I

Nature has offered many intelligent sensors;

Only need is to recognize them.

II

This thesis is dedicated to my friend

Jamil S Moulavi (WIT, India) who passed away in1990.

III

An Enhancement of Elliptical Curve

Cryptography for the Resource

Constrained Wireless Sensor

Network

PRITAM GAJKUMAR SHAH

BACHELOR OF ENGINEERING (ELECTRONICS)

MASTER OF TECHNOLOGY (ELECTRONICS DESIGN)

FACULTY OF INFORMATION SCIENCES AND ENGINEERING

UNIVERSITY OF CANBERRA, AUSTRALIA

THIS DISSERTATION IS SUBMITTED IN PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE AWARD OF THE DEGREE

DOCTOR OF PHILOSOPHY

NOVEMBER 2010

V

© 2010 By Pritam Gajkumar Shah, University of Canberra, Australia. All rights reserved.

VII

Certificate of Authorship of Thesis (Form B)

Except where clearly acknowledged in footnotes, quotations and the bibliography, I certify

that I am the sole author of the thesis submitted today entitled –

―An Enhancement of Elliptic Curve Cryptography for the Resource Constrained Wireless

Sensor Network‖. I further certify that to the best of my knowledge the thesis contains no material previously

published or written by another person except where due reference is made in the text of the

thesis.

The material in the thesis has not been the basis of an award of any other degree or diploma

except where due reference is made in the text of the thesis.

The thesis complies with University requirements for a thesis as set out in Gold Book Part 7:

Examination of Higher Degree by Research Theses Policy, Schedule Two (S2).

Refer to http://www.canberra.edu.au/research-students/goldbook

Signature of Candidate

Date: 22/11/2010

Signature of Chair of the Supervising Panel

Date: 22/11/2010

IX

Abstract

Development in Micro Electro Mechanical Systems (MEMS), Very Large Scale Integration

(VLSI) and Wireless Communication has opened a new domain in networking area called

Wireless Sensor Networks (WSN). WSN is a special case of a Mobile Ad Hoc Networks

(MANET) in which information is gathered, processed and communicated with the help of

tiny wireless sensor nodes that are deployed in the field where ordinary networks are

unreachable for various environmental and strategic reasons. Wireless sensor nodes use radio

frequencies as a communications medium, and are vulnerable to active and passive attacks

from adversaries including node capturing, frequency jamming, and various Denial of

Service (DOS) attacks. Most of the ongoing research is to make WSN secure with Symmetric

Key (SK) protocols but at the same time Public Key Cryptography (PKC) has received little

attention from researchers.

PKC is based on hardness of a mathematical problem like factoring the product of two large

primes which is used in Rivest, Shamir and Adleman (RSA) algorithm or computing a

discrete logarithm used in Elliptical Curve Cryptography (ECC). As compared to RSA, ECC

offers the same security level but with significantly smaller key size and is the potential

candidate in the near future for WSN security. For an example, a 160-bit ECC key provides

the same level of security as a 1024-bit RSA key. A smaller key size in WSN means faster

computation, lower power consumption, memory and bandwidth savings for the sensor

nodes.

Analysis and mathematical modeling of ECC is investigated in this thesis in regard to the

WSN. Novel approaches combing use of mixed coordinate system, recoding of integer with

One‘s Complement Subtraction (OCS) method, OCS window method to avoid Special Power

Analysis (SPA) attacks, use of Dynamic Window method to avoid node failure and use of

hidden generator point to avoid man-in-the-middle attack and use of uni-coordinate public

key for WSN have been proposed. These six innovative, novel and industrially applicable

algorithms are demonstrated which significantly improve performance of scalar

multiplication processes on WSN and demonstrated to achieve node authenticity, data

integrity, confidentiality on 8-bit microcontroller of sensor node. These claims are validated

using simulation results obtained on MIRACL crypto library and using MATLAB analysis,

appropriately provided wherever necessary.

