Performance Evaluation for Group Key Rekeying

1. Performance Evaluation for Group KeyRekeying S1080014 Tsukasa Igarashi Supervised Prof.Hiroshi Toyoizumi

2. Purpose • To evaluate the performance for group key rekeying that is important for computer security. According to the condition, changing rekeying processes. Realizing effective group key rekeying !

3. Generate 2 keys P Sender Public Key P Secret Key S Data Encrypted Data Data Public Key Cryptosystem Receiver Encrypted Data

4. Group Key • Group key is an encryption key that is used among particular group members. • A group key is used on 1 to many communications.

5. Group Key 2 Group Key 1 Group Key 3 GK1 Rekey • Rekey is changing an from old group key to a new one. • Without rekey, illegal access increase by ex-group members. Illegal Access Join Leave

6. Where group key is used? • TV Pay programs (Ex. Wowow, SkyPerfecTV, or for etc.) • Particular Conferences in a company

7. Rekeying Processes • Immediate According to purpose of use, we need to separate 3 rekeying process. Once someone joins or leaves a group, rekey is done. (Ex. Conference, military communication) • Batch In fact, if particular number of members gather, rekey is done. But on analysis reason, according to the probability of α, rekey is done. (Ex. Internet, TV pay program) • Periodic Rekey is done in the constant period. (Ex. Internet, TV pay program)

8. With this expression, we can Calculate the expression of Rekeying processes. :the utilization in the system. :the arrival time in the system. :the variance of the service time in the system. Pollaczek-Khinchin Formula • With this formula, we can lead the expression of M/G/1 in waiting line theory. Below expression means M/G/1 queue expression.

9. Rekey Finish Rekey Finish S1 S2 Y1 W2 Y2 #3 #1 #2 W3 S3 Y3 Immediate Rekeying(Image) Join Leave S:Service Time(Constant) W:Waiting Time #:New Comer of a Group Y:The time from a customer arrives to leaves in the system.

10. With Pollaczek-Khinchin Formula and use Time of spending rekey rate of join or leave Assumption S < When S is small, E[Y] is small. If not, E[Y]  ∞ Immediate Rekeying(Performance)

11. Rekey Start Rekey Start Rekey Start #1 #3 #4 #7 #8 Y8 Y1 Y7 Y4 Y3 Y6 Y9 Y5 Y2 #2 #5 #6 #9 Batch Rekeying(Image) is the probability of rekey Join Leave #:New Comer of a Group

12. ●n:how many members behind a group member until the rekey starts. Assumption S < When α is small, E[Y] is small. If not, E[Y]  ∞ Batch Rekeying(Performance)

13. Rekey Start Rekey Start Rekey Start T T #3 #5 #6 #8 #10 #11 Y10 Y3 Y11 Y6 Y5 Y8 Y4 Y2 Y7 Y12 Y1 #1 #2 #4 #7 #9 Y9 #12 Periodic Rekeying(Image) Join Leave #:New Comer of a Group

14. Constant Period Assumption S <= T When T is small, E[Y] is small. If not, E[Y]  ∞ Periodic Rekeying(Performance)

15. Assumption T = 0.0011 S = 0.001, α = 1/10, n = 10 3 Rekeying Processes Comparison <When λ is small> • Immediate Rekeying • Batch Rekeying • Periodic Rekeying <When λ is big> • Periodic Rekeying • Batch Rekeying • Immediate Rekeying

16. Why ? My partner is #1 ! GK1 GK0 #1 Why ? GK2 GK3 #2 My partner is #2 ! Out-of-Sync Problem • In batch rekeying, the problem that a group member may receive a data encrypted with an old group key, or the group key it has not get yet is occurred. Join Leave

17. Conclusion • According to the number of group members and the purpose of use, the server’s administrator will need to think changing the rekeying processes. • In Batch rekeying, we must think out-of-sync problem.