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A Public Key Infrastructure for Key Distribution in TinyOS Based on Elliptic Curve Cryptography

A Public Key Infrastructure for Key Distribution in TinyOS Based on Elliptic Curve Cryptography. David J. Malan, Matt Welsh, Michael D. Smith Presented by James Balasalle. Overview. Introduction SKIPJACK and TinySEC Elliptic Curve Cryptography Implementation Results Conclusions.

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A Public Key Infrastructure for Key Distribution in TinyOS Based on Elliptic Curve Cryptography

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  1. A Public Key Infrastructure for Key Distribution in TinyOS Based on Elliptic Curve Cryptography David J. Malan, Matt Welsh, Michael D. Smith Presented by James Balasalle

  2. Overview • Introduction • SKIPJACK and TinySEC • Elliptic Curve Cryptography • Implementation • Results • Conclusions

  3. Introduction • Not much data to support claim that PKI is infeasible • ECC Solves key distribution problems • ECC and the Discrete Logarithmic Problem • Implemented • Results • Conclusions

  4. SKIPJACK and TinySEC • Link layer security • Secret keys, possibly global • Re-keying is problematic Transmit time RTT time

  5. SKIPJACK and TinySEC Cont’d. Tiny Sec Size Encryption Time

  6. Elliptic Curve Cryptography • Like other PKI schemes based on DLP (discrete logarithmic problem) • y=(gx)mod p • “Easy” to find y, very difficult to find x • Based on finite fields • Elements in group are points (x,y)

  7. Elliptic Curve Cryptography Cont’d. • y2 = x3 + ax + b Elliptic Curve

  8. Elliptic Curve Cryptography Cont’d. • Point Addition

  9. Elliptic Curve Cryptography Cont’d. • Point Multiplication

  10. Elliptic Curve Cryptography Cont’d. • Q(x,y) = kP(x,y) • Q is public key • Field is set of points on curve up to P, which is large prime • Field can be of different types

  11. Elliptic Curve Cryptography Cont’d.

  12. Implementation • 1st attempt failed – based on code by Michael Rosing • Stack overflow • Memory consumption for multi-word arithmetic – exponential RAM usage for keys above 33 bits

  13. Implementation Cont’d. • 2nd Attempt EccM 2.0 • Based on Dragongate Technologies Limited’s jBorZoi • Keys are broadcast in 2 22-byte messages • Different algorithms are used for multiplication of points, and addition of points • EccM 1.0 is subject to sub exponential attack via MOV reduction with indexed calculus. Eccm 2.0 is not.

  14. Results TinySec Sizes EccM Sizes

  15. Results Cont’d. • 148 times more expensive • 149 times slower

  16. Conclusions • Feasible for infrequent re-keying • Significantly simplifies key distribution • Provides high level of security • Twice as big code size as TinySec • Larger BSS size

  17. Conclusions Cont’d. • Significantly slower • PKI allows more ways for nodes to establish keys – reducing chance of network fragmentation

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