XI

Table of Contents

Certificate of Authorship of Thesis (Form B) ................................................................................ VII

Abstract ................................................................................................................................................IX

Table of Contents ................................................................................................................................XI

List of Figures .................................................................................................................................... XV

List of Algorithms .......................................................................................................................... XVII

List of Tables .................................................................................................................................... XIX

Abbreviations and Definitions ........................................................................................................ XXI

Acknowledgements ....................................................................................................................... XXIII

Chapter 1 Introduction .................................................................................................................. 1

1.1 Background and Motivation...................................................................................................... 1

1.2 Research Questions ................................................................................................................... 4

1.3 Research Tools .......................................................................................................................... 5

1.4 Research Contribution .............................................................................................................. 6

1.5 Thesis Outline ........................................................................................................................... 7

Chapter 2 Wireless Sensor Networks and Security: A Review .................................................. 9

2.1 Introduction ............................................................................................................................... 9

2.2 WSN Architecture ................................................................................................................... 10

2.2.1 WSN Node ...................................................................................................................... 10

2.2.2 Node Power Consumption .............................................................................................. 15

2.3 WSN Protocol Stack ............................................................................................................... 16

2.4 WSN Topology ....................................................................................................................... 18

2.5 Network Layer Protocols Evaluation ...................................................................................... 20

2.6 Possible Attacks on WSN in terms of Layer Wise Security ................................................... 21

2.6.1 Physical Layer .................................................................................................................. 22

2.6.2 Data Link Layer ............................................................................................................... 24

2.6.3 Network Layer ................................................................................................................. 24

2.6.4 Transmission Layer .......................................................................................................... 26

2.6.5 Application Layer ........................................................................................................... 26

2.7 A survey of cryptography protocols for WSN ........................................................................ 26

2.7.1 SPINS: Security Protocol for Sensor Network ................................................................ 27

2.7.2 TinySec: ........................................................................................................................... 29

2.8 Summary ................................................................................................................................. 29

Chapter 3 Elliptical Curve Cryptography Modelling ............................................................... 31

3.1 Introduction ............................................................................................................................. 31

3.2 Definition of Elliptical Curve ................................................................................................. 31

3.3 Pyramid of Elliptical Curve Cryptography ............................................................................. 33

XII

3.4 Elliptic Curve Protocols for WSN .......................................................................................... 34

3.4.1 Elliptic curve key generation ........................................................................................... 34

3.4.2 Definition of Elliptic Curve Discrete Logarithm Problem (ECDLP) .............................. 35

3.4.3 Elliptical Curve Diffie-Hellman Protocol (ECDH) .......................................................... 36

3.4.4 Comparison between RSA and ECC................................................................................ 37

3.4.5 ElGamal Elliptic Curve Protocol ..................................................................................... 39

3.5 Point Addition and Point Doubling on Elliptical Curve ......................................................... 42

3.6 Finite Field Arithmetic ............................................................................................................ 43

3.7 Fields of odd characteristic ..................................................................................................... 44

3.7.1 Moduli of Special form or pre computed moduli ............................................................. 44

3.7.2 Residue number system arithmetic .................................................................................. 45

3.7.3 Barrett Reduction ............................................................................................................. 45

3.7.4 Montgomery Reduction ................................................................................................... 46

3.8 Fields of characteristic two ..................................................................................................... 49

3.8.1 Polynomial Bases ............................................................................................................. 49

3.8.2 Normal bases .................................................................................................................... 51

3.8.3 Subfield bases .................................................................................................................. 54

3.9 Summary ................................................................................................................................. 55

4.1 Introduction ............................................................................................................................. 57

4.2 Coordinate Systems in Elliptical Curve .................................................................................. 58

4.2.1 Affine coordinates ............................................................................................................ 58

4.2.2 Projective Coordinate ....................................................................................................... 59

4.2.3 Jacobian and Chudnovsky Jacobian Coordinates............................................................ 61

4.2.4 Modified Jacobian Coordinates ...................................................................................... 62

