A Survey of Key Management for Secure Group Communications Celia Li

2 Outline Group Communications Security Issues Requirements Classification Group Key Management Protocols

3 Group Communications Internet Group Communications  One-to-many  Many-to-many Advantages  Scalability  Efficiency Applications: Pay-per-view video, distant education, multiplayer games, online chat group NOTE: Broadcast: one-to-all

4 Security Issues Authentication: Identifies the members of the group (senders & receivers) Confidentiality: Content of a message must be shared only by authorized users Integrity: Data cannot be modified without being detected Access control: Ensures that only authorized actions can be performed (e.g., restricting membership, restricting who can send data) Non-repudiation: Ensures that an originator cannot deny sending a message. Availability: Ensures that authorized actions can in fact take place Security Mechanism: Group Key Management

5 Group Key Management To provide secure distributions & handling of cryptographic keying materials Group Key  A piece of secret information that is known only to the current group members  Used to encrypt message Membership changes trigger rekeying process  Join: a new group key must prevent the new member from decoding previous messages  Leave: a new group key must prevent former group members from decoding future messages Group Key Management Problem:  How to ensure that only legitimate users have access to the group key

6 Requirements for Group Key Management (1) Group key secrecy  Computationally infeasible for a passive adversary to discover a group key Forward secrecy  Evicted users cannot learn any future keys Backward secrecy  New users should not have access to any old keys Key independency  Disclosure of a key does not compromise other keys.

7 Requirements for Group Key Management (2) Scalability (1-affects-n)  A membership change should affect only a small subset of members Reliability  Providing a recovery mechanism for missing rekeying messages Resistance to attacks  From both inside and outside the group Low bandwidth overhead  Rekeying should not induce a high number of messages

8 Group Key Management Classification The entity who exercises the group control Centralized Group Control  A single entity is the group controller who is …  Responsible for key generation, key distribution and key refreshment  Ex: Naïve Solution, Key tree-based Approach Subgroup Control  The group is divided into subgroups  Each subgroup is managed by its own controller  Ex: Iolus Framework Member control  No group controller  Each member contributes its share toward group key generation  Ex: Contributory key agreement supported by the Diffie-Hellman algorithm: Cliques

9 Naïve Solution Group Key vs Individual Key  Used to encrypt messages  Used to verify each member’s identity Rekeying Message  Used to notify all members of any key change and the new key information Join  Encrypt new group key with the old group key and multicast to group  Encrypt new group key with new user’s individual key and unicast to the joining user  Number of rekeying messages: O(1) Leave  Encrypt new group key with each user’s individual key and Send it to remaining users one by one  Number of rekeying messages: O(n) Problem  Not scalable when users leave k1k2k3k4 K1-4 m1m2m3m4 k1k2k3 K1-3 m1m2m3 Group key Individual keys m4 leavesm4 joins Member {K1-4} k1-3 {K1-4} k4 {K1-4} k1 {K1-4} k3 {K1-4} k2

10 Key Tree-Based Approach K1-8 K7-8K5-6K3-4K1-2 K1-4 Group key Individual keys Member Intermediate keys GC Central Group Controller Key Tree Root: group key, encrypt/decrypt multicast data packets Leaf: member’s individual key Nodes between leaves and root: intermediate keys, that are used to encrypt other keys instead of actual data Each member stores the keys from leaf to the root m1: {k1, k1-2, k1-4, k1-8} m6: {k6, k5-6, k5-8, k1-8} m8m7m6m5m4m3m2m1 k8k7k6k5k4k3k2k1 K5-8

11 Key Tree-Based Approach: Join K1-8 K7-8 K3-6 Group key Individual keys Member Intermediate keys GC Central Group Controller m9 joins the group: K7-8  K7-9, K1-8  K1-9 GC  {m7, m8}: {K7-9} K7-8 GC  {m1, …, m8}: {K1-9} K1-8 GC  {m9}: {K7-9, K1-9} K9 # of rekeying: At most 2log k n K1-3 Keys along the path need to be changed Every changed key is encrypted with old keys, multicast to the group except newly join member New member gets keys through unicast Number of rekeying messages: O(log k n) m8m7m6m5m4m3m2m1m9 k8k7K6k5k4k3k2k1  K1-8  K1-9  {K1-9} K1-8  {K7-9} K7-8  K7-8  K7-9 K1-9 K7-9  {K7-9} K9  {K1-9} K9 k9

12 Key Tree-Based Approach: Leave K1-9 K7-9 K3-6 Group key Individual keys Member Intermediate keys GC Central Group Controller GC  {m7}: {K7-8} K7 GC  {m7}: {K7-8} K8 GC  {m1, m2, m3}: {K1-8} K1-3 GC  {m4, m5, m6}: {K1-8} K3-6 GC  {m7, m8}: {K1-8} K7-8 # of rekeying: At most klog k n K1-3 m8m7m6m5m4m3m2m1m9 k8k7K6k5k4k3k2k1  K1-9  K1-8  {K1-8} K1-3 K1-8 K7-8 k9  {K7-8} K8  {K7-8} K7  {K1-8} K3-6  {K1-8} K7-8 Keys along the path need to be changed Every changed key is encrypted with each of its children’s keys Number of rekeying messages: O(log k n) m9 leaves the group: K7-8  K7-9, K1-8  K1-9  K7-9  K7-8

