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Authors: Yanchao Zhang, Member, IEEE, Wei Liu, Wenjing Lou,Member, IEEE, and Yuguang Fang, Senior Member, IEEE Source: IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING, 2006 Presenter: Hsin-Ruey, Tsai

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Introduction Related work Design goals and system models IKM design Performance evaluation

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Introduction MANET: Mobile ad hoc network Infrastructureless, autonomous, stand-alone wireless networks. Key management: Serverless Two intuitive symmetric-key solutions: 1. Preload all the nodes with a global symmetric key. 2. Let each pair of nodes maintain a unique secret that is only known to those two nodes.

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Use public-key certificates to authenticate public keys by binding public keys to the owners’ identities. Preload each node with all the others’ public-key certificates prior to network deployment. Certificate-based cryptography(CBC) Drawbacks: network size, key update is not in a secure, cost-effective way.

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ID-based cryptography(IBC) Eliminate the need for public key distribution and certificates. Master-key All/some are shareholders ID-based private keys collaboratively issues Drawbacks: 1. Compromised nodes more than threshold number, 2. Key update is a significant overheads, 3.How to select the secret sharing parameters, 4.No comprehensive argument about the advantages of IBC-based schemes over CBC-based ones.

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ID-based key management (IKM) A novel construction method of ID-based public/ private keys. Determining secret-sharing parameters used with threshold cryptography. Simulation studies of advantages of IKM over CBC-based schemes. Node-specific not jeopardize noncompromised nodes’ private keys Common element efficient key updates via a single broadcast message Each node’s public key and private key is composed of a node-specific, ID-based element and a network-wide common element. IKM has performance equivalent to CBC-based schemes, denoted by CKM while it behaves much better in key updates. Identify pinpoint attacks against shareholders.

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Introduction Related work Design goals and system models IKM design Performance evaluation

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Related work CBC and (t, n) threshold cryptography N is number of nodes. t N N nodes CA’s public key Divided into n shares CA’s private key D-CA Certificate generation and revocation t D-CAs Tolerate the compromise of up to (t-1) D-CAs The failure of up to (n-t) D-CAs

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Pairing Technique p, q be two large primes G 1 a q-order subgroup of the additive group of point of E/F p G 2 a q-order subgroup of the multiplicative group of the finite field F* p^2 e : G 1 *G 1 → G 2 Bilinear: For all P, Q, R, S belong to G 1, Consequently, for all a, b belong to Z* q e(aP, bQ)=e(aP, Q)^b= e(P, bQ)^a=e(P, Q)^ab e(P+Q, R+S)= e(P, R) e(P, S) e(Q, R)e(Q, S)

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Introduction Related work Design goals and system models IKM design Performance evaluation

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Design goals MANETs should satisfy the following requirements: 1. Each node is without attack originally. 2. Compromise-tolerant. 3. Efficiently revoke and update keys of nodes. 4. Be efficient because of resource-constrained.

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Network & Adversary Model Network Model: special-purpose, single-authority MANET consisting of N nodes. Adversary Model: 1. Only minor members are compromised/disrupted. 2. Can’t break any of the cryptographic primitives. 3. Static adversaries. 4. Exhibit detectable misbehavior. Assumption that adversaries can compromise at most (t-1) D-PKGs and can disrupt no more than (n-t) D-PKGs (n is number of D-PKG, t is the threshold number)

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Introduction Related work Design goals and system models IKM design Performance evaluation

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Network Initialization PKG generates the paring parameters (p, q, e) and selects an generator W of G 1. H 1 : hash function maps binary strings to nonzero elements in G 1. K p 1,K p 2 : belong to Z* q and are master-secretes. W p 1 =K p 1 W, W p 2 =K p 2 W PKG preloads parameters (p, q, e, H 1, W, W p 1, W p 2 ) to each node while K p 1,K p 2 should never be disclosed to any single node.

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Secret Sharing Enable key revocation and update. PKG performs a (t, n)-threshold secret sharing of K p 2. (t nodes number of threshold) (n D-PKGs ) (N nodes) PKG n D-PKGs distributes functionality to n D-PKGs reach threshold t PKG preloads to D-PKG: (verifiable) t elements Lagrange interpolation Lagrange coefficient K P 2 can then be reconstructed by computing g(0) with at least t elements.

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Generation of ID-Based Public/Private Keys node-specificphase-specific Our IKM is composed of a number of continuous, nonoverlapping key update phases, denoted by p i for 1 i < M, where M is the maximum possible phase index. p i is associated with a unique binary string, called a phase salt, salt i Vary across key- update phases Remain unchanged and be kept confidential to A itself Due to the difficulty of solving the DLP in G 1, it is computationally infeasible to derive the network mastersecrets KP1 and KP2 from an arbitrary number of public/private key pairs Cannot deduce the private key of any noncompromised node.

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Key Revocation Misbehavior Notification B accuses A timestamp shared key with V communication overheadresilient

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Key Revocation Revocation Generation If over thresholddiagnose joint efforts of t D-PKGs t D-PKGs in with smallest IDs (leader) generates partial revocation revocation leader accumulated all the D-PKGs in generates partial revocation sends revocation leader D-PKGs sends the accumulated accusations response after verify accusation Complete revocation

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Key Revocation Partial revocations Complete revocation Revocation leader denote the t D-PKGs participating in revocation generation It is possible that one or several members of A are unrevoked compromised nodes which might send wrongly computed partial revocations. Revocation leader check If not equivalent Check each node Floods to each node

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Key Revocation If D-PKGs in do not receive a correct revocation against A in a certain time revocation leader itself is a compromised node second lowest ID succeeds as the revocation leader As long as there is at least one noncompromised D-PKG in and there are at least t noncompromised D-PKGs in, a valid accusation against node A can always be generated.

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Key Update Public key: Private key: (B just performs two hash operations) needs the collective efforts of t D-PKGs in randomly selects (t-1) other nonrevoked D-PKGs send request these t D-PKGs including Z itself A generate a partial common private-key element check

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Key Update To propagate securely to all the nonrevoked nodes, we use a variant of the self-healing group key distribution scheme : set of nodes revoked until phase p i Z broadcasts maximum number of compromised nodes PKG picks M distinct degree polynomials, denoted by and M distinct degree polynomials is a point on E=F p, its x-coordinate can be uniquely determined from its y-coordinate. Key-Update Parameters Revoked node

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IKM design Choosing Secret-Sharing Parameter t, n They can only do is to attempt to compromise or disrupt randomly picked nodes with the expectation that those nodes happen to be the D-PKGs. Compromise and disrupt up to N c >=t and N d >=n-t+1 nodes P r c and P r d as the probabilities that at least t out of N c compromised nodes and (n-t+1) out of N d disrupted nodes happen to be D-PKGs

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Introduction Related work Design goals and system models IKM design Performance evaluation

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CKM vs IKM GloMoSim, a popular MANET simulator, on a desktop with an Intel P4 2.4GHz processor and 1 GB memory

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Performance evaluation

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