Common Randomness Principles of Secrecy

This dissertation concerns the secure processing of distributed data by multi- ple terminals, using interactive public communication among themselves, in order to accomplish a given computational task. In the setting of a probabilistic multitermi- nal source model in which several terminals observe correlated random signals, we analyze secure distributed data processing protocols that harness the correlation in the data. The specific tasks considered are: computing functions of the data under secrecy requirements; generating secretly shared bits with minimal rate of public communication; and securely sharing bits in presence of a querying eavesdropper. In studying these various secure distributed processing tasks, we adopt a unified approach that entails examining the form of underlying common randomness (CR) that is generated at the terminals during distributed processing. We make the case that the exact form of established CR is linked inherently to the data processing task at hand, and its characterization can lead to a structural understanding of the associated algorithms. An identification of the underlying CR and its decomposi- tion into independent components, each with a different operational significance, is a recurring fundamental theme at the heart of all the proofs in this dissertation. In addition to leading to new theoretical insights, it brings out equivalences between seemingly unrelated problems. Another distinguishing feature of this work is that it considers interactive communication protocols. In fact, understanding the structure of such interactive communication is a key step in proving our results. We make the following contributions. First, we propose a new information theoretic formulation to study secure distributed computing using public communi- cation. The parties observing distributed data are trusted but an eavesdropper has access to the public communication network. We examine distributed communica- tion protocols that allow the trusted parties to accomplish their required computa- tion tasks while giving away negligible information about a specified portion of the data to an eavesdropper with access to the communication. Our theoretical results provide necessary and sufficient conditions that characterize the feasibility of vari- ous secure computing tasks; in many cases of practical importance, these conditions take a simple form and can be verified easily. When secure computing is feasible, we propose new algorithms in special cases. Next, we revisit the problem of generating shared secret keys (SKs). We investigate minimum communication requirements for generating information theo- retically secure SKs of maximum rates from correlated observations using interactive public communication. In particular, our approach allows us to examine the role of interaction in such communication. On the one hand, we find that interaction is not needed when the observed correlated bits are symmetrically correlated and therefore, in this case, simple noninteractive protocols are the most efficient means of generating optimum rate SKs. On the other hand, we illustrate that interactive pro- tocols can require a strictly lower rate of overall communication than noninteractive protocols. Finally, we consider the task of ensuring security against an eavesdropper who makes queries about a portion of the distributed data that the terminals share by communicating over a public network. We introduce an alternative notion of secrecy which requires rendering the task of a querying eavesdropper as onerous as possible. Our main contribution in this part is the development of a new technique for proving converse results for secrecy problems involving CR with interactive communication, which is employed then to obtain an upper bound for the maximum number of queries that can be inflicted on the eavesdropper for any CR and corresponding communication. Surprisingly, there is an equivalence between this notion of secrecy and that of information theoretic security, which leads to new theoretical results for SK generation; for instance, we prove a strong converse for the SK capacity. We conclude by hypothesizing the basic principles of secrecy generation that emerge from the results developed in this dissertation

Converses for Secret Key Agreement and Secure Computing

We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the secret key length, which is derived using a reduction of binary hypothesis testing to multiparty secret key agreement. Building on this basic result, we derive new converses for multiparty secret key agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to secret key agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses

