Efektiivsed mitteinteraktiivsed nullteadmusprotokollid referentssõne mudelis

Väitekirja elektrooniline versioon ei sisalda publikatsioone.Koos digitaalse ajastu võidukäiguga on interneti vahendusel võimalik sooritada üha ulmelisemana näivaid tegevusi. Täielikule krüpteeringule ehitatud mobiilsed rakendused, nagu näiteks WhatsApp, suudavad tagada, et kõne või sõnum jõuaksid üksnes õige adressaadini. Enamik pangasüsteeme garanteerivad TLS protokolli kasutades, et arvete maksmisel ja ülekannete tegemisel poleks nende andmeid kellelgi võimalik lugeda ega muuta. Mõned riigid pakuvad võimalust elektroonilisel teel hääletada (näiteks Eesti) või referendumeid läbi viia (näiteks Šveits), tagades sealjuures traditsioonilise paberhääletuse tasemel turvalisuse kriteeriumid. Kõik eelnevalt kirjeldatud tegevused vajavad kasutajate turvalisuse tagamiseks krüptograafilist protokolli. Tegelikkuses ei saa me kunagi eeldada, et kõik protokolli osapooled järgivad protokolli spetsifikatsiooni. Reaalses elus peab protokolli turvalisuseks iga osapool tõestama, et ta seda järgis ilma privaatsuse ohverdamiseta. Üks viis seda teha on nullteadmusprotokolli abil. Nullteadmusprotokoll on tõestus, mis ei lekita mingit informatsiooni peale selle, et väide on tõene. Tihti tahame, et nullteadmusprotokoll oleks mitteinteraktiivne. Sellisel juhul piisab, kui tõestus on arvutatud ainult ühe korra ning verifitseerijatel on igal ajal võimalik seda kontrollida. On kaks peamist mudelit, mis võimaldavad mitteinteraktiivsete nullteadmusprotokollide loomist: juhusliku oraakli (JO) mudel ja referentssõne mudel. JO mudeli protokollid on väga efektiivsed, kuid mõningate piirangute tõttu eelistame referentssõne mudelit. Selles töös esitleme kolme stsenaariumit, milles mitteinteraktiivne nullteadmus on asjakohane: verifitseeritav arvutamine, autoriseerimine ja elektrooniline hääletamine. Igas stsenaariumis pakume välja nullteadmusprotokolli referentssõne mudelis, mis on seni efektiivseim ning võrreldava efektiivsusega protokollidega JO mudelis.In the current digital era, we can do increasingly astonishing activities remotely using only our electronic devices. Using mobile applications such as WhatsApp, we can contact someone with the guarantee, using an end-to-end encryption protocol, that only the recipient can know the conversation's contents. Most banking systems enable us to pay our bills and perform other financial transactions, and use the TLS protocol to guarantee that no one can read or modify the transaction data. Some countries provide an option to vote electronically in an election (e.g. Estonia) or referendum (e.g. Switzerland) with similar privacy guarantees to traditional paper voting. In all these activities, a cryptographic protocol is required to ensure users' privacy. In reality, some parties participating in a protocol might not act according to what was agreed in the protocol specification. Hence, for a real world protocol to be secure, we also need each party to prove that it behaves honestly, but without sacrificing privacy of its inputs. This can be done using a zero-knowledge argument: a proof by a polynomial-time prover that gives nothing else away besides its correctness. In many cases, we want a zero-knowledge argument to be non-interactive and transferable, so that it is computed only once, but can be verified by many verifiers at any future time. There are two main models that enable transferable non-interactive zero-knowledge (NIZK) arguments: the random oracle (RO) model and the common reference string (CRS) model. Protocols in the RO model are very efficient, but due to some of its limitations, we prefer working in the CRS model. In this work we provide three scenarios where NIZK arguments are relevant: verifiable computation, authorization, and electronic voting. In each scenario, we propose NIZK arguments in the CRS model that are more efficient than existing ones, and are comparable in efficiency to the best known NIZK arguments in the RO model

Usalduse vähendamine ja turvalisuse parandamine zk-SNARK-ides ja kinnitusskeemides

