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

Continuously non-malleable codes with split-state refresh

Non-malleable codes for the split-state model allow to encode a message into two parts, such that arbitrary independent tampering on each part, and subsequent decoding of the corresponding modified codeword, yields either the same as the original message, or a completely unrelated value. Continuously non-malleable codes further allow to tolerate an unbounded (polynomial) number of tampering attempts, until a decoding error happens. The drawback is that, after an error happens, the system must self-destruct and stop working, otherwise generic attacks become possible. In this paper we propose a solution to this limitation, by leveraging a split-state refreshing procedure. Namely, whenever a decoding error happens, the two parts of an encoding can be locally refreshed (i.e., without any interaction), which allows to avoid the self-destruct mechanism. An additional feature of our security model is that it captures directly security against continual leakage attacks. We give an abstract framework for building such codes in the common reference string model, and provide a concrete instantiation based on the external Diffie-Hellman assumption. Finally, we explore applications in which our notion turns out to be essential. The first application is a signature scheme tolerating an arbitrary polynomial number of split-state tampering attempts, without requiring a self-destruct capability, and in a model where refreshing of the memory happens only after an invalid output is produced. This circumvents an impossibility result from a recent work by Fuijisaki and Xagawa (Asiacrypt 2016). The second application is a compiler for tamper-resilient RAM programs. In comparison to other tamper-resilient compilers, ours has several advantages, among which the fact that, for the first time, it does not rely on the self-destruct feature

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

Relations among notions of complete non-malleability: indistinguishability characterisation and efficient construction without random oracles

We study relations among various notions of complete non-malleability, where an adversary can tamper with both ciphertexts and public-keys, and ciphertext indistinguishability. We follow the pattern of relations previously established for standard non-malleability. To this end, we propose a more convenient and conceptually simpler indistinguishability-based security model to analyse completely non-malleable schemes. Our model is based on strong decryption oracles, which provide decryptions under arbitrarily chosen public keys. We give the first precise definition of a strong decryption oracle, pointing out the subtleties in different approaches that can be taken. We construct the first efficient scheme, which is fully secure against strong chosen-ciphertext attacks, and therefore completely non-malleable, without random oracles.The authors were funded in part by eCrypt II (EU FP7 - ICT-2007-216646) and FCT project PTDC/EIA/71362/2006. The second author was also funded by FCT grant BPD-47924-2008

Round-Optimal Secure Two-Party Computation from Trapdoor Permutations

In this work we continue the study on the round complexity of secure two-party computation with black-box simulation. Katz and Ostrovsky in CRYPTO 2004 showed a 5 (optimal) round construction assuming trapdoor permutations for the general case where both players receive the output. They also proved that their result is round optimal. This lower bound has been recently revisited by Garg et al. in Eurocrypt 2016 where a 4 (optimal) round protocol is showed assuming a simultaneous message exchange channel. Unfortunately there is no instantiation of the protocol of Garg et al. under standard polynomial-time hardness assumptions. In this work we close the above gap by showing a 4 (optimal) round construction for secure two-party computation in the simultaneous message channel model with black-box simulation, assuming trapdoor permutations against polynomial-time adversaries. Our construction for secure two-party computation relies on a special 4-round protocol for oblivious transfer that nicely composes with other protocols in parallel. We define and construct such special oblivious transfer protocol from trapdoor permutations. This building block is clearly interesting on its own. Our construction also makes use of a recent advance on non-malleability: a delayed-input 4-round non-malleable zero knowledge argument

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

Improved Black-Box Constructions of Composable Secure Computation

We close the gap between black-box and non-black-box constructions of $\mathit{composable}$ secure multiparty computation in the plain model under the $\mathit{minimal}$ assumption of semi-honest oblivious transfer. The notion of protocol composition we target is $\mathit{angel\text{-}based}$ security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an $\mathit{angel}$ that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone. Angel-based security can be achieved using non-black-box constructions in $\max(R_{\mathsf{OT}},\widetilde{O}(\log n))$ rounds where $R_{\mathsf{OT}}$ is the round-complexity of the semi-honest oblivious transfer. However, currently, the best known $\mathit{black\text{-}box}$ constructions under the same assumption require $\max(R_{\mathsf{OT}},\widetilde{O}(\log^2 n))$ rounds. If $R_{\mathsf{OT}}$ is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor $\log n$. We close this gap by presenting a $\max(R_{\mathsf{OT}},\widetilde{O}(\log n))$-round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions

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

Malleable Proof Systems and Applications

Malleability for cryptography is not necessarily an opportunity for attack, but in many cases a potentially useful feature that can be exploited. In this work, we examine notions of malleability for non-interactive zero-knowledge (NIZK) proofs. We start by defining a malleable proof system, and then consider ways to meaningfully control the malleability of the proof system, as in many settings we would like to guarantee that only certain types of transformations can be performed. We also define notions for the cases in which we do not necessarily want a user to know that a proof has been obtained by applying a particular transformation; these are analogous to function/circuit privacy for encryption. As our motivating application, we consider a shorter proof for verifiable shuffles. Our controlled-malleable proofs allow us for the first time to use one compact proof to prove the correctness of an entire multi-step shuffle. Each authority takes as input a set of encrypted votes and a controlled-malleable NIZK proof that these are a shuffle of the original encrypted votes submitted by the voters; it then permutes and re-randomizes these votes and updates the proof by exploiting its controlled malleability. As another application, we generically use controlled-malleable proofs to realize a strong notion of encryption security. Finally, we examine malleability in existing proof systems and observe that Groth-Sahai proofs are malleable. We then go beyond this observation by characterizing all the ways in which they are malleable, and use them to efficiently instantiate our generic constructions from above; this means we can instantiate our proofs and all their applications using only the Decision Linear (DLIN) assumption. Work done as an intern at Microsoft Research Redmon