Smooth NIZK Arguments with Applications to Asymmetric UC-PAKE and Threshold-IBE

We introduce a novel notion of smooth (-verifier) non-interactive zero-knowledge proofs (NIZK) which parallels the familiar notion of smooth projective hash functions (SPHF). We also show that the recent single group element quasi-adaptive NIZK (QA-NIZK) of Jutla and Roy (CRYPTO 2014) for linear subspaces can be easily extended to be computationally smooth. One important distinction of the new notion from SPHFs is that in a smooth NIZK the public evaluation of the hash on a language member using the projection key does not require the witness of the language member, but instead just requires its NIZK proof. This has the remarkable consequence that in the Gennaro-Lindell paradigm of designing universally-composable password-authenticated key-exchange (UC-PAKE) protocols, if one replaces the traditionally employed SPHFs with the novel smooth QA-NIZK, one gets highly efficient UC-PAKE protocols that are secure even under dynamic corruption. This simpler and modular design methodology allows us to give the first single-round asymmetric UC-PAKE protocol, which is also secure under dynamic corruption in the erasure model. We also define a related concept of smooth signatures, which we show is black-box equivalent to identity-based encryption (IBE). The novel abstraction allows us to give the first threshold (private-key generation) fully-secure IBE in the standard model

Structure-Preserving Smooth Projective Hashing

International audienceSmooth projective hashing has proven to be an extremely useful primitive, in particular when used in conjunction with commitments to provide implicit decommitment. This has lead to applications proven secure in the UC framework, even in presence of an adversary which can do adaptive corruptions, like for example Password Authenticated Key Exchange (PAKE), and 1-out-of-m Oblivious Transfer (OT). However such solutions still lack in efficiency, since they heavily scale on the underlying message length. Structure-preserving cryptography aims at providing elegant and efficient schemes based on classical assumptions and standard group operations on group elements. Recent trend focuses on constructions of structure- preserving signatures, which require message, signature and verification keys to lie in the base group, while the verification equations only consist of pairing-product equations. Classical constructions of Smooth Projective Hash Function suffer from the same limitation as classical signatures: at least one part of the computation (messages for signature, witnesses for SPHF) is a scalar. In this work, we introduce and instantiate the concept of Structure- Preserving Smooth Projective Hash Function, and give as applications more efficient instantiations for one-round PAKE and three-round OT, and information retrieval thanks to Anonymous Credentials, all UC- secure against adaptive adversaries

A new framework for efficient password-based authenticated key exchange

Protocols for password-based authenticated key exchange (PAKE) allow two users who share only a short, low-entropy password to agree on a cryptographically strong session key. The challenge in designing such protocols is that they must be immune to off-line dictionary attacks in which an eavesdropping adversary exhaustively enumerates the dictionary of likely passwords in an attempt to match a password to the set of observed transcripts. To date, few general frameworks for constructing PAKE protocols in the standard model are known. Here, we abstract and generalize a protocol by Jiang and Gong to give a new methodology for realizing PAKE without random oracles, in the common reference string model. In addition to giving a new approach to the problem, the resulting construction offers several advantages over prior work. We also describe an extension of our protocol that is secure within the universal composability (UC) framework and, when instantiated using El Gamal encryption, is more efficient than a previous protocol of Canetti et al.

Generic Construction of UC-Secure Oblivious Transfer

International audienceWe show how to construct a completely generic UC-secure oblivious transfer scheme from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Our work is based on the work of Abdalla et al. at Asiacrypt 2013, where the authors formalize the notion of SPHF-friendly commitments, i.e. accepting an SPHF on the language of valid commitments (to allow implicit decommitment), and show how to construct from them a UC-secure oblivious transfer in a generic way. But Abdalla et al. only gave a DDH-based construction of SPHF-friendly commitment schemes, furthermore highly relying on pairings. In this work, we show how to generically construct an SPHF-friendly commitment scheme from a collision-resistant CH scheme and an SPHF-friendly CCA encryption scheme. This allows us to propose an instanciation of our schemes based on the DDH, as efficient as that of Abdalla et al., but without requiring any pairing. Interestingly, our generic framework also allows us to propose an instantiation based on the learning with errors (LWE) assumption. For the record, we finally propose a last instanciation based on the decisional composite residuosity (DCR) assumption

