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Key Agreement for Heterogeneous Mobile Ad-hoc Groups (µSTR-H)

Key Agreement for Heterogeneous Mobile Ad-hoc Groups (µSTR-H). Mark Manulis Horst-Görtz Institute, Bochum (Germany). http://www.hgi.rub.de. Mark Manulis, Horst-Görtz Institute, Bochum, Germany. Heterogeneous Mobile Ad-Hoc Group. Mark Manulis, Horst-Görtz Institute, Bochum, Germany.

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Key Agreement for Heterogeneous Mobile Ad-hoc Groups (µSTR-H)

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  1. Key Agreement for Heterogeneous Mobile Ad-hoc Groups(µSTR-H) Mark Manulis Horst-Görtz Institute, Bochum (Germany) http://www.hgi.rub.de

  2. Mark Manulis, Horst-Görtz Institute, Bochum, Germany Heterogeneous Mobile Ad-Hoc Group

  3. Mark Manulis, Horst-Görtz Institute, Bochum, Germany Outline • Elliptic Curve Cryptography • Performance of Mobile Devices • Device Architecture • µSTR-H Protocol Suite • Setting • Requirements • Protocols: Setup, Join, Leave, Merge, Partition • Performance Analysis • Current and Future Work

  4. Mark Manulis, Horst-Görtz Institute, Bochum, Germany Elliptic Curve Cryptography (ECC) • Elliptic curve E over a finite field Fq • q  Primes: y2 = x3 + ax +b , x,y,a,b  Fp and 4a3 + 27b2  0 • q = 2m, mN: y2 + xy = x3 + ax2 + b , x,y,a,b  F2m and b  0 • Group of elliptic points E(Fq) is commutative. Let P,Q  E(Fq) • Negation: –P • Addition: P + Q = R(xR, yR) E(Fq) • Doubling: 2P = R(xR, yR)  E(Fq) • Let G  E(Fq) of prime order t with t | q-1 • Generated additive subgroup <G> = {O, G, 2G, … , (t-1)G} • Scalar-Point Multiplication: r  {1,…,t-1}, rG = R  G Note: R = G + … + G • It is hard to compute r given R and G (EC-Discrete Logarithm Problem) r times

  5. Mark Manulis, Horst-Görtz Institute, Bochum, Germany Performance of Mobile Devices • Benchmark function F • Input: device’ hardware parameters • CPU clocks • memory size • storage capacity • battery power consumption • … • Process: application-specific operations • cryptographic and network operations • Output: performance ratio µ runF(input) getµ

  6. M1 M2 M4 M6 M7 M8 M3 M5 M9 Mark Manulis, Horst-Görtz Institute, Bochum, Germany Performance Ratio Order • Mobile Ad-Hoc Group: M1, … , Mn • Performance ratio order: • P = (M1, … , Mn),  Mi, Mi+1 : µi  µi+1 • e.g.: • Assumption: • µi can be figured out from P

  7. Mark Manulis, Horst-Görtz Institute, Bochum, Germany Homogeneous & Heterogeneous Mobile Ad-Hoc Groups • Homogeneous Mobile Ad-Hoc Group: •  µi, µj  P : |µi - µj|   • Heterogeneous Mobile Ad-Hoc Group: •  µi, µj  P : |µi - µj| >  •  : limit of homogeneity

  8. Mark Manulis, Horst-Görtz Institute, Bochum, Germany CGKA Protocol Requirements • Usual security requirements against passive adversary • Cost fairness (performance requirement) • Homogeneous Groups: • uniform distribution of protocol costs between devices • Heterogeneous Groups: • distribution of protocol costs between devices with respect to P • Performance Honesty (security requirement) • Adversary cannot cheat on its device performance Remark: Adversary is active • Concerns only heterogeneous groups

  9. PCR1 PCR2 PCRl Mark Manulis, Horst-Görtz Institute, Bochum, Germany Abstract Device Architecture based on TCG • Trusted Computing Base Components • Trusted Platform Module (TPM) • Tamper-resistant • Limited computational capabilities • Platform Configuration Registers (PCRs) • Attestation Identity Key Pair (PKAIK, SKAIK) • Trusted Software Component (TSC) • Its measurement S is included in PCRs • Better computational capabilities • Non-Trusted Components • Application isolated from other processes Common OS Application TSC TPM S ... Hardware Plattform

  10. Mark Manulis, Horst-Görtz Institute, Bochum, Germany HGI-Seminar 2005 µSTR-H: Pre-Requisites • Communication Channel • public broadcast / multicast • reliable • Authentication • Every device has CertTPMi = (IDTPMi, PKAIK, SigCA(IDTPMi, PKAIK)) • Assumption: • All protocol messages are authentic • Explicit indication of authentication procedure is omitted