양자 컴퓨터에 대한 암호학적 알고리즘

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 수리과학부, 2022. 8. 이훈희.The advent of a quantum mechanical computer presents a clear threat to existing cryptography. On the other hand, the quantum computer also suggests the possibility of a new cryptographic protocol through the properties of quantum mechanics. These two perspectives, respectively, gave rise to a new field called post-quantum cryptography as a countermeasure against quantum attacks and quantum cryptography as a new cryptographic technology using quantum mechanics, which are the subject of this thesis. In this thesis, we reconsider the security of the current post-quantum cryptography through a new quantum attack, model, and security proof. We present the fine-grained quantum security of hash functions as cryptographic primitives against preprocessing adversaries. We also bring recent quantum information theoretic research into cryptography, creating new quantum public key encryption and quantum commitment. Along the way, we resolve various open problems such as limitations of quantum algorithms with preprocessing computation, oracle separation problems in quantum complexity theory, and public key encryption using group action.양자역학을 이용한 컴퓨터의 등장은 쇼어의 알고리즘 등을 통해 기존 암호학에 명백한 위협을 제시하며, 양자역학의 성질을 통한 새로운 암호프로토콜의 가능성 또한 제시한다. 이러한 두 가지 관점은 각각 이 학위 논문의 주제가 되는 양자공격에 대한 대응책으로써의 대양자암호와 양자역학을 이용한 암호기술인 양자암호라고 불리는 새로운 분야를 발생시켰다. 이 학위 논문에서는 현재 대양자암호의 안전성을 새로운 양자암호 공격 알고리즘과 모델, 안전성 증명을 통해 재고한다. 특히 암호학적 해쉬함수의 일방향함수, 암호학적 의사난수생성기로서의 대양자 암호 안전성의 구체적인 평가를 제시한다. 또한 최근 양자역학의 연구를 양자암호에 도입함으로써 새로운 양자 공개키암호와 양자 커밋먼트 등의 새로운 발견을 제시한다. 이 과정에서 전처리 계산을 포함한 양자알고리즘의 한계, 양자 복잡계들의 오라클분리 문제, 군의 작용을 이용한 공개키 암호 등의 여러 열린문제들의 해결을 제시한다.1 Introduction 1 1.1 Contributions 3 1.2 Related Works 11 1.3 Research Papers 13 2 Preliminaries 14 2.1 Quantum Computations 15 2.2 Quantum Algorithms 20 2.3 Cryptographic Primitives 21 I Post-Quantum Cryptography: Attacks, New Models, and Proofs 24 3 Quantum Cryptanalysis 25 3.1 Introduction 25 3.2 QROM-AI Algorithm for Function Inversion 26 3.3 Quantum Multiple Discrete Logarithm Problem 34 3.4 Discussion and Open problems 39 4 Quantum Random Oracle Model with Classical Advice 42 4.1 Quantum ROM with Auxiliary Input 44 4.2 Function Inversion 46 4.3 Pseudorandom Generators 56 4.4 Post-quantum Primitives 58 4.5 Discussion and Open Problems 59 5 Quantum Random Permutations with Quantum Advice 62 5.1 Bound for Inverting Random Permutations 64 5.2 Preparation 64 5.3 Proof of Theorem 68 5.4 Implication in Complexity Theory 74 5.5 Discussion and Open Problems 77 II Quantum Cryptography: Public-key Encryptions and Bit Commitments 79 6 Equivalence Theorem 80 6.1 Equivalence Theorem 81 6.2 Non-uniform Equivalence Theorem 83 6.3 Proof of Equivalence Theorem 86 7 Quantum Public Key Encryption 89 7.1 Swap-trapdoor Function Pairs 90 7.2 Quantum-Ciphertext Public Key Encryption 94 7.3 Group Action based Construction 99 7.4 Lattice based Construction 107 7.5 Discussion and Open Problems 113 7.6 Deferred Proof 114 8 Quantum Bit Commitment 119 8.1 Quantum Commitments 120 8.2 Efficient Conversion 123 8.3 Applications of Conversion 126 8.4 Discussion and Open Problems 137박

