Concurrent Knowledge-Extraction in the Public-Key Model

Knowledge extraction is a fundamental notion, modelling machine possession of values (witnesses) in a computational complexity sense. The notion provides an essential tool for cryptographic protocol design and analysis, enabling one to argue about the internal state of protocol players without ever looking at this supposedly secret state. However, when transactions are concurrent (e.g., over the Internet) with players possessing public-keys (as is common in cryptography), assuring that entities ``know'' what they claim to know, where adversaries may be well coordinated across different transactions, turns out to be much more subtle and in need of re-examination. Here, we investigate how to formally treat knowledge possession by parties (with registered public-keys) interacting over the Internet. Stated more technically, we look into the relative power of the notion of ``concurrent knowledge-extraction'' (CKE) in the concurrent zero-knowledge (CZK) bare public-key (BPK) model.Comment: 38 pages, 4 figure

Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption

In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for $\mathcal{NP}$ in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in $\mathcal{NP}$ in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.Comment: 19 pag

Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. Furthermore,We show time-efficient instantiations of our protocol based on known number-theoretic assumptions. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages

Improved OR-Composition of Sigma-Protocols

In [CDS94] Cramer, Damg̊ard and Schoenmakers (CDS) devise an OR-composition technique for Σ-protocols that allows to construct highly-efficient proofs for compound statements. Since then, such technique has found countless applications as building block for designing efficient protocols. Unfortunately, the CDS OR-composition technique works only if both statements are fixed before the proof starts. This limitation restricts its usability in those protocols where the theorems to be proved are defined at different stages of the protocol, but, in order to save rounds of communication, the proof must start even if not all theorems are available. Many round-optimal protocols ([KO04, DPV04, YZ07, SV12]) crucially need such property to achieve round-optimality, and, due to the inapplicability of CDS’s technique, are currently implemented using proof systems that requires expensive NP reductions, but that allow the proof to start even if no statement is defined (a.k.a., LS proofs from Lapidot-Shamir [LS90]). In this paper we show an improved OR-composition technique for Σ-protocols, that requires only one statement to be fixed when the proof starts, while the other statement can be define

New Notions of Soundness and Simultaneous Resettability in the Public-Key Model

I n this paper, some new notions of soundness in public-key model are presented. We clarify the relationships among our new notions of soundness and the original 4 soundness notions presented by Micali and Reyzin. Our new soundness notions also characterize a new model for ZK protocols in public key model: weak soundness model. By ``weak” we mean for each common input x selected by a malicious prover on the fly, x is used by the malicious prover at most a-priori bounded polynomial times. The weak soundness model just lies in between BPK model and UPK model. Namely, it is weaker than BPK model but stronger than UPK model. In the weak soundness model (also in the UPK model, since weak soundness model implies UPK model), we get a 3-round black-box rZK arguments with weak resettable soundness for NP. Note that simultaneous resettability is an important open problem in the field of ZK protocols. And Reyzin has proven that there are no ZK protocols with resettable soundness in the BPK model. It means that to achieve simultaneous resettability one needs to augment the BPK model in a reasonable fashion. Although Barak et al. [BGGL01] have proven that any language which has a black-box ZK arguments with resettable soundness is in BPP. It is the weak soundness that makes us to get simultaneous resettability. More interestingly, our protocols work in a somewhat ``parallel repetition” manner to reduce the error probability and the verifier indeed has secret information with respect to historical transcripts. Note that in general the error probability of such protocols can not be reduced by parallel repetition. [BIN97] At last, we give a 3-round non-black-box rZK arguments system with resettable soundness for NP in the preprocessing model in which a trusted third party is assumed. Our construction for such protocol is quite simple. Note that although the preprocessing model is quite imposing but it is still quite reasonable as indicated in [CGGM00]. For example, in many e-commerce setting a trusted third party is often assumed. The critical tools used in this paper are: verifiable pseudorandom functions, zap and complexity leveraging. To our knowledge, our protocols are also the second application of verifiable pseudorandom functions. The first application is the 3-round rZK arguments with one-time soundness for NP in the public-key model as indicated by Micali and Reyzin [MR01a]

