Bài giảng An toàn dữ liệu - Tuần 4

Bài giảng Tuần 4
Trương Thị Thu Hiền
Bộ môn CHTTT
ĐHCN - ĐHQGHN
October 16, 2007
Secret Sharing
Suppose that I have some data that I want to
share amongst three people such that
•
any two can uniquely determine the data
•
but any one alone has no information
whatsoever about the data.
October 16, 2007
Secret Sharing
Some simple cases: “AND”
I have a secret value z that I would like to share
with Alice and Bob such that both Alice and
Bob can together determine the secret at any
time, but such that neither has any information
individually.
October 16, 2007
Secret Sharing – AND
Let z ∈ Z
n
= {0,1,…,m-1} be a secret value to be
shared with Alice and Bob.
Randomly and uniformly select values x and y from Z
m

subject to the constraint that

(x + y) mod m = z.
October 16, 2007
Secret Sharing – AND
The secret value is z = (x + y) mod
m.
October 16, 2007
Me
Secret Sharing – AND
The secret value is z = (x + y) mod m.
x y
October 16, 2007
Alice
Me
Secret Sharing – AND
The secret value is z = (x + y) mod m.
x y
October 16, 2007
Me
Secret Sharing – AND
The secret value is z = (x + y) mod m.
y
October 16, 2007
Me
Bob
Secret Sharing – AND
The secret value is z = (x + y) mod m.
y
October 16, 2007
Me
Secret Sharing – AND

The secret value is z = (x + y) mod m.
October 16, 2007
Secret Sharing – AND
The secret value is z = (x + y) mod m.
October 16, 2007
Alice
Secret Sharing – AND
The secret value is z = (x + y) mod m.
x
October 16, 2007
Bob
Alice
Secret Sharing – AND
The secret value is z = (x + y) mod m.
x y
October 16, 2007
Bob
Alice
Secret Sharing – AND
The secret value is z = (x + y) mod m.
x y
October 16, 2007
Secret Sharing – AND
This trick easily generalizes to more than
two shareholders.
A secret S can be written as
S = (s
1
+ s
2

+ … + s
n
) mod m
for any randomly chosen integer values
s
1
, s
2
, …, s
n
in the range 0 ≤ s
i
< m.
October 16, 2007
Secret Sharing
Some simple cases: “OR”
I have a secret value z that I would like to share
with Alice and Bob such that either Alice or
Bob can determine the secret at any time.
October 16, 2007
Secret Sharing – OR
The secret value is z.
October 16, 2007
Me
Secret Sharing – OR
z z
The secret value is z.
October 16, 2007
Me
Alice

Secret Sharing – OR
z z
The secret value is z.
October 16, 2007
Me
Secret Sharing – OR
z
The secret value is z.
October 16, 2007
Bob
Me
Secret Sharing – OR
z
The secret value is z.
October 16, 2007
Me
Secret Sharing – OR
The secret value is z.
October 16, 2007
Alice
Secret Sharing – OR
z
The secret value is z.
October 16, 2007
Bob
Secret Sharing – OR
z
The secret value is z.
October 16, 2007
Secret Sharing – OR

This case also generalizes easily to more
than two shareholders.