SPHF-Friendly Non-interactive Commitments

Lecture Notes in Computer Science, 2009

We present a new construction of non-committing encryption schemes. Unlike the previous constructions of Canetti et al. (STOC '96) and of Damgård and Nielsen (Crypto '00), our construction achieves all of the following properties:

Lecture Notes in Computer Science, 2009

Designing efficient cryptographic protocols tolerating adaptive adversaries, who are able to corrupt parties on the fly as the computation proceeds, has been an elusive task. Indeed, thus far no efficient protocols achieve adaptive security for general multi-party computation, or even for many specific two-party tasks such as oblivious transfer (OT). In fact, it is difficult and expensive to achieve adaptive security even for the task of secure communication, which is arguably the most basic task in cryptography.

Lecture Notes in Computer Science, 2015

We 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.

Advances in Cryptology – CRYPTO 2013, 2013

Password-authenticated key exchange (PAKE) protocols allow two players to agree on a shared high entropy secret key, that depends on their own passwords only. Following the Gennaro and Lindell's approach, with a new kind of smooth-projective hash functions (SPHFs), Katz and Vaikuntanathan recently came up with the first concrete one-round PAKE protocols, where the two players just have to send simultaneous flows to each other. The first one is secure in the Bellare-Pointcheval-Rogaway (BPR) model and the second one in the Canetti's UC framework, but at the cost of simulation-sound non-interactive zeroknowledge (SS-NIZK) proofs (one for the BPR-secure protocol and two for the UC-secure one), which make the overall constructions not really efficient. This paper follows their path with, first, a new efficient instantiation of SPHF on Cramer-Shoup ciphertexts, which allows to get rid of the SS-NIZK proof and leads to the design of the most efficient one-round PAKE known so far, in the BPR model, and in addition without pairings. In the UC framework, the security proof required the simulator to be able to extract the hashing key of the SPHF, hence the additional SS-NIZK proof. We improve the way the latter extractability is obtained by introducing the notion of trapdoor smooth projective hash functions (TSPHFs). Our concrete instantiation leads to the most efficient oneround PAKE UC-secure against static corruptions to date. We additionally show how these SPHFs and TSPHFs can be used for blind signatures and zero-knowledge proofs with straight-line extractability.

Lecture Notes in Computer Science, 2007

Adaptive security, while more realistic as an adversarial model, is typically much harder to achieve compared to static security in cryptographic protocol design. Universal composition (UC) provides a very attractive framework for the modular design of cryptographic protocols that captures both static and adaptive security formulations. In the UC framework, one can design protocols in hybrid worlds that allow access to idealized functionalities and then apply the universal composition theorem to obtain more concrete protocol instances. The zero-knowledge (ZK) ideal functionality is one of the most useful sub-protocols in modular cryptographic design. Given an adaptively secure protocol in the ideal ZK-hybrid-world do we always need an adaptively secure realization of the ZK functionality in order to preserve adaptive security under composition? In this work, perhaps surprisingly, we find that this is not so and in fact there are useful protocol instances that we can "trade static security for adaptive security." We investigate the above setting, by introducing a weakened ZK ideal functionality, called the ideal leaking-zero-knowledge functionality (LZK) that leaks some information about the witness to the adversary in a certain prescribed way. We show that while LZK is interchangeable to ZK against static adversaries, ZK is more stringent when adaptive adversaries are considered. We then proceed to characterize a class of protocols in the hybrid-ZK-world that can be "transported" to the LZK-hybridworld without forfeiting their security against adaptive adversaries. Our results demonstrate that in such settings a static protocol realization of ZK is sufficient for ensuring adaptive security for the parent hybrid protocol something that enables simplified and substantially more efficient UC realizations of such protocols.

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, 2012

We propose the first black-box construction of non-malleable commitments according to the standard notion of non-malleability with respect to commitment. Our construction additionally only requires a constant number of rounds and is based only on (black-box use of) one-way functions. Prior to our work, no black-box construction of nonmalleable commitments was known (except for relaxed notions of security) in any (polynomial) number of rounds based on any cryptographic assumption. This closes the wide gap existent between black-box and non-black-box constructions for the problem of non-malleable commitments.