Formal Foundations for Anonymous Communication

Mit jeder Online-Tätigkeit hinterlassen wir digitale Fußspuren. Unternehmen und Regierungen nutzen die privaten Informationen, die von den riesigen Datenmengen der Online-Spuren abgeleitet werden können, um ihre Nutzer und Büger zu manipulieren. Als Gegenmaßnahme wurden anonyme Kommunikationsnetze vorgeschlagen. Diesen fehlen jedoch umfassende formale Grundlagen und folglich ist der Vergleich zwischen verschiedenen Ansätzen nur sehr eingeschränkt möglich. Mit einer gemeinsamen Grundlage zwischen allen Forschern und Entwicklern von anonymen Kommunikationsnetzen können Missverständnisse vermieden werden und die dringend benötigte Entwicklung von den Netzen wird beschleunigt. Mit Vergleichbarkeit zwischen den Lösungen, können die für den jeweiligen Anwendungsfall optimalen Netze besser identifiziert und damit die Entwicklungsanstrengungen gezielter auf Projekte verteilt werden. Weiterhin ermöglichen formale Grundlagen und Vergleichbarkeit ein tieferes Verständnis für die Grenzen und Effekte der eingesetzten Techniken zu erlangen. Diese Arbeit liefert zuerst neue Erkenntnisse zu generellen Formalisierungen für anonyme Kommunikation, bevor sie sich dann auf die praktisch am meisten verbreitete Technik konzentriert: Onion Routing und Mix Netzwerke. Als erstes wird die Vergleichbarkeit zwischen Privatsphärezielen sichergestellt, indem sie formal definiert und miteinander verglichen werden. Dabei enteht eine umfangreiche Hierarchie von eindeutigen Privatsphärezielen. Als zweites werden vorgeschlagene Netzwerke analysiert, um deren Grundbausteine zu identifizieren und deren Schutz als Auswirkung in der Hierarchy zu untersuchen. Diese Grunlagen erlauben Konflikte und Schwachstellen in existierenden Arbeiten zu entdecken und aufzuklären. Genauer zeigt sich damit, dass basierend of derselben informalen Definition verschieden stark schützende formale Versionen entstanden sind. Weiterhin werden in dieser Arbeit die Notions genutzt um existierende Unmöglichkeitsresultate für anonyme Kommunikation zu vergleichen. Dabei wird nicht nur die erste vollständige Sicht auf alle bekannten Schranken für anonyme Kommunikationsnetze gegeben, sondern mit einem tiefgründigen Ansatz werden die existierenden Schranken auch gestärkt und zu praktischen, dem Stand der Kunst entsprechenden Netzen in Bezug gesetzt. Letztlich konnten durch die generellen Betrachtungen von vorgeschlagenen Netzwerken und ihren Grundbausteinen, insbesondere auch Angriffe auf die vorherrschende Klasse von anonymen Kommunikationsnetzen gefunden werden: auf Onion Routing und Mix-Netzwerke. Davon motiviert wurden als zweiter Teil dieser Arbeit die formalen Grundlagen und praktisch eingesetzten Lösungen for Onion Routing und Mix-Netzwerke untersucht. Dabei wurde festgestellt, dass die bereits erwähnten Angriffe teilweise auf eine fehlerhafte, aber weit verbreitete Beweisstrategie für solche Netze zurückzuführen sind und es wurde eine sichere Beweisstrategie als deren Ersatz vorgeschlagen. Weiterhin wurde die neue Strategie für ein vorgeschlagenes, aber bisher nicht weiter verwendetes Paketformat eingesetzt und dieses als sicher bewiesen. Dieses Paketformat unterstützt allerdings keine Rückantworten, was höchstwahrscheinlich der Grund ist, aus dem sich aktuelle Netze auf ein unsicheres Paketformat verlassen. Deshalb wurde im Rahmen dieser Arbeit eine konzeptuelle, sichere Lösung für Onion Routing mit Rückantworten entworfen. Als weitere verwandte Beiträge, zeigt die Arbeit Beziehungen von Teilen der generellen Ergebnisse für anonyme Kommunikationsnetze zu ähnlichen, aber bisher hauptsächlich getrennt betrachteten Forschungsbereichen, wie Privatsphäre auf der Bitübertragungsschicht, Kontaktnachverfolgung und privatsphäre-schützenden, digitalen Bezahlsystemen

BLOCKCHAIN SCALABILITY AND SECURITY

Cryptocurrencies like Bitcoin have proven to be a phenomenal success. The underlying techniques hold huge promise to change the future of financial transactions, and eventually the way people and companies compute, collaborate, and interact. At the same time, the current Bitcoin-like proof-of-work based blockchain systems are facing many challenges. In more detail, a huge amount of energy/electricity is needed for maintaining the Bitcoin blockchain. In addition, their security holds if the majority of the computing power is under the control of honest players. However, this assumption has been seriously challenged recently and Bitcoin-like systems will fail when this assumption is broken. This research proposes novel blockchain designs to address the challenges. We first propose a novel blockchain protocol, called 2-hop blockchain, by combining proof-of-work and proof-of-stake mechanisms. That said, even if the adversary controls more than 50% computing power, the honest players still have the chance to defend the blockchain via honest stake. Then we revise and implement the design to obtain a practical cryptocurrency system called Twinscoin. In more detail, we introduce a new strategy for difficulty adjustment in the hybrid blockchain and provide an analysis of it. We also show how to construct a light client for proof-of-stake cryptocurrencies and evaluate the proposal practically. We implement our new design. Our implementation uses a recent modular development framework for blockchains, called Scorex. It allows us to change only certain parts of an application leaving other codebase intact

Bitcoin as a Transaction Ledger: A Composable Treatment

Bitcoin is perhaps the most prominent example of a distributed cryptographic protocol that is extensively used in reality. Nonetheless, existing security proofs are property-based, and as such they do not support composition. In this work we put forth a universally composable treatment of the Bitcoin protocol. We specify the goal that Bitcoin aims to achieve as a ledger functionality in the (G)UC model of Canetti et al. (TCC\u2707). Our ledger functionality is weaker than the one recently proposed by Kiayias, Zhou, and Zikas (EUROCRYPT\u2716), but unlike the latter suggestion, which is arguably not implementable given the Bitcoin assumptions, we prove that the one proposed here is securely UC realized under standard assumptions by an appropriate abstraction of Bitcoin as a UC protocol. We further show how known property-based approaches can be cast as special instances of our treatment and how their underlying assumptions can be cast in (G)UC without restricting the environment or the adversary

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum