Title | Wireless Information Networking Group WING Key Establishment in |
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Wireless Information Networking Group (WING) Key Establishment in Wireless Sensor Networks Yun Zhou Wireless Networks Laboratory Wireless Information Networking Group Department of Electrical & Computer Engineering University of Florida Mar. 28, 2007
Wireless Information Networking Group (WING) Outline • • • Introduction The state of art A scalable approach Analysis and evaluation Conclusions
Wireless Information Networking Group (WING) Wireless Landscape • • • One-hop v. s. multi-hop Internet Static v. s. mobile Small scale v. s. large scale General access v. s. customized application Powerful portable laptop v. s. resource-constrained sensor etc. Mesh Networks WLANs, WMANs Ad Hoc Networks Sensor Networks
Wireless Information Networking Group (WING) Wireless Sensor Networks • Resource-constrained sensors: memory in KBs, 8 -bit CPU, battery-power. • Large scale, multi-hop. • Hostile environments: battle fields, estate monitoring, etc. • Security!
Wireless Information Networking Group (WING) Key Establishment • The first step - Encryption, authentication, signature, etc. • Requirements - Simple - Scalable • Public key v. s. symmetric key
Wireless Information Networking Group (WING) Outline • • • Introduction The state of art A scalable approach Analysis and evaluation Conclusions Future work
Wireless Information Networking Group (WING) Key Agreement Models • Pre-distributed keys - Key subset: each node is preloaded with a key subset selected from a global key set. - Pairwise key: each pair of selected nodes is assigned with a pairwise key. • Eschenauer and Gligor (CCS’ 02), Chan et al. (S&P’ 03, Infocom’ 05), Lee and Stinson (SAC’ 04, WCNC’ 05), Camtepe and Yener (ESORICS’ 04)
Wireless Information Networking Group (WING) Key Agreement Models • Blom matrix (Euro. Crypt’ 84) - Public matrix P(t+1)×N - Secret symmetric matrix S(t+1)×(t+1) - AN×(t+1)=(S·P)T - K=A·P=(S·P)T·P=PT·S·P=(A·P)T=KT - Node i is assigned with the i-th row of A and the i-th column of P. - Nodes i and j exchange columns of P. - Kij = A(i) · Pj = A(j) · Pi = Kji • t-secure: the collusion of less than (t+1) nodes cannot reveal any key shared by any other pair of nodes. • Du et al. (CCS’ 03).
Wireless Information Networking Group (WING) Key Agreement Models • Polynomial, Blundo et al. (Crypto’ 92) - A variant of Blom matrix model - P(t+1)×N is a Vandermonde matrix computed based on node identities. - S(t+1)×(t+1) is a t-degree bivariate symmetric polynomial f(x, y). • t-secure as Blom matrix model. • Liu and Ning (CCS’ 03, SASN’ 03).
Wireless Information Networking Group (WING) Key Establishment • Direct keys - Pre-distributed or computed according to Blom matrix or polynomial models. • Indirect keys - Negotiated along a key path.
Wireless Information Networking Group (WING) Problems • Not scalable - Memory cost O(N) or O(N 1/2) • Node compromise - Direct keys: key reuse (pre-distributed keys), low secure threshold (matrices or polynomials) - Indirect keys: long key path
Wireless Information Networking Group (WING) Outline • • • Introduction The state of art A scalable approach Analysis and evaluation Conclusions Future work
Wireless Information Networking Group (WING) Our Approach • A t-degree multivariate symmetric polynomial f (x 1, x 2, …, xk+1) = f (xσ(1), xσ(2), …, xσ(k), xσ(k+1)) σ : {1, 2, … k, k+1} → {1, 2, … k, k+1}
Wireless Information Networking Group (WING) Our Approach • k credentials, positive and pairwise different • Nodes a=(a 1, a 2, …, ak) and b=(b 1, b 2, …, bk) • Polynomial shares f (a 1, a 2, …, ak, xk+1) and f (b 1, b 2, …, bk, xk+1) • Conditions: - for some 1≤ i ≤ k, ai ≠ bi, and - for j =1, 2, …, k, j ≠ i, aj = bj = cj • Direct key Kab = f (c 1, c 2, …, ci-1, ai, ci+1 , …, ck, bi) = f (c 1, c 2, …, ci-1, bi, ci+1 , …, ck, ai)
Wireless Information Networking Group (WING) Our Approach • Node n=(n 1, n 2, …, nk), ni = 0, 1, 2, …, Ni-1 • Network size N = ∏ki=1 Ni • ID -> credentials c 1 = n 1+1 c 2 = n 2+1+ N 1 c 3 = n 3+1+ N 1 + N 2 …… ck-1 = nk-1+1+ N 1 + … + Nk-2 ck = nk+1+ N 1 + … + Nk-1
Wireless Information Networking Group (WING) Our Approach • Direct key - Only one mismatch in the IDs of two nodes • Indirect key - Negotiation through a key path of fixed length
Wireless Information Networking Group (WING) Outline • • • Introduction The state of art A scalable approach Analysis and evaluation Conclusions Future work
Wireless Information Networking Group (WING) Memory Cost • Security level - Protect direct keys under the node compromise attack. - The global polynomial should not be recovered.
Wireless Information Networking Group (WING) Memory Cost • Node n=(n 1, n 2, …, nk) • For some i, ni = 0, 1, 2, …, Ni-1, credentials {c(0), c(1), …, c(Ni-1)} • Ni(Ni+1)/2 equations f 2 (c(0), c(0)) = K 0, 0 …… f 2 (c(0), c(Ni-1)) = K 0, Ni-1 f 2 (c(1), c(1)) = K 1, 1 …… f 2 (c(Ni-1), c(Ni-1)) = KNi-1, Ni-1
Wireless Information Networking Group (WING) Memory Cost • For all nodes: N = ∏ki=1 Ni • The number of equations: Ne = (N/N 1) ∙ N 1(N 1+1)/2 + (N/N 2) ∙ N 2(N 2+1)/2 + …… + (N/Nk) ∙ Nk(Nk+1)/2 = (1/2) ∙ (∏ki=1 Ni) ∙ (∑ki=1 Ni+k) • The number of coefficients of the t-degree (k+1)-variate symmetric polynomial:
Wireless Information Networking Group (WING) Memory Cost • To protect the global polynomial, we need • Consider Ni=N 1 for i=1, 2, …, k, we get • The optimum degree
Wireless Information Networking Group (WING) Memory Cost • (t+1) coefficients ~ r N 1/k k r t*/N 1 r - t*/N 1 1 0 2 1. 8171 1. 7715 0. 0456 3 2. 4495 2. 3919 0. 0576 4 2. 9926 2. 9219 0. 0707 5 3. 4878 3. 4058 0. 0820 • Conventional schemes: O(N) or O(N 1/2)
Wireless Information Networking Group (WING) Security • Direct keys: secure • Indirect keys: - The number of intermediate nodes along a key path is h, 1≤ h≤ k-1. - The maximum compromise probability: Pc, max=1 - (1 -pc)k-1 • Conventional schemes: - Direct keys can be exposed: key reuse, low secure threshold. - Indirect keys, h can hardly be decided, and can be very large.
Wireless Information Networking Group (WING) Conclusions • Conventional schemes are lack of scalability due to the high memory cost • A scalable key establishment approach: tune k - Given the number of nodes N, the memory cost can be very small.
Wireless Information Networking Group (WING) Q&A Thanks !