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A Secure Key Agreement Scheme in Low-Energy Wireless Sensor Networks

A Secure Key Agreement Scheme in Low-Energy Wireless Sensor Networks International Federation for Information Processing 2006 2007.11.29. Presented by An Dong-hyeok. Table of Contents. 1. Introduction 2. Modified Rivest’s Scheme(MRS) 3. Secure Key Agreement Scheme 4. Performance

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A Secure Key Agreement Scheme in Low-Energy Wireless Sensor Networks

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  1. A Secure Key Agreement Scheme in Low-Energy Wireless Sensor Networks International Federation for Information Processing 2006 2007.11.29 Presented by An Dong-hyeok

  2. Table of Contents 1. Introduction 2. Modified Rivest’s Scheme(MRS) 3. Secure Key Agreement Scheme 4. Performance 5. Security Analysis 6. Conclusion

  3. 1. Introduction • wireless sensor network • faults of sensor nodes, energy depletion and security attack due to resource scarcity • need to the security communication protocol • symmetric cryptographic • the existing protocol, which are based on random key pre-distribution, has some drawbacks

  4. 1. Introduction • open problem in wireless sensor network • how to authenticate the key information of communicating nodes •  solution: key pre-distribution, shared-key discovery, path-key establishment • how to securely set up a session key between communicating nodes • how to minimize the amount of disclosed information about the keys to the other side

  5. 2. Modified Rivest’s Scheme(MRS) • notation • n: size of network • z, s, m: size of the key space, the key pool and the key chain • SK: session key generated between authorized nodes • KA, KB: secret key of node A and B • EK(M), DK(M): message M encrypted and decrypted with key K • h(): one-way hash function • p, q: prime numbers • r (or ri), s (or si): random numbers, 0 ≤ I < m

  6. 2. Modified Rivest’s Scheme(MRS) • MRS scheme is used in the shared-key discovery phase • A = {a1, a2, …, am}, B = {b1, b2, …, bm} • A: fA(x) = (x-a1)(x-a2)…(x-am) = xm + Am-1xm-1 + … + A1x + A0 • A  B: EK(A0), EK(A1), …, EK(Am-1) • B: f’A(x) = xm + EK(Am-1)xm-1 + … + EK(A1)x + EK(A0) • B  A: rf’A(b1), rf’A(b2), …, rf’A(bm) • A: DK(rf’A(bi)) = rfA(bi) • if rfA(bi) is zero, ith key of A is shared with B

  7. 3. Secure Key Agreement Scheme • assumption • sensor networks consist of base station and sensor nodes • base station is computationally robust and installed in a fixed and secure location • path-key establishment phase is used

  8. 3. Secure Key Agreement Scheme • Key Pre-distribution Phase • the base station picks a random key pool out of the total possible key space. • Negotiatory Keys(NKs) • A = {a1(=a11 || a12), a2(=a21 || a22), …, am(=am1 || am2)} • B = {b1(=b11 || b12), b2(=b21 || b22), …, bm (=bm1 || bm2)} • A’s first half of the key • {s11(=a11 || h(a11)), s21(=a21 || h(a21)), …, sm1(=am1 || h(am1))} • {s12(=h(a12) || a12), s22(=h(a22) || a22), …, sm2(=h(am2) || am2)}

  9. 3. Secure Key Agreement Scheme • Shared-Key Discovery(1) • 1) - fA(x) = (x-s11)(x-s21)…(x-sm1) = xm + Am-1xm-1 + … + A1x + A0 • -Alice send encrypted coefficients of fA(x) that are EKA(A0), EKA(A1), …, EKA(Am-1) to Bob • 2) - Bob applies Bob’s keys to f’A(x) and get f’A(ti1). • - Bob calculates M’ = r1’ f’A(t11), r2’f’A(t21), …, rm’f’A(tm1) and send M’ to Alice • - Bob send encrypted coefficients of fB(x) that are EKB(B0), EKB(B1), …, EKB(Bm-1) to Bob • - fB(x) = (x-t12)(x-t22)…(x-tm2) = xm + Bm-1xm-1 + … + B1x + B0

  10. 3. Secure Key Agreement Scheme • Shared-Key Discovery(2) • 3) - Alice decrypts M’, DKA(ri’f’A(ti1)), and calculates an m-bit bitmap with 1 at bits where DKA(ri’f’A(ti1)) is 0 • - If the number of bits with 1 in m-bit bitmap is more than 1, Alice divide bitmap by 2. • - f’B(x) = xm + EKB(Bm-1)xm-1 + … + EKB(B1)x + EKB(B0) • - Alice applies Alice’s keys to f’B(x) and get f’B(si1). • - Alice calculates M = r1f’B(s12), r2f’B(s22), …, rmf’B(sm2) and send M to Bob • - Alice send m-bit bitmap to Bob

  11. 3. Secure Key Agreement Scheme • Shared-Key Discovery(3) • 4) - Bob decrypts M, DKB(rif’B(si2)), and calculates an m-bit bitmap with 1 at bits where DKB(rif’B(si2)) is 0 • - If the number of bits with 1 in m-bit bitmap is more than 1, Alice divide bitmap by 2. • - Alice send m-bit bitmap to Bob • 5) - Each node generates a session key using both m-bit and m’bit bitmap • - A new session key SK is generated as the hashed value of the concatenation of shared key

  12. 4. Performance • key sharing probability Vs key pool size

  13. 4. Performance • session key exposure rate Vs key pool size

  14. 5. Security Analysis • Key Authentication • illegitimate nodes can’t generate a session key because they have no corresponding one-way hash function • reducing the number of disclosing shared keys • it is not difficult to guess any shared keys while the ratio of the shared keys to unshared keys is by higher than the reverse of it • make use of negotiatory keys instead the secret keys and mechanism which restricts the number of disclosed shared keys

  15. 6. Conclusion • negotiatory keys instead of the secret keys • random numbers instead of a random number • why is the proposed scheme proper to wireless sensor network • this paper contain no mention of the low energy • no simulations or experiments about network load and energy of sensor nodes • very simple idea

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