Assumptions, Efficiency and Trust in Non-Interactive Zero-Knowledge Proofs

Vi lever i en digital verden. En betydelig del av livene våre skjer på nettet, og vi bruker internett for stadig flere formål og er avhengig av stadig mer avansert teknologi. Det er derfor viktig å beskytte seg mot ondsinnede aktører som kan forsøke å utnytte denne avhengigheten for egen vinning. Kryptografi er en sentral del av svaret på hvordan man kan beskytte internettbrukere. Historisk sett har kryptografi hovedsakelig vært opptatt av konfidensiell kommunikasjon, altså at ingen kan lese private meldinger sendt mellom to personer. I de siste tiårene har kryptografi blitt mer opptatt av å lage protokoller som garanterer personvern selv om man kan gjennomføre komplekse handlinger. Et viktig kryptografisk verktøy for å sikre at disse protokollene faktisk følges er kunnskapsløse bevis. Et kunnskapsløst bevis er en prosess hvor to parter, en bevisfører og en attestant, utveksler meldinger for å overbevise attestanten om at bevisføreren fulgte protokollen riktig (hvis dette faktisk er tilfelle) uten å avsløre privat informasjon til attestanten. For de fleste anvendelser er det ønskelig å lage et ikke-interaktivt kunnskapsløst bevis (IIK-bevis), der bevisføreren kun sender én melding til attestanten. IIK-bevis har en rekke ulike bruksområder, som gjør de til attraktive studieobjekter. Et IIK-bevis har en rekke ulike egenskaper og forbedring av noen av disse fremmer vår kollektive kryptografiske kunnskap. I den første artikkelen i denne avhandlingen konstruerer vi et nytt ikke-interaktivt kunnskapsløst bevis for språk basert på algebraiske mengder. Denne artikkelen er basert på arbeid av Couteau og Hartmann (Crypto 2020), som viste hvordan man omformer et bestemt interaktivt kunnskapsløst bevis til et IIK-bevis. Vi følger deres tilnærming, men vi bruker et annet interaktivt kunnskapsløst bevis. Dette fører til en forbedring sammenlignet med arbeidet deres på flere områder, spesielt når det gjelder både formodninger og effektivitet. I den andre artikkelen i denne avhandlingen studerer vi egenskapene til ikke-interaktive kunnskapsløse bevis som er motstandsdyktige mot undergraving. Det er umulig å lage et IIK-bevis uten å stole på en felles referansestreng (FRS) generert av en pålitelig tredjepart. Men det finnes eksempler på IIK-bevis der ingen lærer noe privat informasjon fra beviset selv om den felles referansestrengen ble skapt på en uredelig måte. I denne artikkelen lager vi en ny kryptografisk primitiv (verifiserbart-uttrekkbare enveisfunksjoner) og viser hvordan denne primitiven er relatert til IIK-bevis med den ovennevnte egenskapen.We live in a digital world. A significant part of our lives happens online, and we use the internet for incredibly many different purposes and we rely on increasingly advanced technology. It therefore is important to protect against malicious actors who may try to exploit this reliance for their own gain. Cryptography is a key part of the answer to protecting internet users. Historically, cryptography has mainly been focused on maintaining the confidentiality of communication, ensuring that no one can read private messages sent between people. In recent decades, cryptography has become concerned with creating protocols which guarantee privacy even as they support more complex actions. A crucial cryptographic tool to ensure that these protocols are indeed followed is the zero-knowledge proof. A zero-knowledge proof is a process where two parties, a prover and a verifier, exchange messages to convince the verifier that the prover followed the protocol correctly (if indeed the prover did so) without revealing any private information to the verifier. It is often desirable to create a non-interactive zero-knowledge proof (NIZK), where the prover only sends one message to the verifier. NIZKs have found a number of different applications, which makes them an attractive object of study. A NIZK has a variety of different properties, and improving any of these aspects advances our collective cryptographic knowledge. In the first paper in this thesis, we construct a new non-interactive zero-knowledge proof for languages based on algebraic sets. This paper is based on work by Couteau and Hartmann (Crypto 2020), which showed how to convert a particular interactive zero-knowledge proof to a NIZK. We follow their approach, but we start with a different interactive zero-knowledge proof. This leads to an improvement compared to their work in several ways, in particular in terms of both assumptions and efficiency. In the second paper in this thesis, we study the property of subversion zero-knowledge in non-interactive zero-knowledge proofs. It is impossible to create a NIZK without relying on a common reference string (CRS) generated by a trusted party. However, a NIZK with the subversion zero-knowledge property guarantees that no one learns any private information from the proof even if the CRS was generated dishonestly. In this paper, we create a new cryptographic primitive (verifiably-extractable one-way functions) and show how this primitive relates to NIZKs with subversion zero-knowledge.Doktorgradsavhandlin

