Optimal Error Pseudodistributions for Read-Once Branching Programs

In a seminal work, Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$ and width $w$ read-once branching programs with seed length $O(\log n\cdot \log(nw)+\log n\cdot\log(1/\varepsilon))$ and error $\varepsilon$. It remains a central question to reduce the seed length to $O(\log (nw/\varepsilon))$, which would prove that $\mathbf{BPL}=\mathbf{L}$. However, there has been no improvement on Nisan's construction for the case $n=w$, which is most relevant to space-bounded derandomization. Recently, in a beautiful work, Braverman, Cohen and Garg (STOC'18) introduced the notion of a pseudorandom pseudo-distribution (PRPD) and gave an explicit construction of a PRPD with seed length $\tilde{O}(\log n\cdot \log(nw)+\log(1/\varepsilon))$. A PRPD is a relaxation of a pseudorandom generator, which suffices for derandomizing $\mathbf{BPL}$ and also implies a hitting set. Unfortunately, their construction is quite involved and complicated. Hoza and Zuckerman (FOCS'18) later constructed a much simpler hitting set generator with seed length $O(\log n\cdot \log(nw)+\log(1/\varepsilon))$, but their techniques are restricted to hitting sets. In this work, we construct a PRPD with seed length $$O(\log n\cdot \log (nw)\cdot \log\log(nw)+\log(1/\varepsilon)).$$ This improves upon the construction in [BCG18] by a $O(\log\log(1/\varepsilon))$ factor, and is optimal in the small error regime. In addition, we believe our construction and analysis to be simpler than the work of Braverman, Cohen and Garg

Recursive Error Reduction for Regular Branching Programs

In a recent work, Chen, Hoza, Lyu, Tal and Wu (FOCS 2023) showed an improved error reduction framework for the derandomization of regular read-once branching programs (ROBPs). Their result is based on a clever modification to the inverse Laplacian perspective of space-bounded derandomization, which was originally introduced by Ahmadinejad, Kelner, Murtagh, Peebles, Sidford and Vadhan (FOCS 2020). In this work, we give an alternative error reduction framework for regular ROBPs. Our new framework is based on a binary recursive formula from the work of Chattopadhyay and Liao (CCC 2020), that they used to construct weighted pseudorandom generators (WPRGs) for general ROBPs. Based on our new error reduction framework, we give alternative proofs to the following results for regular ROBPs of length $n$ and width $w$, both of which were proved in the work of Chen et al. using their error reduction: $\bullet$ There is a WPRG with error $\varepsilon$ that has seed length $\tilde{O}(\log(n)(\sqrt{\log(1/\varepsilon)}+\log(w))+\log(1/\varepsilon)).$ $\bullet$ There is a (non-black-box) deterministic algorithm which estimates the expectation of any such program within error $\pm\varepsilon$ with space complexity $\tilde{O}(\log(nw)\cdot\log\log(1/\varepsilon)).$ (This was first proved in the work of Ahmadinejad et al., but the proof by Chen et al. is simpler.) Because of the binary recursive nature of our new framework, both of our proofs are based on a straightforward induction that is arguably simpler than the Laplacian-based proof in the work of Chen et al

