textcolor{lightgreen}{0}11
100
\textcolor{red}{1}00
101
\textcolor{red}{1}01
110
\textcolor{red}{1}10
111
\textcolor{red}{1}11
f0
f_0
f1
f_1
f2
f_2
f3
f_3
f4
f_4
f5
f_5
f6
f_6
f7
f_7
flo
\vec{f}_{\textsf{lo}}
fhi
\vec{f}_{\textsf{hi}}
\underbrace{\hspace{3.55cm}}{}
\underbrace{\hspace{3.55cm}}{}
∑
\sum
∑
\sum
(0,1)
(\textcolor{lightgreen}{0},\textcolor{red}{1})
(1,0)
(\textcolor{lightgreen}{1},\textcolor{red}{0})
(−1,2)
(\textcolor{lightgreen}{-1},\textcolor{red}{2})
H(.)
H(.)
((1−r),(r))
\big((\textcolor{lightgreen}{1-r}),(\textcolor{red}{r})\big)
fnext
\vec{f}_{\textsf{next}}
Sumcheck
x1
x_1
x2
x_2
x3
x_3
b
b
bits
\text{bits}
f(b)
f(b)
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
000
\textcolor{lightgreen}{0}00
001
\textcolor{lightgreen}{0}01
010
\textcolor{lightgreen}{0}10
011
\textcolor{lightgreen}{0}11
100
\textcolor{red}{1}00
101
\textcolor{red}{1}01
110
\textcolor{red}{1}10
111
\textcolor{red}{1}11
f0
f_0
f1
f_1
f2
f_2
f3
f_3
f4
f_4
f5
f_5
f6
f_6
f7
f_7
flo
\vec{f}_{\textsf{lo}}
fhi
\vec{f}_{\textsf{hi}}
\underbrace{\hspace{3.55cm}}{}
\underbrace{\hspace{3.55cm}}{}
∑
\sum
∑
\sum
(0,1)
(\textcolor{lightgreen}{0},\textcolor{red}{1})
(1,0)
(\textcolor{lightgreen}{1},\textcolor{red}{0})
(−1,2)
(\textcolor{lightgreen}{-1},\textcolor{red}{2})
H(.)
H(.)
((1−r),(r))
\big((\textcolor{lightgreen}{1-r}),(\textcolor{red}{r})\big)
fnext
\vec{f}_{\textsf{next}}
C
C
Sumcheck
Sumchecks
By Suyash Bagad
Sumchecks
- 76