Abstract by anuja a sonalker on Asymmetric Key Distribution

TABLE OF CONTENTS 
LIST OF TABLES. ………………………………………………………….…………. vi 
LIST OF FIGURES. ………………………………..………………………………….. vii 
Chapter 1 Problem Definition. ………………………………………………………. 1 
1.1 Current work and the need to do more. ..….……………………………… 3 
1.2 Intention of this thesis and layout. …………..………………………….….4 
Chapter 2 Introduction to Threshold Cryptography. ……….………………….…….. 6 
2.1 
Symmetric Key Cryptography. ..……………………………….………… 8 
2.2 
Public Key Cryptography. …………………..…………………….……... 9 
2.3 
Digital Signatures. ………………………………………………………. 10 
2.4 
RSA Algorithm. …………………………..…………………………….. 10 
2.4.1 How the RSA keys are computed. ………………………………11 
2.4.2 Why this works. …………………………………………………11 
2.5 
Distributed Key Structure. ..…………………………………………….. 12 
2.6 
How Threshold Schemes Work. .………………………………………. 13 
2.7 
Threshold RSA. ………………..……………………………………….. 14 
2.8 
Breaking the Algorithm. ……………………………………………….…15 
2.8.1 Factoring N. ………………………………..…………….…….. 15 
2.8.2 Finding p, q instead. …………………………………….……….16 
2.8.3 Guess Attacks and Brute Force Attacks. ……………….………..16 
Chapter 3 Asymmetric Key Distribution …………………………………………... 17 
3.1 
The Model. …….…………………………………………………….…... 18 
3.2 
Trusted Dealer Overview. ……………………………………………….. 19 
3.3 
Description Of Players. ….…………………………………………….… 19 
3.4 
Mathematical Analysis of AKD Algorithm. ……..……..…..…………… 21 
3.5 
Proof of correct signature formation. ………..…………….…………….. 24 

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3.6 
Key Generation by Trusted Dealer. ………………………….…….…..... 25 
3.7 
Secret share generation. ……………….………………………………….26 
3.8 
Key share Reuse. …………………………………………...….………... 30
3.9 
Example. ………………………………………………………………… 32 
3.10 Security Concerns. ………………………………………………………. 33 
3.10.1 Breaking the system. .……………………………………………. 33 
3.10.2 Key Distribution Problem. ………………………………………. 34 
3.10.3 Physical break-ins and Compromising Trusted Dealer. ………… 35 
Chapter 4 Implementation. ……………………....……………………..…….…….. 36 
4.1 Communication mechanisms in Java. …………………………….…..… 36 
4.2 How RMI works. ..…………………………………………………….… 40 
4.2.1 The Registry. .……….………………………………………… 41 
4.3 Implementation. .………..………………………………………………. 41 
4.4 Test Cases. .……………….…………………………………………….. 43 
4.4.1 Test 1: Timing Issues. ...………………………………………. 43 
4.4.1.1 Effect of Key size on key generation time. .……………45 
4.4.1.2 Communication Overheads. ……………………………47 
4.4.1.3 Signature Share generation time. ……..………………. 49 
4.4.1.4 Scalability. ……………………………………………. 49 
4.4.2 Test 2: Improper Special Server share. .………………………. 51 
4.4.3 Test 3: Share Server combined Attack. ………………………. 51 
Chapter 5 Dual Threshold Approach. ……………………………………………... 52 
5.1 Description. ……………………………………………………………. 53 
5.2 Extended Mathematics and Proof. .…………………………………….. 55 
5.3 Advantages. …………………………………………………….………. 56 
Chapter 6 Conclusion. ………….………………………………………….………. 58 
Bibliography. …………………..…………………………………………………….. 60 

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