of
Shamir's Secret Sharing
a =
p =
(Prime number)
Dealer
Secret value : s =
(s = a0)
Random values
a =
Dealer computes Pi =
+
×i
mod
Players
|
|
?
|
of
Verifiable Secret Sharing
G :
H :
Each player sets random numbers
| P | a: | |
| a': |
Each player
| P | |||
| s = f() = | s' = f'() = | ⇒ P |
Each player broadcasts commitments
| P | C = | G + H |
Each player verifies commitments
|
P
|
G + H |
×C
|
⇒
|
Each player broadcasts
| P | A = | G |
Each player verifies
|
P
|
G |
×A
|
⇒
|
A random secret and its public key
A
=
Players
?
of Schnorr's Signature
G :
H :
Key
A =
P =
+
A
Random
B =
R =
+
B
P :
,
r =
h(R,m) =
(Special value to make it easy.)
c :
|
|
?
|
σG =? R + h(R,m)P
Etc
x =
xG =
a =
A =
b =
B =
aA + bB =
|
|
 |