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參數(shù)資料
| 型號： | L13-PALLADIUM |
| 廠商： | Electronic Theatre Controls, Inc. |
| 英文描述： | Palladium, Zero Knowledge |
| 中文描述： | 鈀，零知識 |
| 文件頁數(shù)： | 6/7頁 |
| 文件大小： | 150K |
| 代理商： | L13-PALLADIUM |
6
3
ZERO-KNOWLEDGE PROOFS
Figure 4: Representation of the 6 permutations of a given graph 3-coloring
Private key of prover:
x
s.t. 0
≤
x < q
Do
t
times:
- Prover: picks
k
∈
Z
q
, sends
u
=
g
k
mod
p
- Verifier: computes
b
∈
R
{
0
,
1
}
, sends
b
to Prover
- Prover: sends
l
=
k
+
bx
mod
q
- Verifier: computes
u
×
y
b
=
g
l
mod
p
Note that the Prover can always succeed in each round with probability 1
/
2, by guessing
b
first,
then setting
u
=
g
l
/y
b
.
This protocol is sound and complete. The Verifier will always accept an honest Prover’s proof, and
a cheating prover will be caught with significant probability in each round.
Now the claim is that the protocol is ZK. We can play this game all day long and there is no way
the Verifier will learn any information about
x
. The Verifier just gets a huge list of
u
,
b
, and
l
during
each iteration, but the claim again is that this tells us nothing about
x
.
To demonstrate our claim, we can generate transcripts (on our own) with the proper distribution:
- pick
b
∈
R
{
0
,
1
}
- pick
l
∈
R
Z
q
- pick
u
=
g
l
/y
b
mod
p
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