4.2.5 Mixed Coordinates .......................................................................................................... 62

4.3 Implementation on MIRACL crypto Library .......................................................................... 66

4.4 Summary ................................................................................................................................. 67

Chapter 5 Proposed One’s Complement Subtraction (OCS) algorithm ................................ 69

5.1 Introduction ............................................................................................................................. 69

5.2 ECDH Protocol Implemented on WSN to Achieve Data Confidentiality .............................. 70

5.3 The Existing Methods of Integer Recoding ............................................................................ 71

5.3.1 Binary Method ................................................................................................................. 71

5.3.2 Non Adjacent Form ( NAF) method ............................................................................... 72

5.3.3 Mutual Opposite Form (MOF) Method .......................................................................... 74

5.4 Use of Complementary Methods for Subtraction ................................................................... 75

5.4.1 The 10‟s complement ....................................................................................................... 76

5.4.2 The 9‟s Complement ........................................................................................................ 77

5.4.3 Binary Subtraction by Utilization of 2‟s Complement..................................................... 77

5.5 Proposed One‟s Complement Subtraction (OCS) Algorithm for Recoding of Scalar k ....... 79

5.6 Proposed Two‟s Complement Subtraction (TCS) algorithm .................................................. 82

5.7 Performance Evaluation of OCS algorithm on MATLAB ..................................................... 83

5.8 Summary ................................................................................................................................. 89

Chapter 6 Proposed Window One’s Complement Subtraction Algorithm for Prevention of

SPA ....................................................................................................................................................... 91

6.1 Introduction ............................................................................................................................. 91

6.2 Side channel attacks on WSN node ........................................................................................ 92

XIII

6.2.1 CMOS Inverter Circuit and Simple Power Analysis ....................................................... 92

6.2.2 Enhanced Simple Power Analysis ................................................................................... 94

6.2.3 Differential Power Analysis ............................................................................................. 94

6.2.4 Electromagnetic Analysis ................................................................................................ 95

6.2.5 Fault and Timings Attacks ................................................................................................ 95

6.3 SPA Counter Measures ............................................................................................................ 95

6.3.1 „Double and Add Always ‟Algorithm ............................................................................. 96

6.3.2 Montgomery Ladder ........................................................................................................ 96

6.3.3 Identical formulae for point addition and doublings ......................................................... 97

6.4 A Window OCS Method Proposed To Avoid SPA ................................................................. 97

6.5 Summary .................................................................................................................................. 99

Chapter 7 Proposed Dynamic Window Method of Scalar Multiplication ............................ 101

7.1 Introduction ........................................................................................................................... 101

7.2 Existing Methods for Scalar Multiplication .......................................................................... 101

7.2.1 The Binary Method for Scalar Multiplication ................................................................ 101

7.2.2 The m-ary Method ......................................................................................................... 102

7.2.3 Sliding Window Method ................................................................................................ 103

7.3 Effect of Window Size on Memory Utilization of Mica Nodes ........................................... 108

7.4 Stack Depth Analysis ............................................................................................................ 109

7.5 Proposed Dynamic Window Algorithm for scalar multiplication ........................................ 110

7.6 Fuzzy Controller for ECC ..................................................................................................... 111

7.7 Summary ............................................................................................................................... 117

8.1 Introduction ........................................................................................................................... 119

8.2 Proposed New ECC Protocol Based On Hidden Generator Point ...................................... 120

8.3 Multi-agent System Implementation of ECC Public Key ..................................................... 124

8.3.1 Intelligent agent.............................................................................................................. 125

8.3.2 Classification of environmental properties for intelligent agents .................................. 126

8.3.3 Intelligent Agent capabilities ......................................................................................... 126

8.3.4 Architecture of Intelligent Agents:................................................................................ 127

8.3.5 Definition of Multiagent systems ................................................................................... 128

8.3.6 Problem solving in MAS................................................................................................ 128

