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

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 Contd.
Tiny Sec Size
Encryption Time
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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)

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Elliptic Curve Cryptography Contd.

• y2 x3 ax b

Elliptic Curve
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Elliptic Curve Cryptography Contd.

• Point Addition

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Elliptic Curve Cryptography Contd.

• Point Multiplication

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Elliptic Curve Cryptography Contd.

• 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

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Elliptic Curve Cryptography Contd.
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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

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Implementation Contd.

• 2nd Attempt EccM 2.0
• Based on Dragongate Technologies Limiteds
  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.

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Results
TinySec Sizes
EccM Sizes
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Results Contd.

• 148 times more expensive
• 149 times slower

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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

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Conclusions Contd.

• Significantly slower
• PKI allows more ways for nodes to establish keys
  reducing chance of network fragmentation