Group key management on tree-based braid groups

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Group key management on tree-based braid groups

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Abstract

The characteristic of mobile ad hoc networks (MANETs) build temporary dynamic network without any fixed infrastructure and limitation of power and computing capability present the challenge in secure communication. The existing key management protocols in wire network still do not suitable in MANETs.
In this paper, we propose the secure and efficient contributory group key agreement protocols. The protocols are based on braid groups cryptographic with key tree by avoiding modular exponential operation in Diffie-Hellman protocol. The braid groups and key tree are two techniques what can minimize communication and computing cost of generating group key. The braid groups only use product and inverse operation but sufficient complexity, since the hardness of the generalized conjugacy search problem is applied in our protocol. The dynamic operation protocol, especially join and merge protocol, use maximum signal strength between current member so call "director" and new member in order to achieve minimum hop communication, shortest range and fastest transfer rate. The director of leave and partition protocol is the member that has maximum number of one-hop neighbors for fastest broadcasting the information form director to every members. The constant round in communication of each protocol is designed with computation cost in serial number of braid permutations as O (log n). Our approach is simple, secure and efficiency for group key management in mobile ad hoc networks.

Abstract
Introduction
A braid groups cryptographic
1. Preliminaries of braid Group
2. Hard problem in the braid groups
3. Key exchange on braid groups
4. Multiparty key agreement on braid groups
Tree-based braid groups protocol
1. Key tree
2. Braid groups key exchange
3. Group key management on Tree-Based Braid Groups (TBG)
4. Join protocol
5. Leave protocol
6. Merge protocol
7. Partition protocol
Key security
Performance
Conclusion
References

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[...] Therefore root key that generated by each member node can be session group key Group Key Management on Tree-based Braid Groups (TBG) Our key tree scheme based on that each node can compute intermediate key from own secret key and sibling blinded key of the co-path node. Therefore the member node at leaf knows all keys on the key-path. This instance shows that the member is not necessary to know all blinded keys for generating the group key but knowing the all blinded key in our protocol in each member is provided for membership change to be more efficient and robust. [...]

[...] Section 3 describes the tree-base braid groups protocol for group key management including membership operation, join, leave, merge, partition and key refreshing. Section 4 analyzes the security of our protocol. Section 5 analyzes the performance of our protocol compare with others in communication and computation cost A braid groups cryptographic 2.1 Preliminaries of Braid Group The braid groups were first systematically proposed by Emil Artin. He introduced the Artin generators σ1, σ σn-1 for the n strand braid groups what is denoted as Bn. [...]

[...] The combination of forward and backward secrecy we follow that TBG protocol satisfies key independence Performance This section analyzes the communication and computation cost for join, leave, merge and partition protocol of TGB. We compare both cost with TGDH braid groups based on Diffie-Hellman key agreement and our proposed protocol TBG. We is analyzed the communication and computation costs for join, leave, merge, and partition protocol. The number of rounds, the total number of messages, the serial number of exponentiations, and serial number of braid permutations. Table 1 and Table 2 summarize the communication and computation cost respectively in three protocols. [...]

[...] Conclusion We propose tree-based group using braid groups key exchange for group communication. The modified TGDH using braid groups support dynamic membership group event including join, leave, merge and partition with forward and backward secrecy. Our protocol involves braid groups operation including product and inverse with key tree whose computation is slower than modular exponentiation in TGDH and braid groups on IKA.2. Our protocol is fully contributory scenario for key agreement that not requires the trust party or long-term controller to avoid the problems with the centralized trust and the single point of failure. [...]

[...] This one-way function is based on the generalized conjugacy search problem Key exchange on braid groups In Crypto 2000, Ko et al. proposed a new public-key cryptosystem using braid groups based on hard problem of the conjugacy problem They proposed new key agreement using braid groups which is a Diffie-Hellman version. The key agreement protocol is shown as follow: Preparation step : Assume Alice and Bob want to securely communicate on public channel. It mean Alice and Bob have to share a secrete key. [...]

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