Securing mobile code.

If software is designed so that the software can issue functions that will move that software from one computing platform to another, then the software is said to be 'mobile'. There are two general areas of security problems associated with mobile code. The 'secure host' problem involves protecting the host from malicious mobile code. The 'secure mobile code' problem, on the other hand, involves protecting the code from malicious hosts. This report focuses on the latter problem. We have found three distinct camps of opinions regarding how to secure mobile code. There are those who believe special distributed hardware is necessary, those who believe special distributed software is necessary, and those who believe neither is necessary. We examine all three camps, with a focus on the third. In the distributed software camp we examine some commonly proposed techniques including Java, D'Agents and Flask. For the specialized hardware camp, we propose a cryptographic technique for 'tamper-proofing' code over a large portion of the software/hardware life cycle by careful modification of current architectures. This method culminates by decrypting/authenticating each instruction within a physically protected CPU, thereby protecting against subversion by malicious code. Our main focus is on the camp that believes that neither specialized software nor hardware is necessary. We concentrate on methods of code obfuscation to render an entire program or a data segment on which a program depends incomprehensible. The hope is to prevent or at least slow down reverse engineering efforts and to prevent goal-oriented attacks on the software and execution. The field of obfuscation is still in a state of development with the central problem being the lack of a basis for evaluating the protection schemes. We give a brief introduction to some of the main ideas in the field, followed by an in depth analysis of a technique called 'white-boxing'. We put forth some new attacks and improvements on this method as well as demonstrating its implementation for various algorithms. We also examine cryptographic techniques to achieve obfuscation including encrypted functions and offer a new application to digital signature algorithms. To better understand the lack of security proofs for obfuscation techniques, we examine in detail general theoretical models of obfuscation. We explain the need for formal models in order to obtain provable security and the progress made in this direction thus far. Finally we tackle the problem of verifying remote execution. We introduce some methods of verifying remote exponentiation computations and some insight into generic computation checking

SoK: Computer-Aided Cryptography

Computer-aided cryptography is an active area of research that develops and applies formal, machine-checkable approaches to the design, analysis, and implementation of cryptography. We present a cross-cutting systematization of the computer-aided cryptography literature, focusing on three main areas: (i) design-level security (both symbolic security and computational security), (ii) functional correctness and efficiency,and (iii) implementation-level security (with a focus on digital side-channel resistance). In each area, we first clarify the role of computer-aided cryptography—how it can help and what the caveats are—in addressing current challenges. We next present a taxonomy of state-of-the-art tools, comparing their accuracy,scope, trustworthiness, and usability. Then, we highlight their main achievements, trade-offs, and research challenges. After covering the three main areas, we present two case studies. First, we study efforts in combining tools focused on different areas to consolidate the guarantees they can provide. Second, we distill the lessons learned from the computer-aided cryptography community’s involvement in the TLS 1.3 standardization effort.Finally, we conclude with recommendations to paper authors,tool developers, and standardization bodies moving forward

Agora: A Privacy-Aware Data Marketplace

We propose Agora, the first blockchain-based data marketplace that enables multiple privacy-concerned parties to get compensated for contributing and exchanging data, without relying on a trusted third party during the exchange. Agora achieves data privacy, output verifiability, and atomicity of payments by leveraging cryptographic techniques, and is designed as a decentralized application via smart contracts. Particularly, data generators provide encrypted data to data brokers who use a functional secret key to learn nothing but the output of a specific, agreed upon, function over the raw data. Data consumers can purchase decrypted outputs from the brokers, accompanied by corresponding proofs of correctness. We implement a working prototype of Agora on Ethereum and experimentally evaluate its performance and deployment costs. As a core building block of Agora, we propose a new functional encryption scheme with additional public parameters that operate as a trust anchor for verifying decrypted results

