Secure group key management based on hyper-sphere
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This document proposes a provably secure group key management approach based on hyper-spheres. It describes how a hyper-sphere, the generalization of a sphere to higher dimensions, can be used to model a group key. The key is updated by periodically constructing new hyper-spheres. Modules are presented for initialization, adding members, removing members, massively changing membership, and periodic key update. The approach aims to provide a secure, efficient, and scalable solution for group communication systems.
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Secure group key management based on hyper-sphere
- 1. Provably Secure Group Key Management Approach Based upon Hyper-Sphere By, D.Darling Jemima
- 2. Problem statement • The rapid development of Internet technology are playing important roles. • Protection of communication security is becoming more and more significant. • A secure group communication system accommodates perfect scalability.
- 3. Contd.., • A secure, efficient, and robust group key management approach is essential to a secure group communication system. • The security could be provided to group communication system using mathematical concept called hyper-sphere.
- 4. Abstract • A hyper-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. • The distance from any point on the hyper sphere to the central point of the hyper-sphere is identical. • A secure group key management scheme could be designed using mathematical model hyper sphere.
- 5. Contd.., • The group key is updated periodically to protect its secrecy. • Each key is completely independent from any previously used and future keys. • A formal security proof could be generated under the assumption of pseudorandom functions (PRF).
- 6. Hyper-Sphere in Euclidean Space • An N-sphere of radius r ϵ R with a central point C =( ) ϵ is defined as the set of points in (N+1) dimensional Euclidean space which are at distance r from the central point C. • Representation: ncccc ,...,, 210 1N R
- 7. Euclidean space for N+2 points For any given N+2 points in the hyper-space
- 8. Hyper-Sphere over Finite Field
- 9. Modules for building security using hyper-sphere Initialization Adding members Removing members Massively Adding and Removing Members Periodically Update
- 10. Module 1:Initialization • Step 1: Group controller selects two private point say s0 and s1. • Step 2: GC chooses a two dimensional private point A1=(a10,a11) random for the user U1. • Step 3: GC selects a random number u ϵ GF(p) and compute
- 11. Contd… • Step 4: The GC establishes a hyper-sphere, here in a circle, in two-dimensional space using the points B0 and B1. • Step 5: The GC delivers the public rekeying information C and u to the member U1 • Step 6: The member U1 can calculate the group key by using its private point A1=(a10,a11) along with the public information C and u.
- 12. Module 2:Adding members • Step 1:After the new user is authenticated the GC selects two dimensional private point. • Step 2: The GC sends the point to the user via a secure channel. • Step 3:The GC selects a different random number u ϵ GF(p) and computes
- 13. Contd… • Step 4:The GC multicasts the public re-keying information C and u to all group members. • Step 5:Each group member U can calculate the group key by using its private point A along with the information C.
- 14. Module 3:Removing member • Step 1:The GC deletes the leaving members’ private two dimensional points. • Step 2:The GC’s private two-dimensional points S0 and S1, and the remaining members’ private points A1;A2 ; . . .;AN should be stored securely by the GC. • Step 3-6: Similar to adding member in a group.
- 15. Module 4:Massively adding and removing members • Step 1. The GC deletes the leaving members’ private two dimensional points, and let new users join in at the same time. • Step 2:The GC sends the private point A to the user U via a secure channel. • Step 3:constructs a new hypersphere, and publishes the new random number u and the new central point C of the hyper-sphere.
- 16. Module 4:Periodically update • Update procedure is to renew the group key to safeguard the secrecy of group communication. • The GC needs to select a new random number u ϵ GF(p), then construct a new hyper sphere. • The steps are the same as Steps 3-6 in “Adding Members” phase.