8.3.7 Programming for Multi-Agent Systems ......................................................................... 131

8.3.8 Proposed MAS framework for ECC .............................................................................. 132

8.4 Summary ............................................................................................................................... 133

9.1 Introduction ........................................................................................................................... 135

9.2 Quadratic equations in field of odd characteristics ............................................................... 135

9.3 Solving quadratic equations in binary field .......................................................................... 137

9.4 Summary ............................................................................................................................... 138

Chapter 10 Conclusion and Future Work .............................................................................. 139

10.1 Thesis Summary .................................................................................................................. 139

10.2 Future Work ........................................................................................................................ 141

Bibliography ...................................................................................................................................... 145

Appendix A NIST Recommended Curves for Cryptography ................................................ 153

Appendix B List of My Publications and Patents ................................................................... 167

XIV

Publications ..................................................................................................................................... 167

Patents ............................................................................................................................................. 169

Invited Talk ..................................................................................................................................... 171

Appendix C Results Obtained On MIRACL Crypto Library ............................................... 173

Appendix D Sample Source Codes Written in C, C++ for ECC ............................................ 183

XV

List of Figures

Figure 2. 1 A Typical WSN Architecture .................................................................................... 9

Figure 2. 2 Block Diagram of WSN Node ................................................................................. 11

Figure 2. 3 Fleck3B WSN Node by CSIRO [34] ....................................................................... 11

Figure 2. 4 Images of MICA Node (on Left) and Telos Node (on Right) .................................. 13

Figure 2. 5 WSN Protocol Stack with Proposed Security Plane ................................................. 17

Figure 2. 6 Deployment of Nodes in Delphi Distribution ........................................................... 19

Figure 2. 7 Deployment of Nodes in Gaussian Distribution ....................................................... 19

Figure 2. 8 Deployment of Nodes in Exponential Distribution .................................................. 20

Figure 2. 9 Classical flooding protocol results ........................................................................... 21

Figure 2. 10 Power Traces of SC140DS Processor [47] ............................................................... 23

Figure 2. 11 μTESLA One Way Key Function [52] ..................................................................... 28

Figure 3. 1 An Elliptical Curve Example .................................................................................... 32

Figure 3. 2 An Elliptical Curve and Its Group Elements ............................................................ 32

Figure 3. 3 ECC Operational Pyramid [21] ................................................................................ 34

Figure 3. 4 Diffie Hellman Key Exchange Protocol ................................................................... 39

Figure 3. 5 Point Addition, Point Doubling Operations in Elliptic Curve .................................. 42

Figure 4. 1 Evaluation of Coordinates for ECDH and ECDSA protocol on MIRACL Library . 67

Figure 5. 1 ECDH Protocol Implemented on WSN .................................................................... 70

Figure 5. 2 MATLAB code for Decimal to Binary Conversion .................................................. 84

Figure 5. 3 MATLAB Code for Decimal to MOF Form ............................................................ 85

Figure 5. 4 MATLAB Code for Decimal To NAF Form............................................................. 86

Figure 5. 5 MATLAB code for OCS Algorithm .......................................................................... 87

Figure 5. 6 MATLAB code for TCS algorithm .......................................................................... 88

Figure 5. 7 Comparison of OCS with other algorithms on MATLAB ........................................ 89

Figure 6. 1 Power traces revealing value of private key of the WSN node [63] ........................ 91

Figure 6. 2 Block diagram of SPA setup .................................................................................... 92

Figure 6. 3 CMOS Logic Inverter Circuit [80] ........................................................................... 92

Figure 6. 4 Example of Power Consumption Information Leakage [82] .................................... 94

Figure 7. 1 Trade-off between Window size and computational cost....................................... 107

Figure 7. 2 Trade off between window size and number of pre-computations ......................... 107

Figure 7. 3 Memory model for Tiny OS on MICA mote .......................................................... 109

Figure 7. 4 Three inputs and one output fuzzy window control system ................................... 112