13 Centralized Group Control Advantages  Key tree structure reduces the number of rekey message to O(log k n)  Suitable for general multicast sessions having small to medium sizes such as Internet radio and stock quote services Disadvantages  Single point of failure at the central controller  Not scalable for very large groups

14 Subgroup Control: Iolus Framework Sender SGC1 mm SK1 SGC2 mmm SGC3 mm SK2SK3 SGC: subgroup controller Ki: subgroup controller’s individual key SKi: subgroup key Sender generates a random number to encrypt actual data The random number is encrypted by each subgroup controller’s individual key  {Data} Rand # |{Rand #} k3 SGC31 mmm SK31 SGC11 mmm SK11  {Data} Rand # |{Rand #} SK3  {Data} Rand # |{Rand #} SK31 K3K2K1 new member joins/leaves local subgroup Subgroup controller changes its subgroup key Other subgroup keys do not need to be changed

15 Subgroup Control: Iolus Framework Advantages  Easier group management as a large multicast group is organized into smaller subgroups  Eliminating the problem of concentrating the workload on a single group controller  Suitable for general multicast sessions with globally distributed members such as pay-per view international news and movie systems Disadvantages  Members cannot access group communications if their subgroup controller fails  Introducing message delivery delay as subgroup controllers have to perform key translation  Not suitable for real-time multicast applications such as video-conferencing

16 Member Control No group controller Every member contributes a share towards the group key Requires knowledge of group membership Example protocol: Contributory key agreement supported by the Diffie-Hellman algorithm: Cliques

17 Diffie-Hellman A = g a mod p K= B a mod p K= A b mod p B = g b mod p A B AliceBob K=A b mod p = B a mod p = g ab mod p DH allows two individuals to agree on a common symmetric key It has been proved that nobody else can compute the shared key g ab in a reasonable amount of time even though they know g a and g b g a is used to represent g a mod p p: large prime (e.g. 512 or 1024 bits) g: base generator a: Alice’s secret integer b: Bob’s secret integer

18 Member Control: Cliques Stage 1:m1m2m3 m4 g s1 g s1s2 Stage 2: Stage 3: Stage 4: m1 m2 m3 m4 g s1s2s3 m1 m2 g s2s3 g s1s3 m3 m4 g s1s2 m1 m2 g s2s3s4 g s1s3s4 m3 m4 g s1s2s4 Group Key m1 m2 m3 m4 g s1s2s3s4 =g (s2s3s4)s1 =g (s1s3s4)s2 =g (s1s2s4)s3 =g (s1s2s3)s4 Cliques arranges the group member in a logical liner structure and passes key information sequentially Group members are indexed The last two members (having the highest indices) are responsible for taking part in key distribution The last member does the key distribution

19 Cliques: Join Stage 1: m4m5 {g s1s2s3, g s1s2s4’, g s1s3s4’, g s2s3s4’ } Stage 2: m1 m2 g s2s3s4’s5 g s1s3s4’s5 m3 m5 g s1s2s4’s5 New Group Key m1 m2 m3 m4 m5 g s1s2s3s4’s5 = g (s2s3s4’s5)s1 =g (s1s3s4’s5)s2 =g (s1s2s4’s5)s3 =g (s1s2s3s5)s4’ =g (s1s2s3s4’)s5 m4 g s1s2s3s5 new member m n+1 replaces member m n to distribute partial keys m n factorizes out his secret number from all factorized partial keys; adds a newly generated secret number s n ’; sends it to m n+1 m n+1 adds his own secret number and sends the new partial keys back to the corresponding members m1 m2 g s2s3s4 g s1s3s4 m3 m4 g s1s2s4 m5 joins Old Group Key g s1s2s3s4 s4  s4’

20 Cliques: Leave m1 m2 g s2s3s4 g s1s3s4 m3 m4 g s1s2s4 New Group Key m1 m3 m4 m2 g s1s3s4’ = g (s3s4’)s1 = g (s1s4’)s3 = g (s1s3)s4’ ? m1g s3s4’ m3 m4 g s1s4’ m2 leaves m n generates a new secret number s n ’ m n computes new partial keys excluding departure member’s secret number; sends them to the other members Departure member has no information to compute the new group key Old Group Key g s1s2s3s4 s4  s4’

21 Member Control: Cliques Advantages  No single point of failure (no central controller)  Robust due to self-stabilization  Single function handles join and leave  Suitable for a multicast system having a small size and a less powerful server or no centralized server, such as video conferencing Disadvantages  Heavy workload on the member who does key distribution  Not scalable: number of rekeying messages is O(n)  Requires knowledge of group membership

22 Conclusion Key Management for Secure Group Communications Centralized Control  Easy to implement; concentrated high overhead on a single entity; not scalable Subgroup Control  Membership changes in a subgroup does not affect other subgroups  more scalable Member Control  Member-driven design; higher workload on the member who does key distribution