Väitekirja elektrooniline versioon ei sisalda publikatsioonezk-SNARK-id on tõhusad ja praktilised mitteinteraktiivsed tõestussüsteemid, mis on konstrueeritud viitestringi mudelis ning tänu kompaktsetele tõestustele ja väga tõhusale verifitseeritavusele on need laialdaselt kasutusele võetud suuremahulistes praktilistes rakendustes. Selles töös uurime zk-SNARK-e kahest vaatenurgast: nende usalduse vähendamine ja turvalisuse tugevdamine. Esimeses suunas uurime kui palju saab vähendada usaldust paaristuspõhiste zk-SNARK-ide puhul ilma nende tõhusust ohverdamata niiviisi, et kasutajad saavad teatud turvataseme ka siis kui seadistusfaas tehti pahatahtlikult või kui avalikustati seadistusfaasi salajane teave. Me pakume välja mõned tõhusad konstruktsioonid, mis suudavad takistada zk-SNARK-i seadistusfaasi ründeid ja mis saavutavad senisest tugevama turvataseme. Näitame ka seda, et sarnased tehnikad võimaldavad leevendada usaldust tagauksega kinnitusskeemides, mis on krüptograafiliste primitiivide veel üks silmapaistev perekond ja mis samuti nõub usaldatud seadistusfaasi. Teises suunas esitame mõned tõhusad konstruktsioonid, mis tagavad parema turvalisuse minimaalsete lisakuludega. Mõned esitatud konstruktsioonidest võimaldavad lihtsustada praegusi TK-turvalisi protokolle, nimelt privaatsust säilitavate nutilepingusüsteemide Hawk ja Gyges konstruktsiooni, ja parandada nende tõhusust. Uusi konstruktsioone saab aga otse kasutada uutes protokollides, mis soovivad kasutada zk-SNARK-e. Osa väljapakutud zk-SNARK-e on implementeeritud teegis Libsnark ja empiirilised tulemused kinnitavad, et usalduse vähendamiseks või suurema turvalisuse saavutamiseks on arvutuslikud lisakulud väikesed.Zero-knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKs) are an efficient family of NIZK proof systems that are constructed in the Common Reference String (CRS) model and due to their succinct proofs and very efficient verification, they are widely adopted in large-scale practical applications. In this thesis, we study zk-SNARKs from two perspectives, namely reducing trust and improving security in them. In the first direction, we investigate how much one can mitigate trust in pairing-based zk-SNARKs without sacrificing their efficiency. In such constructions, the parties of protocol will obtain a certain level of security even if the setup phase was done maliciously or the secret information of the setup phase was revealed. As a result of this direction, we present some efficient constructions that can resist against subverting of the setup phase of zk-SNARKs and achieve a certain level of security which is stronger than before. We also show that similar techniques will allow us to mitigate the trust in the trapdoor commitment schemes that are another prominent family of cryptographic primitives that require a trusted setup phase. In the second direction, we present some efficient constructions that achieve more security with minimal overhead. Some of the presented constructions allow to simplify the construction of current UC-secure protocols and improve their efficiency. New constructions can be directly deployed in any novel protocols that aim to use zk-SNARKs. Some of the proposed zk-SNARKs are implemented in Libsnark, the state-of-the-art library for zk-SNARKs, and empirical experiences confirm that the computational cost to mitigate the trust or to achieve more security is practical.https://www.ester.ee/record=b535927

On a New, Efficient Framework for Falsifiable Non-interactive Zero-Knowledge Arguments

Et kunnskapsløst bevis er en protokoll mellom en bevisfører og en attestant. Bevisføreren har som mål å overbevise attestanten om at visse utsagn er korrekte, som besittelse av kortnummeret til et gyldig kredittkort, uten å avsløre noen private opplysninger, som for eksempel kortnummeret selv. I mange anvendelser er det ønskelig å bruke IIK-bevis (Ikke-interaktive kunnskapsløse bevis), der bevisføreren produserer kun en enkelt melding som kan bekreftes av mange attestanter. En ulempe er at sikre IIK-bevis for ikke-trivielle språk kun kan eksistere ved tilstedeværelsen av en pålitelig tredjepart som beregner en felles referansestreng som blir gjort tilgjengelig for både bevisføreren og attestanten. Når ingen slik part eksisterer liter man av og til på ikke-interaktiv vitne-uskillbarhet, en svakere form for personvern. Studiet av effektive og sikre IIK-bevis er en kritisk del av kryptografi som har blomstret opp i det siste grunnet anvendelser i blokkjeder. I den første artikkelen konstruerer vi et nytt IIK-bevis for språkene som består av alle felles nullpunkter for en endelig mengde polynomer over en endelig kropp. Vi demonstrerer nytteverdien av beviset ved flerfoldige eksempler på anvendelser. Særlig verdt å merke seg er at det er mulig å gå nesten automatisk fra en beskrivelse av et språk på et høyt nivå til definisjonen av IIK-beviset, som minsker behovet for dedikert kryptografisk ekspertise. I den andre artikkelen konstruerer vi et IIV-bevis ved å bruke en ny kompilator. Vi utforsker begrepet Kunnskapslydighet (et sterkere sikkerhetsbegrep enn lydighet) for noen konstruksjoner av IIK-bevis. I den tredje artikkelen utvider vi arbeidet fra den første artikkelen ved å konstruere et nytt IIK-bevis for mengde-medlemskap som lar oss bevise at et element ligger, eller ikke ligger, i den gitte mengden. Flere nye konstruksjoner har bedre effektivitet sammenlignet med allerede kjente konstruksjoner.A zero-knowledge proof is a protocol between a prover, and a verifier. The prover aims to convince the verifier of the truth of some statement, such as possessing credentials for a valid credit card, without revealing any private information, such as the credentials themselves. In many applications, it is desirable to use NIZKs (Non-Interactive Zero Knowledge) proofs, where the prover sends outputs only a single message that can be verified by many verifiers. As a drawback, secure NIZKs for non-trivial languages can only exist in the presence of a trusted third party that computes a common reference string and makes it available to both the prover and verifier. When no such party exists, one sometimes relies on non interactive witness indistinguishability (NIWI), a weaker notion of privacy. The study of efficient and secure NIZKs is a crucial part of cryptography that has been thriving recently due to blockchain applications. In the first paper, we construct a new NIZK for the language of common zeros of a finite set of polynomials over a finite field. We demonstrate its usefulness by giving a large number of example applications. Notably, it is possible to go from a high-level language description to the definition of the NIZK almost automatically, lessening the need for dedicated cryptographic expertise. In the second paper, we construct a NIWI using a new compiler. We explore the notion of Knowledge Soundness (a security notion stronger than soundness) of some NIZK constructions. In the third paper, we extended the first paper’s work by constructing a new set (non-)membership NIZK that allows us to prove that an element belongs or does not belong to the given set. Many new constructions have better efficiency compared to already-known constructions.Doktorgradsavhandlin

