1. Broadcast Encryption Scheme Based on Binary Cubes Alexey Urivskiy JSC «InfoTeCS», Moscow, Russia alexey.urivskiy@mail.ru

2. What is Broadcast Encryption? Center Channel Message Privileged usersRevoked users Alexey Urivskiy ACCT'2014

3. Purpose Securely broadcast a message to an arbitrary dynamically changing subset of stateless receivers. Alexey Urivskiy ACCT'2014

4. Typical BE-Applications pay-TV systems; tactical radio; positioning systems; digital rights management solutions; etc. Alexey Urivskiy ACCT'2014

5. Preliminary Phase: Key Distribution 4 Center 1 2 3 Alexey Urivskiy ACCT'2014

6. 1234

7. Broadcast Phase: Message Index = Information on which users are in which subset Ciphertexts = The Session Key encrypted on Key Encryption Keys (KEK) Encrypted message = The Message encrypted on the Session Key IndexCiphertextsEncrypted message HEADER BODY Alexey Urivskiy ACCT'2014

8. Performance Parameters Transmission overhead the header’s length User key block the number of KEKs of the user Processing complexity Security focus only on information-theoretic secure Alexey Urivskiy ACCT'2014

9. Designing a good BES? Provided the BES is secure computationally efficient given the network size the number of the revoked users to balance the size of the user key block and the transmission overhead Alexey Urivskiy ACCT'2014

10. Naive Scheme 1234 Alexey Urivskiy ACCT'2014

11. Properties Transmission overhead Largest possible User key block Smallest possible = 1 Key Processing complexity Low Alexey Urivskiy ACCT'2014

12. Trivial Scheme 1234 12 3 4 5 6 7 8 9 10 11 12 13 14 15 Alexey Urivskiy ACCT'2014

13. Properties Transmission overhead Smallest possible = 1 KEK User key block Largest possible Processing complexity Low Alexey Urivskiy ACCT'2014

14. The CuBES Cubes Based Broadcast Encryption Scheme Alexey Urivskiy ACCT'2014

15. Why we say ‘CUBES’? xyz 111 110 101 011 100 010 001 000 y x z (1,1,1) (0,1,1) (0,0,1) (1,0,1) (0,1,0)(0,0,0) (1,1,0) (1,0,0) Binary cube of dimension 3 Alexey Urivskiy ACCT'2014

16. 1234 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 111 111 111 1 1 1 11 11 11 11 11 11 1 1 1 1 0 0 0 0 00 0 0 00 00 0 00 0 000 00 0 0 0 00 0 0 0 0 00 Binary cube of dimension 4 Alexey Urivskiy ACCT'2014

17. 1234 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Properties for N users 2 N -1 keys in total 2 N-1 keys for every user 1 KEK to handle any configuration of revoked users Limitation: in practice N ≤ 20 Alexey Urivskiy ACCT'2014

18. Approach Partition users into small group. Apply the trivial scheme to every group. Apply a logical hierarchy to group of users – a tree-like construction. Alexey Urivskiy ACCT'2014

19. Hierarchy Example - 24 users Binary cube (keys) for 2 (virtual) users Binary cube (keys) for 3 (virtual) users Binary cube (keys) for 4 users User Alexey Urivskiy ACCT'2014

20. Users Key Block Example 3 Alexey Urivskiy ACCT'2014

21. 1234 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 1 2 3 3 Users Key Block Example Alexey Urivskiy ACCT'2014

22. 3 2 1414 1 2 4 5 7 9 1 1 2 4 6 1 Users Key Block Example Alexey Urivskiy ACCT'2014

23. Example 4x3x2 User’s storage 14 KEKs Coverage 5 KEKs Alexey Urivskiy ACCT'2014

24. Example 6x4 User’s storage 47 KEKs Coverage 4 KEKs Alexey Urivskiy ACCT'2014

25. Example 8x3 User’s storage 131 KEKs Coverage 3 KEKs Alexey Urivskiy ACCT'2014

26. Worst case analysis # Revoked users Coverage, # KEKs Alexey Urivskiy ACCT'2014

27. Scheme Transmission overhead, KEKs User key block, KEKs 8x8x4x4x4x4x4x4x4 ~82000304 9x9x6x6x6x5x4x3 ~ 78500 629 10x10x7x7x6x6x6 ~ 76000 1242 Users: N=2 20 Revoked users: r=2 16 CuBES Example Alexey Urivskiy ACCT'2014

28. Coverage, # KEKs # Revoked users 8x8x4x4x4x4x4x4x49x9x6x6x6x5x4x310x10x7x7x6x6x6 Alexey Urivskiy ACCT'2014

29. Thank you! Questions? Alexey Urivskiy ACCT'2014