Figure 7. 5 Proposed Algorithm of Dynamic Window for Scalar Multiplication [91, 92] ....... 113

Figure 7. 6 The block diagram of current fuzzy controller ....................................................... 115

XVI

Figure 7. 7 The output of the surface for the StorageRoom vs. PreComputing ......................... 115

Figure 7. 8 The output of the surface for the StorageRoom vs. Doubling ................................ 116

Figure 7. 9 The output of the Surface for PrecComputing vs. Doubling. ................................. 116

Figure 8. 1 Man-in-Middle Attack in WSN .............................................................................. 119

Figure 8. 2 Distribution of Elliptic Group E23 (1, 1). .............................................................. 122

Figure 8. 3 A new protocol protecting the man-in-the-middle attack. ...................................... 122

Figure 8. 4 Block diagram for hidden generator point principle. ............................................. 123

Figure 8. 5 A protocol for ECC with hidden generator point ................................................... 123

Figure 8. 6 An agent in its environment ................................................................................... 125

Figure 8. 7 CDPS Protocol ....................................................................................................... 129

Figure 8. 8 Task and Results sharing in MAS .......................................................................... 130

Figure 8. 9 Block Diagram of MAS Framework for ECC [109] .............................................. 133

Figure 10. 1 Cloud Computing Architecture for WSN ................................................................ 141

XVII

List of Algorithms

Algorithm 3. 1 Elliptic Curve Key Pair Generation.................................................................... 35

Algorithm 3. 2 Elliptical Curve Diffie-Hellman Protocol .......................................................... 36

Algorithm 3. 3 Algorithm 3.3 Basic ElGamal Encryption Algorithm [47] ................................ 39

Algorithm 3. 4 Basic ElGamal Decryption Algorithm [47] ........................................................ 40

Algorithm 3. 5 Point Addition .................................................................................................... 43

Algorithm 3. 6 Point Doubling ................................................................................................... 43

Algorithm 3. 7 Reduction Modulo .............................................................................................. 45

Algorithm 3. 8 Barrett Reduction Algorithm .............................................................................. 46

Algorithm 3. 9 Montgomery Reduction Simple Case................................................................. 47

Algorithm 3. 10 Modified Montgomery Reduction ..................................................................... 47

Algorithm 3. 11 )2(mod1 wx Computing ................................................................................. 48

Algorithm 3. 12 Montgomery Multiplication .............................................................................. 48

Algorithm 3. 13 .0,1Re nt xxf(x) uloductionMod tn ............................................ 49

Algorithm 4. 1 Point Addition and Point Doubling in Affine Coordinate System ..................... 59

Algorithm 4. 2 Point Addition and Point Doubling in Projective Coordinate ............................ 60

Algorithm 4. 3 Point Addition and Point Doubling in Jacobian Coordinate .............................. 61

Algorithm 4. 4 Conversion of Affine Coordinates to other Coordinates .................................... 62

Algorithm 4. 5 Conversion of Projective Coordinate to other Coordinates ................................ 63

Algorithm 4. 6 Conversion of Jacobian Coordinates to other Coordinates ................................ 63

Algorithm 5. 1 Left to Right Binary Method .............................................................................. 71

Algorithm 5. 2 Right to Left Binary Method .............................................................................. 71

Algorithm 5. 3 Computing the NAF of a Positive Integer .......................................................... 73

Algorithm 5. 4 Binary NAF Method for Point Multiplication .................................................... 74

Algorithm 5. 5 Conversion from Binary to NAF ........................................................................ 74

Algorithm 5. 6 Left to Right Processing from Binary to MOF ................................................... 75

Algorithm 5. 7 OCS Algorithm Proposed for Recoding Positive Integer in WSN ...................... 82

Algorithm 5. 8 TCS Algorithm for a Positive Integer ................................................................ 83

Algorithm 6. 1 SPA Resistant Double and Always Method ....................................................... 96

Algorithm 6. 2 Montegomery Ladder to Avoid SPA.................................................................. 97

