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

Four-Round Concurrent Non-Malleable Commitments from One-Way Functions

How many rounds and which assumptions are required for concurrent non-malleable commitments? The above question has puzzled researchers for several years. Pass in [TCC 2013] showed a lower bound of 3 rounds for the case of black-box reductions to falsifiable hardness assumptions with respect to polynomial-time adversaries. On the other side, Goyal [STOC 2011], Lin and Pass [STOC 2011] and Goyal et al. [FOCS 2012] showed that one-way functions (OWFs) are sufficient with a constant number of rounds. More recently Ciampi et al. [CRYPTO 2016] showed a 3-round construction based on subexponentially strong one-way permutations. In this work we show as main result the first 4-round concurrent non-malleable commitment scheme assuming the existence of any one-way function. Our approach builds on a new security notion for argument systems against man-in-the-middle attacks: Simulation-Witness-Independence. We show how to construct a 4-round one-many simulation-witnesses-independent argument system from one-way functions. We then combine this new tool in parallel with a weak form of non-malleable commitments constructed by Goyal et al. in [FOCS 2014] obtaining the main result of our work

Constant-Round Concurrent Non-Malleable Zero Knowledge in the Bare Public-Key Model

One of the central questions in Cryptography is the design of round-efficient protocols that are secure under concurrent man-in-the- middle attacks. In this paper we present the first constant-round concurrent non-malleable zero-knowledge argument system for NP in the Bare Public-Key model [Canetti et al., STOC 2000], resolving one of the major open problems in this area. To achieve our result, we introduce and study the notion of non-malleable witness indistinguishability, which is of independent interest. Previous results either achieved relaxed forms of concurrency/security or needed stronger setup assumptions or required a non-constant round complexity

Another Step Towards Realizing Random Oracles: Non-Malleable Point Obfuscation

The random oracle paradigm allows us to analyze the security of protocols and constructions in an idealized model, where all parties have access to a truly random function. This is one of the most popular and well-studied models in cryptography. However, being such a strong idealized model, it is known to be susceptible to various weaknesses when implemented naively in ``real-life\u27\u27, as shown by Canetti, Goldreich and Halevi (J. ACM 2004). As a counter-measure, one could try to identify and implement only one or few of the properties a random oracle possesses that are needed for a specific setting. Such a systematic study was initiated by Canetti (CRYPTO 1997), who showed how to implement the property that the output of the function does not reveal anything regarding the input by constructing a point function obfucator. This property turned out to suffice in many follow-up works and applications. In this work, we tackle another natural property of random oracles and implement it in the standard model. The property we focus on is non-malleability, where it is required that the output on an input cannot be used to generate an output on any related point. We construct a point obfuscator that is both hiding (a la Canetti) and is non-malleable for a non-trivial class of mauling functions. Our construction does not use heavy cryptographic machinery (such as zero-knowledge proofs) and is comparable to that of Canetti in terms of time complexity and obfuscation size. The security of our construction relies on variants of the DDH and power-DDH assumptions. On the technical side, we introduce a new technique for proving security of a construction based on a DDH-like assumption. We call this technique ``double-exponentiation\u27\u27 and believe it will be useful in the future

Composability in quantum cryptography

In this article, we review several aspects of composability in the context of quantum cryptography. The first part is devoted to key distribution. We discuss the security criteria that a quantum key distribution protocol must fulfill to allow its safe use within a larger security application (e.g., for secure message transmission). To illustrate the practical use of composability, we show how to generate a continuous key stream by sequentially composing rounds of a quantum key distribution protocol. In a second part, we take a more general point of view, which is necessary for the study of cryptographic situations involving, for example, mutually distrustful parties. We explain the universal composability framework and state the composition theorem which guarantees that secure protocols can securely be composed to larger applicationsComment: 18 pages, 2 figure

Concurrent Secure Computation with Optimal Query Complexity

The multiple ideal query (MIQ) model [Goyal, Jain, and Ostrovsky, Crypto\u2710] offers a relaxed notion of security for concurrent secure computation, where the simulator is allowed to query the ideal functionality multiple times per session (as opposed to just once in the standard definition). The model provides a quantitative measure for the degradation in security under concurrent self-composition, where the degradation is measured by the number of ideal queries. However, to date, all known MIQ-secure protocols guarantee only an overall average bound on the number of queries per session throughout the execution, thus allowing the adversary to potentially fully compromise some sessions of its choice. Furthermore, [Goyal and Jain, Eurocrypt\u2713] rule out protocols where the simulator makes only an adversary-independent constant number of ideal queries per session. We show the first MIQ-secure protocol with worst-case per-session guarantee. Specifically, we show a protocol for any functionality that matches the [GJ13] bound: The simulator makes only a constant number of ideal queries in every session. The constant depends on the adversary but is independent of the security parameter. As an immediate corollary of our main result, we obtain the first password authenticated key exchange (PAKE) protocol for the fully concurrent, multiple password setting in the standard model with no set-up assumptions

4-Round Concurrent Non-Malleable Commitments from One-Way Functions

How many rounds and which computational assumptions are needed for concurrent non-malleable commitments? The above question has puzzled researchers for several years. Recently, Pass in [TCC 2013] proved a lower bound of 3 rounds when security is proven through black-box reductions to falsifiable assumptions. On the other side, positive results of Goyal [STOC 2011], Lin and Pass [STOC 2011] and Goyal et al. [FOCS 2012] showed that one-way functions are sufficient with a constant (at least 6) number of rounds. More recently Ciampi et al. [CRYPTO 2016] showed that subexponentially strong one-way permutations are sufficient with just 3 rounds. In this work we almost close the above open question by showing a 4-round concurrent non-malleable commitment scheme that only needs one-way functions. Our main technique consists in showing how to upgrade basic forms of non-malleability (i.e., non-malleability w.r.t. non-aborting adversaries) to full-fledged non-malleability without penalizing the round complexity

New-Age Cryptography

We introduce new and general complexity theoretic hardness assumptions. These assumptions abstract out concrete properties of a random oracle and are significantly stronger than traditional cryptographic hardness assumptions; however, assuming their validity we can resolve a number of longstandingopen problems in cryptography