Arbitrary Univariate Function Evaluation and Re-Encryption Protocols over Lifted-ElGamal Type Ciphertexts

Homomorphic encryption (HE) is one of the main tools in secure multiparty computation (MPC), and the (elliptic-curve) lifted-ElGamal cryptosystem is certainly the most efficient among the existing HE schemes. However, the combination of MPC with this most efficient HE has rarely appeared in the literature. This is mainly because the major known techniques for (additively) HE-based MPC are not available for this scheme due to its typical restriction that only a plaintext in a small range can be efficiently decrypted. In this paper, we resolve this problem. By our technique, a Server having a lifted-ElGamal ciphertext $[[m]]$ with unknown small plaintext $m$ can obtain a ciphertext $[[ \varphi(m) ]]$ for an arbitrary function $\varphi$ by just one-round communication with a semi-honest Client (and also two-rounds with a malicious Client) having a decryption key, where $m$ is kept secret for both parties. This property enlarges much the variations of MPC based on the most efficient lifted-ElGamal cryptosystem. As an application, we implemented MPC for exact edit distance between two encrypted strings; our experiment for strings of length $1024$ shows that the protocol takes only $45$ seconds in LAN environments and about $3$ minutes even in WAN environments. Moreover, our technique is also available with other lifted-ElGamal type HE schemes and admits different keys/schemes for the original and the resulting ciphertexts. For example, we can securely convert a level-2 (i.e., after multiplication) ciphertext for some two-level HE schemes into a level-1 (i.e., before multiplication) ciphertext, and securely apply arbitrary functions $\varphi(m)$ to encrypted plaintexts for some attribute-based HE schemes. This is the first result (even by using communication) on realizing these two functionalities

The DEMOS family of e-voting systems: End-to-end verifiable elections in the standard model

Η παρούσα διδακτορική διατριβή εισάγει τα συστήματα ηλεκτρονικής ψηφοφορίας DEMOS-A και DEMOS-2 τα οποία επιτυγχάνουν άμεση επαληθευσιμότητα (end-to-end verifiability) για πρώτη φορά. Προγενέστερα της διατριβής, όλα τα κορυφαία συστήματα ηλεκτρονικής ψηφοφορίας (π.χ. SureVote, JCJ, Pret a Voter, Helios, Scantegrity, etc.) προϋπέθεταν το αδιάβλητο των συσκευών ψηφοφορίας, το μοντέλο τυχαίου μαντείου, ή την ύπαρξη μια έμπιστης πηγής τυχαιότητας για την επίτευξη άμεσης επαληθευσιμότητας. Στον πυρήνα των DEMOS-A και DEMOS-2 , βρίσκεται ένας νέος μηχανισμός εξαγωγής τυχαιότητας απαιτούμενης για την επαλήθευση από την εντροπία που παράγουν οι ψηφοφόροι κατά τη συμμετοχή τους στην ψηφοφορία. Η εν λόγω εντροπία είναι εσωτερική ως προς το εκλογικό περιβάλλον, επομένως απαλείφεται η ανάγκη για εμπιστοσύνη σε μία εξωτερική πηγή τυχαιότητας. Η ανάλυση ασφάλειας διεξάγεται υπό ένα νέο κρυπτογραφικό πλαίσιο το οποίο συνιστά επιπρόσθετη συνεισφορά της διατριβής. Τα θεωρήματα άμεσης επαλήθευσιμότητας των DEMOS-A και DEMOS-2 μαρτυρούν μία στενή συσχέτιση του επιπέδου ασφάλειας με την συμπεριφορά του εκλογικού σωμάτος κατά την επαλήθευση. Βάσει αυτού του ευρήματος και της εργασίας του Ellison το 2007, η παρούσα διατριβή επεκτείνει το πλαίσιο μοντελοποιώντας τα συστήματα ηλεκτρονικής ψηφοφορίας ως ceremonies. Ως υπόδειγμα μελέτης ενός ceremony ηλεκτρονικής ψηφοφορίας, η παρούσα διατριβή μελετά την ασφάλεια του καθιερωμένου συστήματος ηλεκτρονικής ψηφοφορίας Helios.This PhD thesis introduces the DEMOS-A and DEMOS-2 e-voting systems that achieve end-to-end verifiability in the standard model for the first time. Prior to this thesis, all top-tier e-voting systems (e.g. SureVote, JCJ, Pret a Voter, Helios, Scantegrity, etc.) assumed honesty of the voting clients, the random oracle model, or the existence a randomness beacon to achieve end-to-end verifiability. In the core of DEMOS-A and DEMOS-2, is a novel mechanism that extracts the randomness required for verification from the entropy generated by the voters, when they engage in the voting phase. This entropy is internal with respect to the election environment, therefore the need for trusting an outer source of randomness is removed. The security analysis is performed under a novel cryptographic framework that constitutes an additional contribution of this thesis. The end-to-end verifiability theorems for DEMOS-A and DEMOS-2 reveal that the security level is in high correlation with the auditing behaviour of the electorate. Motivated by this finding, this thesis extends the framework by modelling e-voting systems as ceremonies, inspired by the work of Ellison in 2007. As a case study of an e-voting ceremony, this thesis investigates the security of the well-known Helios e-voting system

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

Distributed, end-to-end verifiable, and privacy-preserving internet voting systems

