1. Computer Science 1 CSC 774 Advanced Network Security Secure Group Communications Using Key Graphs Presented by: Siddharth Bhai 9 th Nov 2005

2. Computer Science 2 Imagine… A 24 x 7 x 365 business –Internet: the content distribution medium Convenient for everyone Everyone.. Including the eavesdroppers! –Pay-per-view revenue model –Dynamic content –Several users Teleconference Collaborative work

3. Computer Science 3 Roadmap The problem Existing techniques Key graphs Rekeying strategies Iolus v/s the key-graph approach Conclusions and future work

4. Computer Science 4 The Problem Securing group communications  Authenticity  Confidentiality  Integrity Scalability Joins/leaves

5. Computer Science 5 Existing Techniques Group Key Agreement –Diffie Hellman –Group-based Diffie-Hellman –Tree-based GDH Group Key Distribution –Naïve solution: 1 group key 1 unicast key per user –Iolus

6. Computer Science 6 “Secure group” (U, K, R) –U is a finite and non-empty set of users –K is a finite and non-empty set of keys –R is a binary relation between U and K User ‘u’ has key ‘k’ if and only if (u,k) is in R Group server –Knows U & K –Maintains user-key relation R –Generates and securely distributes keys in K to users in the group

7. Computer Science 7 Key Graphs A Directed Acyclic graph U-nodes 1 or more outgoing edges 1 incoming edge K-nodes 1 or more incoming edges –Root u1 u4 u3 u2 k1234 k234 k12 k4 k3 k2 k1

8. Computer Science 8 Key Graphs (contd..) A key graph specifies a secure group Group key is the root k-node Join/ Leave Special classes: –Star Naïve solution –Tree Logical Key hierarchy –Complete Every non-empty subset of users share a unique key!

9. Computer Science 9 Rekeying Strategies Depends on class of key graph Strategies for join and leave Key star: naïve solution Key tree –User-oriented rekeying –Key-oriented rekeying –Group-oriented rekeying

10. Computer Science 10 Key Tree u1 u4 u3 u2 k 45 k 123 k4 k3 k2 k1 k5 k 12345 u5 u1 u4 u3 u2 k 456 k 123 k4 k3 k2 k1 k5 k 123456 u5 k6 u6 U6 leaves U6 joins

11. Computer Science 11 Join: user-oriented rekeying Concept: –For each user, the server constructs a rekey message that contains precisely the new keys needed by the user How? –For each key node (x) whose key has been changed (k to k’), server constructs a rekey message by encrypting the new keys of k-node x and all its ancestors by the old key k. –For the new user, one rekey message

12. Computer Science 12 Join: user-oriented rekeying (contd..) What will be the rekey messages? u1 u4 u3 u2 k 45 k 123 k4 k3 k2 k1 k5 k 12345 u5 u1 u4 u3 u2 k 456 k 123 k4 k3 k2 k1 k5 k 123456 u5 k6 u6 U6 joins

13. Computer Science 13 Join: user-oriented rekeying (contd..) What will be the rekey messages?  S {u1,u2,u3}: {k 123456 }k 12345  S {u4, u5}:{k 123456, k 456 }k 45  S {u6}:{k 123456, k 456 }k 6 No. of rekey messages = height of the tree Encryption cost for server = [h(h+1)/2] - 1

14. Computer Science 14 Join: key-oriented rekeying Concept: –Each new key is encrypted individually (except keys for joining user) How? –For each key node (x) whose key has been changed (k to k’), server constructs 2 rekey messages –1 st : Encrypt new key k’ with old key k, send this to all users who hold k –2 nd : Encrypt k’ with individual key of joining user

15. Computer Science 15 Join: key-oriented rekeying (contd..) What will be the rekey messages? u1 u4 u3 u2 k 45 k 123 k4 k3 k2 k1 k5 k 12345 u5 u1 u4 u3 u2 k 456 k 123 k4 k3 k2 k1 k5 k 123456 u5 k6 u6 U6 joins

16. Computer Science 16 Join: key-oriented rekeying (contd..) What will be the rekey messages?  S {u1,u2,u3, u4, u5}: {k 123456 }k 12345  S {u6}:{k 123456 }k 6  S {u4,u5}:{k 456 }k 45  S {u6}:{k 456 }k 6 No. of rekey messages = height of the tree Encryption cost for server = 2 (h-1)

17. Computer Science 17 Join: group-oriented rekeying Concept: –A single rekey message containing all the keys, multicasted to the entire group –1 message for the joining user Why? –No need for subgroup multicast –Fewer rekey messages server’s per-rekey message overheads are reduced

18. Computer Science 18 Join: group-oriented rekeying (contd..) What will be the rekey messages? u1 u4 u3 u2 k 45 k 123 k4 k3 k2 k1 k5 k 12345 u5 u1 u4 u3 u2 k 456 k 123 k4 k3 k2 k1 k5 k 123456 u5 k6 u6 U6 joins

19. Computer Science 19 Join: group-oriented rekeying (contd..) What will be the rekey messages?  S {u1,u2,u3, u4, u5}: {k 123456 }k 12345,, {k 456 }k 45  S {u6}:{k 123456, k 456 }k 6 No. of rekey messages = 2 Encryption cost for server = 2 (h-1)

20. Computer Science 20 IOLUS v/s key-graph Key-Graph Hierarchy of multiple keys Each user – multiple keys More work is done when a join/leave takes place Single trusted entity: the key server Iolus Hierarchy of multiple GSAs Each user – one key (for it’s subgroup) More work is done when a message is to be sent to the entire group Multiple trusted entities: GSC, several GSAs..

21. Computer Science 21 Conclusion and Possible Future Work Performance on the server-side: –Best: Group-oriented rekeying –Worst: User-oriented rekeying Performance on the client-side: –Best: user-oriented rekeying –Worst: group-oriented rekeying Why do we need key graphs at all? –Isn’t a key-tree good enough? Future work