Transcript KMS.ppt
Key Management Protocols
STR Protocol (Distributed
GKMP)
It is totally decentralized and based on equal contributions from all the
members.
It provides basic requirements like forward secrecy, backward secrecy
and key independence.
It also requires smaller number of unicasts and multicasts to compute a
new group key after a member leave or join.
7/17/2016
2
STR Protocol
Unbalanced tree of height n-1 where n
is current group size.
Final group key :
Kn g
g r 2. r 1
rn. g rn1...
Important Recurrence
ki (bki 1 ) ri mod p (bri ) ki 1 mod p
All bri’s and bki’s are known to
all members.
bri g ri mod p
bki g ki mod p
7/17/2016
3
STR Protocol (Cont.)
Initialization :
M1 computes
k2 (br2 ) r1 mod p g r1r 2 mod p, bk2 g k 2 mod p
k3 (br3 ) k 2 mod p, bk3 g k 3 mod p
k n (brn ) k n1 mod p
M1 broadcasts all bki’s to members
Each member then computes the
group key from bki’s.
For ex:
k3 (bk 2 ) r 3
M3 computes
7/17/2016
bri g ri mod p
bki g ki mod p
ki (bki 1 ) ri mod p (bri ) ki 1 mod4 p
STR Protocol (Cont.)
Join :
M5 broadcasts br5 to all members.
Each member then computes
new key.
M4 sends all previous bri’s and bki’s
to M5 who then computes
new key k5.
bri g ri mod p
bki g ki mod p
7/17/2016
ki (bki 1 ) ri mod p (bri ) ki 1 mod5 p
STR Protocol (Cont.)
Leave :
If Mn leaves then Mn-1 takes
responsibility to create new key.
Everybody renumbers the node.
Mn-1 selects new random key
r’n-1. Computes all bki’s and
broadcasts it to all members.
bri g ri mod p
bki g ki mod p
7/17/2016
ki (bki 1 ) ri mod p (bri ) ki 1 mod6 p
TGDH protocol
The TGDH protocol uses binary trees; every node is
either a leaf or a parent of two nodes.
The nodes are denoted as < l, v >, where 0 < v < 2l − 1 since
each level l hosts at most 2l nodes.
Each node < l, v > is associated with the key K < l, v >and the
public blinded key (bkey) BK < l, v >= f(K < l, v >)
where the function f ( ) is modular exponentiation in prime
order groups, i.e. f(K) = gkmodp.
Computing a key at < l, v > requires the knowledge of the key
of one of the two child nodes and the bkey of the other child
node.
7/17/2016
7
TGDH
7/17/2016
8
The final group key K < 0, 0 > is : K < 0, 0 >=
7/17/2016
9