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Performance Evaluation for Group Key Rekeying

Performance Evaluation for Group Key Rekeying. S1080014 Tsukasa Igarashi Supervised Prof. Hiroshi Toyoizumi. Purpose. To evaluate the performance for group key rekeying that is important for computer security. According to the condition, changing rekeying processes.

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Performance Evaluation for Group Key Rekeying

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  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.

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