Algorithm 6. 3 Proposed Window OCS Method for Scalar Multiplication ................................ 98

Algorithm 7. 1 Multiplication by m-ary Method ...................................................................... 103

Algorithm 7. 2 Sliding Window Method .................................................................................. 104

Algorithm 8. 1 Proposed Protocol to Avoid Man-in-the-Middle Attack [91,92] ..................... 124

Algorithm 9. 1 Legendre Symbol [17] ...................................................................................... 136

XVIII

Algorithm 9. 2 Square Root Modulo p [17] .............................................................................. 137

XIX

List of Tables

Table 2. 1 Family of Berkeley Nodes [35] ................................................................................. 12

Table 2. 2 Specifications of First Generation Nodes [1] ............................................................ 13

Table 2. 3 Specifications of Imote2 [1] ...................................................................................... 13

Table 3. 1 Nomenclature in ECC ................................................................................................ 33

Table 3. 2 NIST Guidelines for Key Sizes [59] .......................................................................... 37

Table 4. 1 Comparison of binary and prime field on Motorola processor .................................. 57

Table 4. 2 Cost of Conversion To and From Various Coordinate Systems [64] ........................ 64

Table 4. 3 Cost of Operations In Mixed Coordinates [30].......................................................... 65

Table 4. 4 Representation of Point in Various Coordinate Systems[30] .................................... 66

Table 4. 5 Comparison of Coordinate for ECDH and ECDSA Protocol for WSN .................... 67

Table 5. 1 Comparison of OCS with other methods on MATLAB (Execution time in ms)....... 89

XXI

Abbreviations and Definitions

The following abbreviations of standard phrases are used throughout the thesis:

AES Advanced Encryption Standard

AES 128 AES with a 128-bit key

AES 192 AES with a 192-bit key

AES 256 AES with a 256-bit key

CM Complex Multiplication

CRT Chinese Remainder Theorem

CMOS Complementary Metal Oxide Semiconductor

DES Data Encryption Standard

DLP Discrete Logarithm Problem

DoS Denial-of-Service

DSA Digital Signature Algorithm

ECC Elliptical Curve Cryptography

ECDH Elliptical Curve Diffie-Hellman

ECDLP Elliptical Curve Discrete Logarithmic Problem

ECDSA Elliptical Curve Digital Signature Algorithm

GCD Greatest Common Divisor

IEEE Institute of Electrical and Electronics Engineers

ISM Industrial, Scientific and Medical band

JSF Joint Sparse Form

µTESLA Micro timed Efficient Stream Loss Tolerant Authentication

MAC Media Access Control

MANET Mobile Adhoc Networks

MEMS Micro Electro Mechanical Systems

MIRACL Multiprecision Integer and Rational Arithmetic C/C++ Library

NAF Non Adjacent Form

NIST National Institute of Standards and Technology

ONB Optimal Normal Basis

PKC Public Key Cryptography

RAM Random Access Memory

XXII

ROM Read Only Memory

RSA Rivest Shamir Adleman algorithm

SD Signed Digits

SNEP Sensor Network Encryption Protocol

SPA Simple Power Analysis

SPIN Security Protocol for Sensor Networks

VLSI Very Large Scale Integration

WSN Wireless Sensor Networks

XXIII

Acknowledgements

My sincere thanks to PhD Supervisor and Chair Dr. Xu Huang whose faith in my work and

constant support at all academic and research levels were priceless factors that helped me to

achieve more than I thought possible.

Special gratitude is to Honourable Dean Prof. Dr. Dharmendra Sharma who offered me an

opportunity to do research in one of Australia‟s best universities, and for co-supervising the

work.

I would like to thank my parents, wife Rakhee, daughters Darshana and Namita for their

endless support and understanding through the last five years of my research. Their love and

confidence in me were the constant source of inspiration to offer the best of myself to this

research.

I also extend my sincere thanks to Mr and Mrs Subhash Jalota for their support during my

initial days in Canberra.