  11. Mark Manulis, Horst-Görtz Institute, Bochum, Germany HGI-Seminar 2005 µSTR-H: Parameters and Notations • E(Fq), q is prime or 2m, mN • <G> = {O, G, 2G, … , (t-1)G}, t is prime, t | q-1 auxiliary keys group key (performance ratio order) • User Mi computes: • riR {1, … , t-1} • Ri= riG • ki= map(riKi-1); for all 2<i<j≤n: kj = map(kj-1Rj) exception: k2 = map(r1R2) = map(r2R1) • Ki = kiG • Example M3: • r3R {1, … , t-1} • k3= map(r3K2) • k4 = map(k3R4) • k5 = map(k4R5)

  12. PCR Mark Manulis, Horst-Görtz Institute, Bochum, Germany HGI-Seminar 2005 Achieving Performance Honesty • Tasks of TPMi • Choose ri and compute Ri • Seal ri under µi and Si • Generate σi = SignSK_AIK_i(Ri, µi) • Compute riKi-1 given Ki-1 • Tasks of TSCi • Compute all secret keys ki, … ,kn • Compute all public keys Ki, … , Kn-1 • Tasks of untrusted µSTR-H • Send and receive protocol messages • Verify received σj • Compute P • Store Ri performance ratio µi Common OS µSTR-H ki, … ,kn TSCi TPMi Si ri Hardware Plattform ri

  13. PCR Mark Manulis, Horst-Görtz Institute, Bochum, Germany Message Exchange between Components Ri+1,…,Rn Ki,…,Kn-1 µi, Ri, σi, CertTPMi performance ratio µi Common OS µSTR-H µSTR-H (non trusted) ki, … ,kn TSCi Ri+1,…,Rn Ki,…,Kn-1 TPMi µi, Ri, σi, CertTPMi Si TSCi ri riKi-1 Ki-1 Hardware Plattform µi, Ri, σi, CertTPMi TPMi

  14. K2 K3 K4 K5 K6 K7 k2 k3 k4 k5 k6 k7 k8 8 4 1 7 6 3 2 5 4 8 6 3 5 2 7 1 M1 M2 M4 M5 M6 M7 M3 M8 Mark Manulis, Horst-Görtz Institute, Bochum, Germany µSTR-H: Setup k1 µi P • TPMi selects ri, computes Ri and σi. Mi broadcasts (µi, Ri, σi, CertTPMi). • Mi verifies all σj, computes P, stores Ri+1,…, Rn. TPM1 computes r1R2. TSC1 computes k1 = (k2,…, kn) and (K2,…, Kn-1). M1 broadcasts (K2,…, Kn-1). • Mi stores Ki-1. TPMi computes riKi-1. TSCi computes ki = (ki,…, kn).

  15. R´3, K´3 K´4 K´5 k´1 k´2 k´4 k´5 k´6 M1 M1 M2 M2 Mj M4 M3 M3 M4 M5 M6 M5 Mark Manulis, Horst-Görtz Institute, Bochum, Germany µSTR-H: Join µj µ3>µj>µ4 k´3 P sponsor

  16. R´2, K´2 K´3 K´4 k´1 k´3 k´4 k´5 M1 M1 M2 M2 M4 M3 M3 M5 M4 M5 M6 Mark Manulis, Horst-Görtz Institute, Bochum, Germany µSTR-H: Leave k´2 P sponsor

  17. R´2, K´2 K´3 K´4 K´5 K´6 K´7 k´1 k´3 k´4 k´5 k´6 k´8 k´7 µi 8 7 6 5 4 3 2 1 P 6 4 3 2 8 7 5 1 M1 M21 M2 M22 M4 M23 M5 M12 M6 M13 M14 M7 M11 M3 M24 M8 Mark Manulis, Horst-Görtz Institute, Bochum, Germany µSTR-H: Merge k´2 sponsor R11 R21 µ1i µ2i P1 P2

  18. µi µi 8 8 7 6 6 5 4 4 3 2 2 1 1 R´1 K´2 K´3 K´4 k´2 k´3 k´5 k´4 P P M1 M1 M2 M4 M5 M3 M6 M7 M4 M3 M2 M5 M8 Mark Manulis, Horst-Görtz Institute, Bochum, Germany µSTR-H: Partition k´1 sponsor

  19. Mark Manulis, Horst-Görtz Institute, Bochum, Germany HGI-Seminar 2005 Performance Analysis S – setup, J – join, L – leave, M – merge, P – partition, original STR costs n – initial group size, i (s) – index of member (sponsor), v – size of partition

  20. Mark Manulis, Horst-Görtz Institute, Bochum, Germany • Future Work • Consider various protocols in MANETs where applied techniques (non-uniform distribution of protocol costs, enforcement of a property compliance) are useful, e.g. multicast routing, threshold crypto, … Thank You !!!

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