臺灣博碩士論文加值系統

眾所皆知，於量子計算機上運行多項式時間攻擊能夠破壞傳統的加密協議，因此非常需要能夠提供數據完整性、消息機密性、用戶身份驗證和授權的量子強算法，為了設計具有這些能力的量子強協定，需要探索如何使用知名加密工具的新方法，在此項工作中，我們展示了四種不同的結果，以巧妙的方式使用單向雜湊函數結合其他數學對象（如同態、符號計算封閉形式解、多項式環等），這可以提供所需的能力。


我們的第一個項目是 O2MD2 密碼系統，它是Ring Learning With Errors（RLWE）問題，結合環中的算術函數和單向雜湊函數作為其安全基礎，該系統提供具有分佈式密鑰刷新的一對多私鑰/公鑰架構，它具有三種不同的框架，可達到 AES-256 等效安全性，並提供消息完整性和真實性驗證，我們還提出了六種不同的實現，它們達到了 NIST 後量子密碼標準化項目中提出的安全級別 1、3 和 5，最後，我們使用 NIST 統計測試套件來驗證我們生成密文對抗隨機生成干擾的不可區分性。

我們的第二個項目提出了O2MD2 密碼系統的兩個概念可行性驗證fixed-point FPGA 實現，其中計算了整數陣列多項式乘法逆運算的符號封閉形式解，它被嵌入到一個預先計算好的表中，從而產生 O2MD2 密鑰生成、加密和解密算法，同時在所有模塊中保持定點運算，第一個實現在加密和解密時的吞吐量分別為 473.875 Mbps 和 448.129 Mbps，而第二個實現的吞吐量分別為 416.56 Mbps 和 335.35 Mbps，我們展示了三種算法的總gate count、估計的時脈週期、綜合後和實施後的時序分析，以及實現的延遲和間隔，最後，我們將我們的硬件實現與其對應的軟件以及 NTRU 框架系列的硬件實現進行速度比較。

我們第三個項目介紹了信任鏈身份驗證協議 (DHCT) 框架中的分佈式雜湊，該框架基於挑戰執行分佈式及動態雜湊基礎的使用者身份驗證。每個挑戰對於每次通信嘗試都是獨一無二的，並為控制面帶來安全性，防止暴力、字典和重放攻擊。DHCT 框架以線性時間運行，創建一個信任鏈，其中消息僅通過受信任的實體傳輸，並提供重新握手協議，使得當用戶重新連接到網絡時，無需再次執行整個握手。在測試環境中，DHCT 框架允許受信任的實體忽略和丟棄來自假用戶的通信嘗試，並保持信任鏈以在受信任的用戶之間進行通信。

我們最後的項目提出了基於單向雜湊和同態基礎的物聯網設備供應鏈安全協議 (OHSA) 框架，該框架允許硬件製造商向供應鏈中的其他製造商提供對硬件組件內部數據的訪問，而不需明確披露嵌入的憑據。 OHSA 框架使用憑證的metadata和meta-meta data工作，允許硬件組件授權用戶，通過密封-解密封-重新密封(seal-deseal-reseal)保護firmware更新。在測試環境中，OHSA 框架不僅可以檢測損壞的firmware更新，還可以通過firmware安全封條檢測來自未經授權製造商的有效更新。

Polynomial-time attacks designed to run on quantum computers and capable of breaking traditional cryptographic protocols are already known. Quantum-strong algorithms capable of providing data integrity, messages confidentiality, user authentication and authorization are highly desirable. In order to design quantum-strong protocols with these capabilities, new approaches on how to use well-known cryptographic tools should be explored. In this work, we present four different results where one-way hash functions used in a clever way with additional mathematical objects like homomorphisms, symbolic computed closed-form solutions, polynomial rings and many more can provide the required capabilities.


Our first work is the O2MD2 cryptosystem, which uses the ring learning with errors (RLWE) problem combined with arithmetic functions and one-way hash functions in rings as its security basis. This system provides a one-to-many private/public key architecture with a distributed key refresh. It has three different frameworks that reach AES-256 equivalent security, and provides message integrity and authenticity verifications. We also propose six different implementations that reach the security levels 1, 3 and 5 proposed in the NIST Post-Quantum Cryptography Standardization project. Finally, we used the NIST Statistical Test Suite to verify the indistinguishability of our produced ciphertexts against randomly generated noise.