2010

Motivated by the question of basing cryptographic protocols on stateless tamper-proof hardware tokens, we revisit the question of unconditional two-prover zero-knowledge proofs for NP. We show that such protocols exist in the interactive PCP model of Kalai and Raz (ICALP ’08), where one of the provers is replaced by a PCP oracle. This strengthens the feasibility result of Ben-Or, Goldwasser, Kilian, and Wigderson (STOC ’88) which requires two stateful provers. In contrast to previous zero-knowledge PCPs of Kilian, Petrank, and Tardos (STOC ’97), in our protocol both the prover and the PCP oracle are efficient given an NP witness. Our main technical tool is a new primitive that we call interactive locking, an efficient realization of an unconditionally secure commitment scheme in the interactive PCP model. We implement interactive locking by adapting previous constructions of interactive hashing protocols to our setting, and also provide a direct construction which uses a minimal amount of interaction and improves over our interactive hashing based constructions. Finally, we apply the above results towards showing the feasibility of basing unconditional cryptography on stateless tamper-proof hardware tokens, and obtain the following results. (1) We show that if tokens can be used to encapsulate other tokens, then there exist unconditional and statistically secure (in fact, UC secure) protocols for general secure computation. (2) Even if token encapsulation is not possible, there are unconditional and statistically secure commitment protocols and zero-knowledge proofs for NP. (3) Finally, if token encapsulation is not possible, then no protocol can realize statistically secure oblivious transfer.

Lecture Notes in Computer Science, 2009

We present a compiler for transforming an oblivious transfer (OT) protocol secure against an adaptive semi-honest adversary into one that is secure against an adaptive malicious adversary. Our compiler achieves security in the universal composability framework, assuming access to an ideal commitment functionality, and improves over previous work achieving the same security guarantee in two ways: it uses black-box access to the underlying protocol and achieves a constant multiplicative overhead in the round complexity. As a corollary, we obtain the first constructions of adaptively secure protocols in the stand-alone model using black-box access to a low-level primitive.

Lecture Notes in Computer Science, 2004

Committed Oblivious Transfer (COT) is a useful cryptographic primitive that combines the functionalities of bit commitment and oblivious transfer. In this paper, we introduce an extended version of COT (ECOT) which additionally allows proofs of relations among committed bits, and we construct an efficient protocol that securely realizes an ECOT functionality in the universalcomposability (UC) framework in the common reference string (CRS) model. Our construction is more efficient than previous (non-UC) constructions of COT, involving only a constant number of exponentiations and communication rounds. Using the ECOT functionality as a building block, we construct efficient UC protocols for general two-party and multi-party functionalities (in the CRS model), each gate requiring a constant number of ECOT's.

Lecture Notes in Computer Science, 2016

Authenticated Key Exchange (AKE) protocols have been widely deployed in many real-world applications for securing communication channels. In this paper, we make the following contributions. First, we revisit the security modelling of leakage-resilient AKE protocols, and show that the existing models either impose some unnatural restrictions or do not sufficiently capture leakage attacks in reality. We then introduce a new strong yet meaningful security model, named challenge-dependent leakage-resilient eCK (CLR-eCK) model, to capture challenge-dependent leakage attacks on both long-term secret key and ephemeral secret key (i.e., randomness). Second, we propose a general framework for constructing one-round CLR-eCK-secure AKE protocols based on smooth projective hash functions (SPHFs). This framework ensures the session key is private and authentic even if the adversary learns a large fraction of both long-term secret key and ephemeral secret key, and hence provides stronger security guarantee than existing AKE protocols which become insecure if the adversary can perform leakage attacks during the execution of a session. Finally, we also present a practical instantiation of the general framework based on the Decisional Diffie-Hellman assumption without random oracle. Our result shows that the instantiation is efficient in terms of the communication and computation overhead and captures more general leakage attacks.