We present the D-DEMOS suite of distributed, privacy-preserving, and end-to-end verifiable e-voting systems; one completely asynchronous and one with minimal timing assumptions but better performance. Their distributed voting operation is human verifiable; a voter can vote over the web, using an unsafe web client stack, without sacrificing her privacy, and get recorded-as-cast assurance. Additionally, a voter can outsource election auditing to third parties, still without sacrificing privacy. We provide a model and security analysis of the systems, implement prototypes of the complete systems, measure their performance experimentally, demonstrate their ability to handle large-scale elections, and demonstrate the performance trade-offs between the two versions

Survey on Fully Homomorphic Encryption, Theory, and Applications

Data privacy concerns are increasing significantly in the context of Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next generation networks. Homomorphic Encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages without decryption. This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption (FHE). It consequently covers design fundamentals and security properties of FHE and describes the main FHE schemes based on various mathematical problems. On a more practical level, the paper presents a view on privacy-preserving Machine Learning using homomorphic encryption, then surveys FHE at length from an engineering angle, covering the potential application of FHE in fog computing, and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art FHE libraries and tools, implemented in software and hardware, and the performance thereof

Studies on the Security of Selected Advanced Asymmetric Cryptographic Primitives

The main goal of asymmetric cryptography is to provide confidential communication, which allows two parties to communicate securely even in the presence of adversaries. Ever since its invention in the seventies, asymmetric cryptography has been improved and developed further, and a formal security framework has been established around it. This framework includes different security goals, attack models, and security notions. As progress was made in the field, more advanced asymmetric cryptographic primitives were proposed, with other properties in addition to confidentiality. These new primitives also have their own definitions and notions of security. This thesis consists of two parts, where the first relates to the security of fully homomorphic encryption and related primitives. The second part presents a novel cryptographic primitive, and defines what security goals the primitive should achieve. The first part of the thesis consists of Article I, II, and III, which all pertain to the security of homomorphic encryption schemes in one respect or another. Article I demonstrates that a particular fully homomorphic encryption scheme is insecure in the sense that an adversary with access only to the public material can recover the secret key. It is also shown that this insecurity mainly stems from the operations necessary to make the scheme fully homomorphic. Article II presents an adaptive key recovery attack on a leveled homomorphic encryption scheme. The scheme in question claimed to withstand precisely such attacks, and was the only scheme of its kind to do so at the time. This part of the thesis culminates with Article III, which is an overview article on the IND-CCA1 security of all acknowledged homomorphic encryption schemes. The second part of the thesis consists of Article IV, which presents Vetted Encryption (VE), a novel asymmetric cryptographic primitive. The primitive is designed to allow a recipient to vet who may send them messages, by setting up a public filter with a public verification key, and providing each vetted sender with their own encryption key. There are three different variants of VE, based on whether the sender is identifiable to the filter and/or the recipient. Security definitions, general constructions and comparisons to already existing cryptographic primitives are provided for all three variants.Doktorgradsavhandlin

Hardware Attacks against Hash-based Cryptographic Algorithms

This thesis surveys the current state of the art of hash-based cryptography with a view to finding vulnerabilities related to side-channel attacks and fault attacks. For side-channel investigation, we analyzed the power consumption of an Arduino Due microcontroller running a custom ARM implementation of SPHINCS-256---the most advanced digital signature scheme based on hash functions. Simple power analysis (SPA) was applied on a single trace to obtain a first insight into the implementation, and then on multiple traces to identify an initial data dependence of the power consumption on the hash functions involved in the instance. Based on this result, differential power analysis (DPA), with difference of means, V-test, and Pearson correlation, was applied to further investigate the leakage relating to BLAKE-256, as this function is used within SPHINCS-256 several times with the same secret key but applied on different known addresses. Concerning fault attacks, using instances of one-time signature (OTS) or few-times signatures (FTS) to sign a same message has been shown to theoretically make many schemes, such as LD-OTS, W-OTS, and HORS, existentially forgeable with non-invasive attacks. These vulnerabilities are fatal for the Merkle signature schemes which implement the tree chaining method (CMSS). When the schemes provide n/2 = 128 bits of quantum security, a universal forgery can be created with around q = 20 different faulty signatures. This thesis demonstrates a practical application of fault attacks to create this universal forgery using voltage glitching on the previously mentioned ARM implementation of SPHINCS-256. An invasive attack performing key recovery against W-OTS by forcing bits of two quantities to be zero is also described. Countermeasures to thwart all the described attacks are discussed

Ethical and Unethical Hacking

The goal of this chapter is to provide a conceptual analysis of ethical, comprising history, common usage and the attempt to provide a systematic classification that is both compatible with common usage and normatively adequate. Subsequently, the article identifies a tension between common usage and a normativelyadequate nomenclature. ‘Ethical hackers’ are often identified with hackers that abide to a code of ethics privileging business-friendly values. However, there is no guarantee that respecting such values is always compatible with the all-things-considered morally best act. It is recognised, however, that in terms of assessment, it may be quite difficult to determine who is an ethical hacker in the ‘all things considered’ sense, while society may agree more easily on the determination of who is one in the ‘business-friendly’ limited sense. The article concludes by suggesting a pragmatic best-practice approach for characterising ethical hacking, which reaches beyond business-friendly values and helps in the taking of decisions that are respectful of the hackers’ individual ethics in morally debatable, grey zones