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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)： | 3/7頁 |
| 文件大?。?/td> | 150K |
| 代理商： | L13-PALLADIUM |
3.1
The General Set-up
3
3.1
The General Set-up
P = Prover
V = Verifier
wants to prove he knows
m
wants to learn if P knows
m
→
←
→
test (
c,w,x,y
).
Accept if OK, reject otherwise.
We want the protocol to satisfy the following properties:
1. If
P
does know
m
, then
V
always accepts. (Completeness)
2. If
P
does not know
m
, then
P
is unlikely to convince
V
. (Soundness)
Soundness may be shown by demonstrating that if
P
is prepared to respond to several different
challenges (for the same witness), then in fact
P
must know (or must be able to easily compute)
m
.
We would also like to have that the protocol be
zero-knowledge
: the Verifier learns nothing (zero),
aside from the fact that
P
knows
m
.
3.2
3-Colorability Example
We have an undirected graph with 5 vertices. Can we color the vertices with three colors so that no
two adjacent vertices have the same color
A given graph may have many possible colorings, only one coloring, or no colorings at all. Suppose
I have a graph with a million vertices and I tell you I know how to color it using 3 colors. I want to
convince you that the graph is 3-colorable without telling you what the coloring is. Is there some
way I can convince a remote computer, the skeptic, that I know how to do the coloring without
saying what the coloring is
Consider the following exchange between the Prover (you, the person who knows the 3-coloring) and
the Verifier (the remote computer you are trying to convince):
For a given graph coloring, there are 6 different permutations of the coloring possible: RGB, RBG,
BRG, BGR, GBR, GRB. That is, you take one coloring and just permute the color assignments
(e.g. from RGB to RBG, all vertices that are R are still R, all vertices that are G are now B, etc.).
Again, this is just for one coloring that the Prover picks. We can represent each permutation as a
sheet of paper with the graph and coloring on it (see Figure 4 below).
[Figure 4: Representation of the 6 permutations of a given graph 3-coloring]
Do
t
times: Prover: picks a sheet (graph with a coloring permutation) from a random pile (Verifier
doesn’t know which pile Prover picks) and puts it on the table covering up vertices with little stickies
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