SRAM PUF Analysis and Fuzzy Extractors

security

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Project Number: WJM5000

SRAM PUF Analysis and Fuzzy Extractors

A Major Qualifying Project Report:

submitted to the faculty of the

WORCESTER POLYTECHNIC INSTITUTE

in partial fulfillment of the requirements for the

Degree of Bachelor of Science

by:

_______________________________________

Isaac Edwards

_______________________________________

Patrick Newell

_______________________________________

Chris Trufan

Date: March 1, 2010

Approved:

________________________________________

Professor William J. Martin, Major Advisor

________________________________________

Professor Berk Sunar, Co-Advisor

Table of Contents

1 Introduction .......................................................................................................................................... 1

2 Background ........................................................................................................................................... 4

2.1 Fuzzy Extractors and Physically Unclonable Functions ................................................................. 4

2.2 BCH Codes ..................................................................................................................................... 6

2.2.1 Galois Fields .......................................................................................................................... 7

2.2.2 Primitive Polynomials ............................................................................................................ 8

2.2.3 Minimal Polynomials ............................................................................................................. 9

2.2.4 BCH Generator Polynomial ................................................................................................. 10

2.2.5 BCH Encoding ...................................................................................................................... 11

2.2.6 Syndrome Computation ...................................................................................................... 12

2.2.7 Error Locator Polynomial .................................................................................................... 15

2.2.8 Chien’s Search ..................................................................................................................... 16

2.3 Hashing ........................................................................................................................................ 17

2.3.1 Universal Hashing ................................................................................................................ 18

2.3.2 Theoretical Background ...................................................................................................... 18

2.3.3 Privacy Amplification .......................................................................................................... 19

2.3.4 Universal Class of Hash Functions Used in this System ...................................................... 19

2.4 Enrollment and Authentication .................................................................................................. 21

2.4.1 The Enrollment Process ...................................................................................................... 22

2.4.2 The Authentication Process ................................................................................................ 24

3 System Design ..................................................................................................................................... 27

3.1 Data Analysis ............................................................................................................................... 27

3.1.1 Data Format ........................................................................................................................ 27

3.1.2 Selecting Bit Extraction Pattern .......................................................................................... 28

3.2 Calculating Optimal Parameters ................................................................................................. 36

3.2.1 Calculating Range of N and K Values................................................................................... 36

3.2.2 Calculating Number of Errors to Correct ............................................................................ 39

3.2.3 Optimal Parameters for Single Codeword .......................................................................... 39

3.2.4 Concatenation ..................................................................................................................... 40

4 MATLAB Framework ........................................................................................................................... 44

4.1 Architecture ................................................................................................................................ 44

4.1.1 The Device Package ............................................................................................................. 47

4.1.2 The Core Package ................................................................................................................ 50

4.1.3 The Encoder Package .......................................................................................................... 52

4.1.4 The Hash Package ............................................................................................................... 54

4.2 Building a Simple Authentication System ................................................................................... 55

4.3 Extending the Framework ........................................................................................................... 58

4.3.1 Creating a New Class File .................................................................................................... 58

4.3.2 Implementing the New Class .............................................................................................. 59

4.3.3 Testing the New Class ......................................................................................................... 65

5 BCH C Implementation ........................................................................................................................ 66

5.1 Mathematical Representation .................................................................................................... 66

5.2 Finding Primitive Polynomials ..................................................................................................... 66

5.3 Generating Minimal Polynomials ................................................................................................ 67

5.4 Generating BCH Generator Polynomials and BCH Encoding ...................................................... 67

5.5 Computing Syndrome Components ............................................................................................ 68

5.6 Computing the Error Locator Polynomial ................................................................................... 68

5.7 Chien’s Search and BCH Correction and Decoding ..................................................................... 68

6 Future Work ........................................................................................................................................ 70

7 Works Cited ......................................................................................................................................... 72

1 Introduction

In today’s world of globalization in the electronics industry, the continuing search for the lowest

bidder often results in components that underperform, perform incorrectly or simply don’t perform at

all. In the consumer electronics market, this is usually only a minor annoyance as a legitimate supplier

will generally refund or replace the components in question. However, in a secure or other high-risk

situation, not only must the components perform reliably and correctly, but they must also only perform

the operations the original manufacturer specifies. Many companies manufacture components outside

of their supervision where defects or malicious functionality can be easily introduced. For example, it is

often cheaper for a company to design a component in the U.S. and have it manufactured in another

country with cheaper labor rates. To put this into perspective, the Pentagon produces in secure facilities

only about two percent of the components used in military systems [1]. Recently, in 2008, the F.B.I. and

the Pentagon discovered that a large amount of counterfeit networking components were being used by

U.S. military agencies [2]. While these components in particular were not constructed with malicious

intent, the possibility of a hostile entity hiding the relatively small amount of functionality needed to

compromise secure systems within the highly complex hardware used today is very real and dangerous.

To solve this problem, we need an inexpensive form of hardware authentication for both

components within secure systems and components that interface with those systems. This

authentication is beneficial for all parties involved with the secure application. For the designers of the

secure application, it ensures that they are using the correct components within their system and that

those components will withstand given tolerances and handle given situations. For the manufacturers

of the components, it ensures that the components being used in a system are produced following their

specifications and are not counterfeit or otherwise defective. For the users of the system, it ensures

that both the system and the user are legitimately engaging in use of the system and activities on that

system are done so over a defined set of rules and security levels. For example, the components of a life

support system must be of the highest quality so that those relying on the system are not put in danger.

At any given point during the life cycle of the system, we should know that every component is working

as specified.

To achieve these goals in a hardware-based environment, we call upon the services of PUFs or

Physically Unclonable Functions. The term PUF is used to describe a broad class of algorithms and

measuring protocols that produce uniquely random data thanks to miniscule differences in construction

brought about by the fact that we live in an analog world. We can use these PUFs as a sort of fingerprint

for hardware devices, a way to identify and differentiate them from the time they are born, that is when

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