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

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Efficient NIZKs for Algebraic Sets

Significantly extending the framework of (Couteau and Hartmann, Crypto 2020), we propose a general methodology to construct NIZKs for showing that an encrypted vector $\vec{\chi}$ belongs to an algebraic set, i.e., is in the zero locus of an ideal $\mathscr{I}$ of a polynomial ring. In the case where $\mathscr{I}$ is principal, i.e., generated by a single polynomial $F$, we first construct a matrix that is a ``quasideterminantal representation\u27\u27 of $F$ and then a NIZK argument to show that $F (\vec{\chi}) = 0$. This leads to compact NIZKs for general computational structures, such as polynomial-size algebraic branching programs. We extend the framework to the case where \IDEAL is non-principal, obtaining efficient NIZKs for R1CS, arithmetic constraint satisfaction systems, and thus for $\mathsf{NP}$. As an independent result, we explicitly describe the corresponding language of ciphertexts as an algebraic language, with smaller parameters than in previous constructions that were based on the disjunction of algebraic languages. This results in an efficient GL-SPHF for algebraic branching programs

Reusable, Instant and Private Payment Guarantees for Cryptocurrencies

Despite offering numerous advantages, public decentralized cryptocurrencies such as Bitcoin suffer from scalability issues such as high transaction latency and low throughput. The vast array of so-called Layer-2 solutions tackling the scalability problem focus on throughput, and consider latency as a secondary objective. However, in the context of retail payments, instant finality of transactions is arguably a more pressing concern, besides the overarching concern for privacy. In this paper, we provide an overlay network that allows privacy-friendly low latency payments in a retail market. Our approach follows that of a recent work called Snappy, which achieved low latency but exposed identities of customers and their transaction histories. Our construction ensures this data is kept private, while providing merchants with protection against double-spending attacks. Although our system is still based upon customers registering with a collateral, crucially this collateral is reusable over time. The technical novelty of our work comes from randomness-reusable threshold encryption (RRTE), a cryptographic primitive we designed specifically for the following features: our construction provably guarantees payments to merchants, preserves the secret identity of honest customers and prevents their transactions from being linked. We also present an implementation of our construction, showing its capacity for fast global payments in a retail setting with a delay of less than 1 second