Our second work presents two proof-of-concept fixed-point FPGA implementations of the O2MD2 cryptosystem, where the symbolic closed-form solution of the polynomial multiplicative inverse of an array of integers was calculated. It was embedded in a library of pre-computed tables, yielding as result the O2MD2 key generation, encryption and decryption algorithms, while maintaining a fixed-point arithmetic throughout all the modules. The first implementation has a throughput of 473.875 Mbps and 448.129 Mbps while encrypting and decrypting, while the second has a throughput of 416.56 Mbps and 335.35 Mbps, respectively. We show the total gates count, the estimated clock cycles, timing analysis for post-synthesis and post-implementation of the three algorithms, and achieved latencies and intervals. Finally, we present a speed comparison of our hardware implementation versus its software counterpart, and against hardware implementations of the NTRU frameworks family.


Our third work introduces the Distributed Hashing in Chain-of-Trust Authentication Protocols (DHCT) framework, which performs a distributed and dynamic hash-based user authentication based on challenges. Each challenge is unique for each communication attempt, and brings security to the control plane, preventing brute-force, dictionary and replay attacks. The DHCT framework runs in linear time, creates a chain-of-trust where messages are transported only via trusted entities, and provides a re-handshake protocol which makes unnecessary to perform a whole handshake over again when a user reconnects to the network. In test environments, the DHCT framework allowed trusted entities to ignore and discard communication attempts from fake users and keep a chain-of-trust to communicate between trusted ones.


Our final work presents the One-way Hash and Homomorphisms-based Protocol for Supply Chain Security in IoT Devices (OHSA) framework, which allows to hardware manufacturers to provide access to other manufacturers down in the supply chain to the inner data of the hardware components, without explicitly disclosing the embedded credentials. The OHSA framework works using metadata and meta-metadata of the credentials, allowing the hardware components to authorize users, protecting firmware updates by means of a seal-deseal-reseal. In test environments, the OHSA framework can detect not only corrupted firmware updates, but also valid updates coming from unauthorized manufacturers, by means of the firmware security seal.

Contents

摘要 i
Abstract iii
Contents v
List of Tables x
List of Figures xiii

1 Introduction 1
1.1 Roadmap 3
1.2 O2MD2: A new post-quantum cryptosystem with one-to-many distributed key management based on prime modulo double encapsulation 5
1.3 A Closed-form Solution to Polynomial Ring Multiplicative Inverses: an FPGA Implementation of the Post Quantum O2MD2 Cryptosystem 12
1.4 DHCT: Distributed Hashing in Chain-of-Trust Authentication Protocols for Secure M2M Communications 14


2 O2MD2: A new post-quantum cryptosystem with one-to-many distributed key management based on prime modulo double encapsulation 16
2.1 Introduction 16

2.2 Related work 19
2.3 Problem statement and solution overview 24
2.4 Solution 28
2.5 Proof of correctness 46
2.6 Security analysis 53
2.7 Performance analysis 66
2.8 Conclusion and future work 66
2.9 Appendix - Example 69

3 A Closed-form Solution to Polynomial Ring Multiplicative Inverses: an FPGA Implementation of the Post-Quantum O2MD2 Cryptosystem 73
3.1 Introduction 73
3.2 Background 75
3.3 Problem statement and solution overview 78
3.4 Hardware design 83
3.5 Hardware implementation 95
3.6 Experimental Results and Performance Analysis 99
3.7 Conclusions and future work 106


4 DHCT: Distributed Hashing in Chain-of-Trust Authentication Protocols for Secure M2M Communications 108
4.1 Introduction 108
4.2 Background 112
4.3 Problem Statement 115
4.4 The DHCT Framework 116
4.5 Proof of correctness 128
4.6 Analysis 132
4.7 Implementation and Performance Evaluation 135
4.8 Conclusions and future work 139

5 OHSA: One-way Hash and Homomorphisms-based Protocol for Supply Chain Security in IoT Devices 140
5.1 Introduction 140
5.2 Background 141
5.3 Problem Statement 144
5.4 Solution 144
5.5 Performance Evaluation 152
5.6 Conclusions and Future Work 152

6 Conclusions and Future Work 153
6.1 Conclusions 153
6.2 Future Work 155

A O2MD2: Additional Examples 156
A.1 Introduction 156
A.2 Preliminaries 156
A.3 Example 157
A.4 Multiple sessions 167
A.5 Conclusions 170
A.6 Appendix 170

B O2MD2: MATLAB Library 1.0 & c Implementation User Manual 174
B.1 Introduction 174
B.2 MATLAB Library 174
B.3 MATLAB: Installation 184
B.4 MATLAB: Execution 184
B.5 MATLAB: Results 184
B.6 c implementation 193

References 207

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