Concurrent/Resettable Zero-Knowledge With Concurrent Soundness in the Bare Public-Key Model and Its Applications

In this work, we investigate concurrent knowledge-extraction (CKE) and concurrent non-malleability (CNM) for concurrent (and stronger, resettable) ZK protocols in the bare public-key model. We formulate, driven by concrete attacks, and achieve CKE for constant-round concurrent/resettable arguments in the BPK model under standard polynomial assumptions. We get both generic and practical implementations. Here, CKE is a new concurrent verifier security that is strictly stronger than concurrent soundness in public-key model. We investigate, driven by concrete attacks, and clarify the subtleties in formulating CNM in the public-key model. We then give a new (augmented) CNM formulation in the public-key model and a construction of CNMZK in the public-key model satisfying the new CNM formulation

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

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

Secure computation under network and physical attacks

2011 - 2012This thesis proposes several protocols for achieving secure com- putation under concurrent and physical attacks. Secure computation allows many parties to compute a joint function of their inputs, while keeping the privacy of their input preserved. It is required that the pri- vacy one party's input is preserved even if other parties participating in the protocol collude or deviate from the protocol. In this thesis we focus on concurrent and physical attacks, where adversarial parties try to break the privacy of honest parties by ex- ploiting the network connection or physical weaknesses of the honest parties' machine. In the rst part of the thesis we discuss how to construct proto- cols that are Universally Composable (UC for short) based on physical setup assumptions. We explore the use of Physically Uncloneable Func- tions (PUFs) as setup assumption for achieving UC-secure computa- tions. PUF are physical noisy source of randomness. The use of PUFs in the UC-framework has been proposed already in [14]. However, this work assumes that all PUFs in the system are trusted. This means that, each party has to trust the PUFs generated by the other parties. In this thesis we focus on reducing the trust involved in the use of such PUFs and we introduce the Malicious PUFs model in which only PUFs generated by honest parties are assumed to be trusted. Thus the secu- rity of each party relies on its own PUF only and holds regardless of the goodness of the PUFs generated/used by the adversary. We are able to show that, under this more realistic assumption, one can achieve UC- secure computation, under computational assumptions. Moreover, we show how to achieve unconditional UC-secure commitments with (ma- licious) PUFs and with stateless tamper-proof hardware tokens. We discuss our contribution on this matter in Part I. These results are contained in papers [80] and [28]. In the second part of the thesis we focus on the concurrent setting, and we investigate on protocols achieving round optimality and black- box access to a cryptographic primitive. We study two fundamental functionalities: commitment scheme and zero knowledge, and we focus on some of the round-optimal constructions and lower bounds con- cerning both functionalities. We nd that such constructions present subtle issues. Hence, we provide new protocols that actually achieve the security guarantee promised by previous results. Concerning physical attacks, we consider adversaries able to re- set the machine of the honest party. In a reset attack a machine is forced to run a protocol several times using the same randomness. In this thesis we provide the rst construction of a witness indistinguish- able argument system that is simultaneous resettable and argument of knowledge. We discuss about this contribution in Part III, which is the content of the paper. [edited by author]XI n.s

Concurrent Non-Malleable Commitments (and More) in 3 Rounds

The round complexity of commitment schemes secure against man-in-the-middle attacks has been the focus of extensive research for about 25 years. The recent breakthrough of Goyal et al. [22] showed that 3 rounds are sufficient for (one-left, one-right) non-malleable commitments. This result matches a lower bound of [41]. The state of affairs leaves still open the intriguing problem of constructing 3-round concurrent non-malleable commitment schemes. In this paper we solve the above open problem by showing how to transform any 3-round (one-left one-right) non-malleable commitment scheme (with some extractability property) in a 3-round concurrent nonmalleable commitment scheme. Our transform makes use of complexity leveraging and when instantiated with the construction of [22] gives a 3-round concurrent non-malleable commitment scheme from one-way permutations secure w.r.t. subexponential-time adversaries. We also show a 3-round arguments of knowledge and a 3-round identification scheme secure against concurrent man-in-the-middle attacks