The Study of a Fair Electronic Payment System for Digital Content

因為網路的流行和方便，使得越來越多的消費者透過網路購買數位產品。然而，大量的數位內容產品也變得更容易偽造和取得。因此，如何證明誰是合法數位內容的擁有者成為一個重要問題。許多研究者提出不同買賣浮水印的機制，在安全付款系統藉此保護消費者的所有權。在本文中，我們將藉由潛隱通道的觀念來維護客戶的所有權，並提出一個完整的仲裁機制，以解決消費者和商家雙方之間的公平交易。為了實現上述目標，此協定的安全性基於五種加密技術，包含：潛隱通道，Nyberg-Rueppel機制，單向赫序函數，Schnorr簽章法和RSA密碼系統。我們提出了兩個付款方案:建立在解離散對數安全性問題的線上交易系統和建立在解質因數分解安全性問題的離線交易系統。我們的方案不僅可以保護客戶合法的數位內容擁有權，而且可以達到交易的公平性和客戶的隱密性，提款現金的所有權追蹤和交易過程的安全性。More and more customers purchase digital contents through the Internet due to its b popularity and convenience. However, there are a multitude of pirated editions of digital products that have become more available and easier to attain. Therefore, proving the legal ownership of digital contents has becomes more important than ever before. Many researchers have proposed various schemes to protect consumer''s ownership with watermarking mechanisms on secure payment systems. In this paper, we want to preserve customer's ownership via subliminal message and propose an intact arbitration mechanism to solve the fairness of transactions between both the customer and the shop. In order to achieve above objectives, the security of this protocol employs five cryptographic techniques including the subliminal channel, Nyberg-Rueppel scheme, one-way hash function, Schnorr signature scheme and RSA cryptosystem. We propose two payment schemes: on-line payment system based on discrete logarithms problem and off-line payment system based on factoring problem. Our schemes not only protect customer's legal ownership of digital content, but also achieve fair transaction, customer anonymity, owner tracing of coin and payment security.Abstract I 中文摘要 II Table of Contents III List of Tables VI List of Figures VII Chapter 1 Introduction 1 1.1 Motivations 1 1.2 Related works 2 1.3 Thesis Organization 3 Chapter 2 Preliminaries 4 2.1 Nyberg-Rueppel scheme 4 2.2 One-way hash function 4 2.3 Schnorr signature scheme 4 2.4 RSA digital signature 5 Chapter 3 6 A fair online payment system for digital content via subliminal channel 6 3.1 Our proposed scheme 6 3.1.1 Open account phase 7 3.1.2 The Withdrawal phase 8 3.1.3 The Payment phase 10 3.1.4 The fair arbitration phase 14 3.1.5 The legal owner arbitration phase 16 3.2 Security analyses and discussions of online scheme 17 3.2.1 Security analyses 17 3.2.1.1 The replay attack issue 17 3.2.1.2 Conspiracy attack issue 18 3.2.1.3 The DoS attack issue 19 3.2.1.4 Man-in-the-middle attack issue 19 3.2.1.5 Double spending issue 19 3.2.2 Unforgeability 19 3.2.3 Anonymity 20 3.2.4 Non-repudiation 20 3.2.5 Fairness issue 22 3.2.6 Piracy tracing problem issue 23 3.2.7 Discussions 24 Chapter 4 26 A fair offline digital content transaction system on RSA 26 4.1 Our proposed scheme 26 4.1.1 The registration phase 27 4.1.2 The Withdrawal phase 28 4.1.3 The transaction phase 30 4.1.4 The deposit phase 33 4.1.5 The fair arbitration phase 33 4.1.6 The legal owner arbitration phase 35 4.2 Security analyses and discussions of offline scheme 36 4.2.1 Security analyses 36 4.2.1.1 The replay attack issue 36 4.2.1.2 Conspiracy attack issue 37 4.2.1.3 The DoS attack issue 37 4.2.1.4 Man-in-the-middle attack issue 37 4.2.2 Unforgeability 37 4.2.3 Anonymity 38 4.2.4 Non-repudiation 38 4.2.5 Fairness issue 39 4.2.6 Owner tracing of E-cash issue 39 4.2.7 Discussions 39 Chapter 5 Conclusions 43 References 4

Non-Covalently Functionalized Boron Nitride Mediated by a Highly Self-Assembled Supramolecular Polymer

A new method for exfoliation of hexagonal boron nitride (h-BN) into few-layered nanosheets has been developed by employing noncovalent assembly of networks upon association with a supramolecular polymer. In this work, we developed a simple, reliable, effective approach for preparation of exfoliated h-BN nanosheets from bulk h-BN via liquid-phase exfoliation using a low-molecular weight adenine-functionalized polypropylene glycol (A-PPG) supramolecular polymer. A-PPG self-assembled into either long-range ordered lamellar or micelle-like structures on the surface of h-BN because of the strong specific interactions between A-PPG and h-BN. The level of h-BN nanosheet exfoliation could be controlled by adjusting the amount of A-PPG incorporated. This newly developed composite exhibited excellent phase transition behavior and thermal stability, and few-layer thickness with good dispersion of h-BN nanosheets, indicating self-assembled A-PPG functions as an efficient dispersant and stabilizer to manipulate the physical and morphological properties of exfoliated h-BN. This method of producing multifunctional exfoliated h-BN provides a unique paradigm for developing the next generation of thermoconductive devices and solution-processed semiconductors

Self-Assembled pH-Responsive Polymeric Micelles for Highly Efficient, Noncytotoxic Delivery of Doxorubicin Chemotherapy To Inhibit Macrophage Activation: <i>In Vitro</i> Investigation

Self-assembled pH-responsive polymeric micelles, a combination of hydrophilic poly­(ethylene glycol) segments and hydrogen bonding interactions within a biocompatible polyurethane substrate, can spontaneously self-assemble into highly controlled, nanosized micelles in aqueous solution. These newly developed micelles exhibit excellent pH-responsive behavior and biocompatibility, highly controlled drug (doxorubicin; DOX) release behavior, and high drug encapsulation stability in different aqueous environments, making the micelles highly attractive potential candidates for safer, more effective drug delivery in applications such as cancer chemotherapy. In addition, <i>in vitro</i> cell studies revealed the drug-loaded micelles possessed excellent drug entrapment stability and low cytotoxicity toward macrophages under normal physiological conditions (pH 7.4, 37 °C). When the pH of the culture media was reduced to 6.0 to mimic the acidic tumor microenvironment, the drug-loaded micelles triggered rapid release of DOX within the cells, which induced potent antiproliferative and cytotoxic effects <i>in vitro</i>. Importantly, fluorescent imaging and flow cytometric analyses confirmed the DOX-loaded micelles were efficiently delivered into the cytoplasm of the cells via endocytosis and then subsequently gradually translocated into the nucleus. Therefore, these multifunctional micelles could serve as delivery vehicles for precise, effective, controlled drug release to prevent accumulation and activation of tumor-promoting tumor-associated macrophages in cancer tissues. Thus, this unique system may offer a potential route toward the practical realization of next-generation pH-responsive therapeutic delivery systems