Exponentiating in Pairing Groups

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols

Secure and Efficient Delegation of Elliptic-Curve Pairing

Many public-key cryptosystems and, more generally, cryp- tographic protocols, use pairings as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client del- egates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's pairing inputs and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's at- tempt to convince the client of an incorrect pairing result. In this paper we show that the computation of bilinear pairings in all known pairing-based cryptographic protocols can be eciently, privately and securely delegated to a single, possibly malicious, server. Our tech- niques provides eciency improvements over past work in all input sce- narios, regardless on whether inputs are available to the parties in an oine phase or only in the online phase, and on whether they are public or have privacy requirements. The client's online runtime improvement is, for some of our protocols almost 1 order of magnitude, no matter which practical elliptic curve, among recently recommended ones, is used for the pairing realization

A note on group membership tests for \G_1, \G_2 and \G_T on BLS pairing-friendly curves

Here we consider a method for quickly testing for group membership in the groups \G_1, \G_2 and \G_T (all of prime order $r$) as they arise on a type-3 pairing-friendly curve. As is well known endomorphisms exist for each of these groups which allows for faster point multiplication for elements of order $r$. The endomorphism applies if an element is of order $r$. Here we show that, under relatively mild conditions, the endomorphism applies {\bf if and only if} an element is of order $r$. This results in a faster method of confirming group membership. In particular we show that the conditions are met for the popular BLS family of curves

Algorithmes de délégation de calcul de couplage

International audienceWe address the question of how a computationally limited device may outsource pairing computation in cryptography to another, potentially malicious, but much more computationally powerful device. We introduce two new efficient protocols for securely outsourcing pairing computations to an untrusted helper. The first generic scheme is proven computationally secure (and can be proven statistically secure at the expense of worse performance). It allows various communication-efficiency trade-offs. The second specific scheme -- for optimal Ate pairing on a Barreto-Naehrig curve -- is unconditionally secure, and do not rely on any hardness assumptions. Both protocols are more efficient than the actual computation of the pairing by the restricted device and in particular they are more efficient than all previous proposals

Group Signature without Random Oracles from Randomizable Signatures

Group signature is a central tool for privacy-preserving protocols, ensuring authentication, anonymity and accountability. It has been massively used in cryptography, either directly or through variants such as direct anonymous attestations. However, it remains a complex tool, especially if ones wants to avoid proving security in the random oracle model. In this work, we propose a new group signature scheme proven secure without random oracles which significantly decreases the complexity in comparison with the state-of-the-art. More specifically, we halve both the size and the computational cost compared to the most efficient alternative in the same model. Moreover, our construction is also competitive against the most efficient ones in the random oracle model. Our construction is based on a tailored combination of two popular signatures, which avoids the explicit use of encryption schemes or zero-knowledge proofs while signing. It is flexible enough to achieve security in different models and is thus suitable for most contexts

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

Software implementation of an Attribute-Based Encryption scheme

A ciphertext-policy attribute-based encryption protocol uses bilinear pairings to provide control access mechanisms, where the set of user\u27s attributes is specified by means of a linear secret sharing scheme. In this paper we present the design of a software cryptographic library that achieves record timings for the computation of a 126-bit security level attribute-based encryption scheme. We developed all the required auxiliary building blocks and compared the computational weight that each of them adds to the overall performance of this protocol. In particular, our single pairing and multi-pairing implementations achieve state-of-the-art time performance at the 126-bit security level

A Shuffle Argument Secure in the Generic Model

We propose a new random oracle-less NIZK shuffle argument. It has a simple structure, where the first verification equation ascertains that the prover has committed to a permutation matrix, the second verification equation ascertains that the same permutation was used to permute the ciphertexts, and the third verification equation ascertains that input ciphertexts were ``correctly\u27\u27 formed. The new argument has $3.5$ times more efficient verification than the up-to-now most efficient shuffle argument by Fauzi and Lipmaa (CT-RSA 2016). Compared to the Fauzi-Lipmaa shuffle argument, we (i) remove the use of knowledge assumptions and prove our scheme is sound in the generic bilinear group model, and (ii) prove standard soundness, instead of culpable soundness

Prover-Efficient Commit-And-Prove Zero-Knowledge SNARKs

Zk-SNARKs (succinct non-interactive zero-knowledge arguments of knowledge) are needed in many applications. Unfortunately, all previous zk-SNARKs for interesting languages are either inefficient for the prover, or are non-adaptive and based on a commitment scheme that depends both on the prover\u27s input and on the language, i.e., they are not commit-and-prove (CaP) SNARKs. We propose a proof-friendly extractable commitment scheme, and use it to construct prover-efficient adaptive CaP succinct zk-SNARKs for different languages, that can all reuse committed data. In new zk-SNARKs, the prover computation is dominated by a linear number of cryptographic operations. We use batch-verification to decrease the verifier\u27s computation; importantly, batch-verification can be used also in QAP-based zk-SNARKs