Distributed Smooth Projective Hashing and its Application to Two-Server PAKE

Smooth projective hash functions have been used as building block for various cryptographic applications, in particular for password-based authentication. In this work we propose the extended concept of distributed smooth projective hash functions where the computation of the hash value is distributed across $n$ parties and show how to instantiate the underlying approach for languages consisting of Cramer-Shoup ciphertexts. As an application of distributed smooth projective hashing we build a new framework for the design of two-server password authenticated key exchange protocols, which we believe can help to explain the design of earlier two-server password authenticated key exchange protocols

One-round strong oblivious signature-based envelope

Oblivious Signature-Based Envelope (OSBE) has been widely employed for anonymity-orient and privacy-preserving applications. The conventional OSBE execution relies on a secure communication channel to protect against eavesdroppers. In TCC 2012, Blazy, Pointcheval and Vergnaud proposed a framework of OSBE (BPV-OSBE) without requiring any secure channel by clarifying and enhancing the OSBE security notions. They showed how to generically build an OSBE scheme satisfying the new strong security in the standard model with a common-reference string. Their framework requires 2-round interactions and relies on the smooth projective hash function (SPHF) over special languages, i.e., languages from encryption of signatures. In this work, we investigate the study on the strong OSBE and make the following contributions. First, we propose a generic construction of one-round yet strong OSBE system. Compared to the 2-round BPV-OSBE, our one-round construction is more appealing, as its noninteractive setting accommodates more application scenarios in the real word. Moreover, our framework relies on the regular (identity-based) SPHF, which can be instantiated from extensive languages and hence is more general. Second, we also present an efficient instantiation, which is secure under the standard model from classical assumptions, DDH and DBDH, to illustrate the feasibility of our one-round framework. We remark that our construction is the first one-round OSBE with strong securit

Adaptive Oblivious Transfer and Generalization

International audienceOblivious Transfer (OT) protocols were introduced in the seminal paper of Rabin, and allow a user to retrieve a given number of lines (usually one) in a database, without revealing which ones to the server. The server is ensured that only this given number of lines can be accessed per interaction, and so the others are protected; while the user is ensured that the server does not learn the numbers of the lines required. This primitive has a huge interest in practice, for example in secure multi-party computation, and directly echoes to Symmetrically Private Information Retrieval (SPIR). Recent Oblivious Transfer instantiations secure in the UC framework suf- fer from a drastic fallback. After the first query, there is no improvement on the global scheme complexity and so subsequent queries each have a global complexity of O(|DB|) meaning that there is no gain compared to running completely independent queries. In this paper, we propose a new protocol solving this issue, and allowing to have subsequent queries with a complexity of O(log(|DB|)), and prove the protocol security in the UC framework with adaptive corruptions and reliable erasures. As a second contribution, we show that the techniques we use for Obliv- ious Transfer can be generalized to a new framework we call Oblivi- ous Language-Based Envelope (OLBE). It is of practical interest since it seems more and more unrealistic to consider a database with uncontrolled access in access control scenarii. Our approach generalizes Oblivious Signature-Based Envelope, to handle more expressive credentials and requests from the user. Naturally, OLBE encompasses both OT and OSBE, but it also allows to achieve Oblivious Transfer with fine grain access over each line. For example, a user can access a line if and only if he possesses a certificate granting him access to such line. We show how to generically and efficiently instantiate such primitive, and prove them secure in the Universal Composability framework, with adaptive corruptions assuming reliable erasures. We provide the new UC ideal functionalities when needed, or we show that the existing ones fit in our new framework. The security of such designs allows to preserve both the secrecy of the database values and the user credentials. This symmetry allows to view our new approach as a generalization of the notion of Symmetrically PIR