Information Technology Reference
In-Depth Information
2 Key Refreshment
Let
r
be the symmetric encryption key to be multicast, and let
n
be the number of
members at a given time. The process can be divided in several phases.
Phase 1. Member ticket assignment.
When a member
i
enters the system, he joins the
group and a member ticket
x
i
is assigned by the Key server. Every ticket
x
i
is a large
prime and is transmitted to the corresponding member under a secure channel. It is
important to note that this communication is performed once per member only, in
such a way that the ticket
x
i
is used by the member
i
for the whole time he is in the
group. Furthermore, all tickets must be different from each other.
Therefore,
x
i
is only known by its owner and the Key server, while
r
will be shared
by all group members and the Key server.
Phase 2. Distribution
. This phase is performed by several steps.
Step 1.
The Key server selects the parameters of the system to generate the encryp-
tion key
r
. It selects:
•
Two large prime numbers,
m
and
p
, such that
p
divides
m
- 1.
•
δ
<
x
i
for every
i
= 1, ..., n
•
k
such that
δ
=
k
+
p
.
g such that
g
p
= 1 mod
m
.
The encryption key
r
is computed as
r
=
g
k
mod
m.
Step 2
. The Key server calculates
•
n
i
∏
=
L
=
x
.
(1)
1
The parameter
L
is kept private in the Key server.
Step 3
. The Key server computes
u
and
v
by means of the Extended Euclidean al-
gorithm [4], such that
(2)
u
·
δ
+
v·L
= 1 .
Step 4
. The Key server multicasts
g
,
m
and
u
as plain text.
Step 5
. Each member
i
calculates
=
u
-1
mod
x
i
to obtain the encryption key
r
by
δ
means of the equation
g
δ
mod
m
=
g
k
mod
m
=
r .
(3)
Each refreshment of the encryption key
r
, implies the generation of new values for
m
,
g
,
p
and/or
k
. As a consequence,
δ
,
u
and
v
will be also refreshed.
Phase 3. Arrival of a member j
. In this case, the ticket
x
j
is assigned to member
j
by
the Key server. Then, the ticket is included in the encryption key generation by
means of equation 1, since the parameter
L
is the product of all the tickets. In this
way, the encryption key
r
does not change, and thus the rest of the members do not
need to refresh the key. The only operation the Key server must perform is a multi-
plication to obtain the new value for
L
.
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