McFly: Verifiable Encryption to the Future Made Practical

Blockchain protocols have revolutionized the way individuals and devices can interact and transact over the internet. More recently, a trend has emerged to harness blockchain technology as a catalyst to enable advanced security features in distributed applications, in particular fairness. However, the tools employed to achieve these security features are either resource wasteful (e.g., time-lock primitives) or only efficient in theory (e.g., witness encryption). We present McFly, a protocol that allows one to efficiently ``encrypt a message to the future\u27\u27 such that the receiver can decrypt the message almost effortlessly. Towards this goal, we design and implement a novel primitive we call signature-based witness encryption and combine it with a BFT blockchain (or a blockchain finality layer) in such a way that the decryption of the message can be piggybacked on the tasks already performed by the blockchain committee, resulting in almost-for-free decryption. To demonstrate the practicality of the McFly protocol, we implemented our signature-based witness encryption scheme and evaluated it on a standard laptop with Intel i7 @2,3 GHz. For the popular BLS12-381 curve, a $381$-bit message and a committee of size $500$ the encryption time is $9.8s$ and decryption is $14.8 s$. The scheme remains practical for a committee of size $2000$ with an encryption time of $58 s$ and decryption time of $218 s$

Formally Verified Verifiable Electronic Voting Scheme

Since the introduction of secret ballots in Victoria, Australia in 1855, paper (ballots) are widely used around the world to record the preferences of eligible voters. Paper ballots provide three important ingredients: correctness, privacy, and verifiability. However, the paper ballot election brings various other challenges, e.g. it is slow for large democracies like India, error prone for complex voting method like single transferable vote, and poses operational challenges for large countries like Australia. In order to solve these problems and various others, many countries are adopting electronic voting. However, electronic voting has a whole new set of problems. In most cases, the software programs used to conduct the election have numerous problems, including, but not limited to, counting bugs, ballot identification, etc. Moreover, these software programs are treated as commercial in confidence and are not allowed to be inspected by members of the public. As a consequence, the result produced by these software programs can not be substantiated. In this thesis, we address the three main concerns posed by electronic voting, i.e. correctness, privacy, and verifiability. We address the correctness concern by using theorem prover to implement the vote counting algorithm, privacy concern by using cryptography, and verifiability concern by generating a independently checkable scrutiny sheet (certificate). Our work has been carried out in the Coq theorem prover

Constant-Round YOSO MPC Without Setup

YOSO MPC (Gentry et al., Crypto 2021) is a new MPC framework where each participant can speak at most once. This models an adaptive adversary’s ability to watch the network and corrupt or destroy parties it deems significant based on their communication. By using private channels to anonymous receivers (e.g. by encrypting to a public key whose owner is unknown), the communication complexity of YOSO MPC can scale sublinearly with the total number N of available parties, even when the adversary’s corruption threshold is linear in N (e.g. just under N/2). It was previously an open problem whether YOSO MPC can achieve guaranteed output delivery in a constant number of rounds without relying on trusted setup. In this work, we show that this can indeed be accomplished. We demonstrate three different approaches: the first two (which we call YaOSO and YOSO-GLS) use two and three rounds of communication, respectively. Our third approach (which we call YOSO-LHSS) uses O(d) rounds, where d is the multiplicative depth of the circuit being evaluated; however, it can be used to bootstrap any constant-round YOSO protocol that requires setup, by generating that setup within YOSO-LHSS. Though YOSO-LHSS requires more rounds than our first two approaches, it may be more practical, since the zero knowledge proofs it employs are more efficient to instantiate. As a contribution of independent interest, we introduce a verifiable state propagation UC functionality, which allows parties to send private message which are verifiably derived in the “correct” way (according to the protocol in question) to anonymous receivers. This is a natural functionality to build YOSO protocols on top of