February 19, 2002
Practical Aspects of Modern Cryptography
31
Verifiable Secret Sharing
n
Select a polynomial with secret
a
0
as
n
P(
x
) =
a
k
-1
x
k
-1
+ … +
a
2
x
2
+
a
1
x + a
0
.
n
Commit to the coefficients by publishing
n
g
a
0
,
g
a
1
,
g
a
2
, …,
g
a
k
-1
.
n
Compute a commitment to
P(
i
)
from public
values as
n
g
P(
i
)
=
g
a
0
i
0
g
a
1
i
1
g
a
2
i
2
…
g
a
k
-1
i
k
-
1
.