Mitte-interaktiivsed nullteadmusprotokollid nõrgemate usalduseeldustega

Väitekirja elektrooniline versioon ei sisalda publikatsiooneTäieliku koosluskindlusega (TK) kinnitusskeemid ja nullteadmustõestused on ühed põhilisemad krüptograafilised primitiivid, millel on hulgaliselt päriselulisi rakendusi. (TK) Kinnitusskeem võimaldab osapoolel arvutada salajasest sõnumist kinnituse ja hiljem see verifitseeritaval viisil avada. Täieliku koosluskindlusega protokolle saab vabalt kombineerida teiste täieliku koosluskindlusega protokollidega ilma, et see mõjutaks nende turvalisust. Nullteadmustõestus on protokoll tõestaja ja verifitseerija vahel, mis võimaldab tõestajal veenda verifitseerijat mingi väite paikapidavuses ilma rohkema informatsiooni lekitamiseta. Nullteadmustõestused pakuvad suurt huvi ka praktilistes rakendustes, siinkohal on olulisemateks näideteks krüptorahad ja hajusandmebaasid üldisemalt. Siin on eriti asjakohased just lühidad mitteinteraktiivsed nullteadmustõestused (SNARKid) ning kvaasiadaptiivsed mitteinteraktiivsed nullteadmustõestused (QA-NIZKid). Mitteinteraktiivsetel nullteadmustõestustel juures on kaks suuremat praktilist nõrkust. Esiteks on tarvis usaldatud seadistusfaasi osapoolte ühisstringi genereerimiseks ja teiseks on tarvis täielikku koosluskindlust. Käesolevas doktoritöös me uurime neid probleeme ja pakume välja konkreetseid konstruktsioone nende leevendamiseks. Esmalt uurime me õõnestuskindlaid SNARKe juhu jaoks, kus seadistusfaasi ühisstring on õõnestatud. Me konstrueerime õõnestuskindla versiooni seni kõige tõhusamast SNARKist. Samuti uurime me QA-NIZKide õõnestuskindlust ja konstrueerime kõige efektiivsemate QA-NIZKide õõnestuskindla versiooni. Mis puutub teise uurimissuunda, nimelt täielikku koosluskindlusesse, siis sel suunal kasutame me pidevaid projektiivseid räsifunktsioone. Me pakume välja uue primitiivi, kus eelmainitud räsifunktsioonid on avalikult verifitseeritavad. Nende abil me konstrueerime seni kõige tõhusama mitteinteraktiivse koosluskindla kinnitusskeemi. Lõpetuseks me töötame välja uue võtte koosluskindlate kinnitusskeemide jaoks, mis võimaldab ühisarvutuse abil luua nullteadmustõestuste ühisstringe.Quite central primitives in cryptographic protocols are (Universally composable (UC)) commitment schemes and zero-knowledge proofs that getting frequently employed in real-world applications. A (UC) commitment scheme enables a committer to compute a commitment to a secret message, and later open it in a verifiable manner (UC protocols can seamlessly be combined with other UC protocols and primitives while the entire protocol remains secure). A zero-knowledge proof is a protocol usually between a prover and a verifier that allows the prover to convince the verifier of the legality of a statement without disclosing any more information. Zero-knowledge proofs and in particular Succinct non-interactive zero-knowledge proofs (SNARKs) and quasi adaptive NIZK (QA-NIZK) are of particular interest in the real-world applications, with cryptocurrencies or more generally distributed ledger technologies being the prime examples. The two serious issues and the main drawbacks of the practical usage of NIZKs are (i) the demand for a trusted setup for generating the common reference string (CRS) and (ii) providing the UC security. In this thesis, we essentially investigate the aforementioned issues and propose concrete constructions for them. We first investigate subversion SNARKs (Sub zk-SNARKs) when the CRS is subverted. In particular, we build a subversion of the most efficient SNARKs. Then we initiate the study of subversion QA-NIZK (Sub-QA-NIZK) and construct subversion of the most efficient QA-NIZKs. For the second issue, providing UC-security, we first using hash proof systems or smooth projective hash functions (SPHFs), we introduce a new cryptographic primitive called publicly computable SPHFs (PC-SPHFs) and construct the currently most efficient non-interactive UC-secure commitment. Finally, we develop a new technique for constructing UC-secure commitments schemes that enables one to generate CRS of NIZKs by using MPC in a UC-secure mannerhttps://www.ester.ee/record=b535926

P4TC - Provably-Secure yet Practical Privacy-Preserving Toll Collection

Electronic toll collection (ETC) is widely used all over the world not only to finance our road infrastructures, but also to realize advanced features like congestion management and pollution reduction by means of dynamic pricing. Unfortunately, existing systems rely on user identification and allow tracing a user’s movements. Several abuses of this personalized location data have already become public. In view of the planned Europeanwide interoperable tolling system EETS and the new EU General Data Protection Regulation, location privacy becomes of particular importance. In this paper, we propose a flexible security model and crypto protocol framework designed for privacy-preserving toll collection in the most dominant setting, i.e., Dedicated Short Range Communication (DSRC) ETC. A major challenge in designing the framework at hand was to combine provable security and practicality, where the latter includes practical performance figures and a suitable treatment of real-world issues, like broken onboard units etc. To the best of our knowledge, our work is the first in the DSRC setting with a rigorous security model and proof and arguably the most comprehensive formal treatment of ETC security and privacy overall. Additionally, we provide a prototypical implementation on realistic hardware which already features fairly practical performance figures. An interaction between an onboard unit and a road-side unit is estimated to take less than a second allowing for toll collection at full speed assuming one road-side unit per lane