International Association
for Cryptologic Research

Non-malleable zero-knowledge (NMZK), originally introduced in the seminal work of Dolev, Dwork, and Naor (STOC 91), is a fundamental concept for modeling the security of proof systems against man-in-the-middle attacks. After 30 years of active research, Kim, Liang, and Pandey (CRYPTO 2022) presented the first efficient constant-round NMZK argument system based solely on symmetric-key cryptography. Their construction relies on a non-black-box use of the involved cryptographic primitives and on multiple executions of Ligero (CCS 2017) that affect both the round complexity and the computational efficiency of their protocol. Their work left open the natural important challenge of achieving NMZK using the underlying primitives only in a black-box fashion (regardless of the number of rounds and actual efficiency). In this paper, we solve the aforementioned open problem by presenting the first NMZK argument system based on the black-box use of cryptographic primitives. Our work is optimal in the use of primitives since we only need one-way functions, and asymptotically optimal in the number of rounds since we only require a constant number of rounds. Our argument system is non-malleable with respect to the strong ``simulation-extractability'' flavor of non-malleability. Furthermore, we also show that our construction can be efficiently instantiated in Minicrypt, significantly improving upon the work of Kim et al., both in terms of round complexity and computational efficiency.

Publicly Verifiable Zero-Knowledge proofs are known to exist only from setup assumptions such as a trusted common reference string or a random oracle. Unfortunately, the former requires a trusted party while the latter does not exist. Blockchains are distributed systems that already exist and provide certain security properties (under some honest majority assumption), hence, a natural recent research direction has been to use a blockchain as an alternative setup assumption. In TCC 2017 Goyal and Goyal proposed a construction of a publicly verifiable zero-knowledge (pvZK) proof system for some proof-of-stake blockchains. The zero-knowledge property of their construction however relies on some additional and not fully specified assumptions about the current and future behavior of honest blockchain players. In this paper, we provide several contributions. First, we show that when using a blockchain to design a provably secure protocol, it is dangerous to rely on demanding additional requirements on behaviors of the blockchain players. We do so by showing an ``attack of the clones'' whereby a malicious verifier can use a smart contract to slyly (not through bribing) clone capabilities of honest stakeholders and use those to invalidate the zero-knowledge property of the proof system by Goyal and Goyal. Second, we propose a new publicly verifiable zero-knowledge proof system that relies on non-interactive commitments and on an assumption on the min-entropy of some blocks appearing on the blockchain. Third, motivated by the fact that blockchains are a recent innovation and their resilience, in the long run, is still controversial, we introduce the concept of collapsing blockchain, and we prove that the zero-knowledge property of our scheme holds even if the blockchain eventually becomes insecure and all blockchain players eventually become dishonest.

For more than 30 years, cryptographers have been looking for public sources of uniform randomness in order to use them as a set-up to run appealing cryptographic protocols without relying on trusted third parties. Unfortunately, nowadays it is fair to assess that assuming the existence of physical phenomena producing public uniform randomness is far from reality.  It is known that uniform randomness cannot be extracted from a single weak source. A well-studied way to overcome this is to consider several independent weak sources. However, this means we must trust the various sampling processes of weak randomness from physical processes. Motivated by the above state of affairs, this work considers a set-up where players can access multiple {\em potential} sources of weak randomness, several of which may be jointly corrupted by a computationally unbounded adversary. We introduce {\em SHELA} (Somewhere Honest Entropic Look Ahead) sources to model this situation. We show that there is no hope of extracting uniform randomness from a {\em SHELA} source. Instead, we focus on the task of {\em Somewhere-Extraction} (i.e., outputting several candidate strings, some of which are uniformly distributed -- yet we do not know which). We give explicit constructions of {\em Somewhere-Extractors} for {\em SHELA} sources with good parameters. Then, we present applications of the above somewhere-extractor where the public uniform randomness can be replaced by the output of such extraction from corruptible sources, greatly outperforming trivial solutions. The output of somewhere-extraction is also useful in other settings, such as a suitable source of random coins for many randomized algorithms. In another front, we comprehensively study the problem of {\em Somewhere-Extraction} from a {\em weak} source, resulting in a series of bounds. Our bounds highlight the fact that, in most regimes of parameters (including those relevant for applications), {\em SHELA} sources significantly outperform {\em weak} sources of comparable parameters both when it comes to the process of {\em Somewhere-Extraction}, or in the task of amplification of success probability in randomized algorithms. Moreover, the low quality of somewhere-extraction from weak sources excludes its use in various efficient applications.

A proof system is publicly verifiable, if anyone, by looking at the transcript of the proof, can be convinced that the corresponding theorem is true. Public verifiability is important in many applications since it allows to compute a proof only once while convincing an unlimited number of verifiers.Popular interactive proof systems (e.g., $$\varSigma $$-protocols) protect the witness through various properties (e.g., witness indistinguishability (WI) and zero knowledge (ZK)) but typically they are not publicly verifiable since such proofs are convincing only for those verifiers who contributed to the transcripts of the proofs. The only known proof systems that are publicly verifiable rely on a non-interactive (NI) prover, through trust assumptions (e.g., NIZK in the CRS model), heuristic assumptions (e.g., NIZK in the random oracle model), specific number-theoretic assumptions on bilinear groups or relying on obfuscation assumptions (obtaining NIWI with no setups).In this work we construct publicly verifiable witness-indistinguishable proof systems from any $$\varSigma $$-protocol, based only on the existence of a very generic blockchain. The novelty of our approach is in enforcing a non-interactive verification (thus guaranteeing public verifiability) while allowing the prover to be interactive and talk to the blockchain (this allows us to circumvent the need of strong assumptions and setups). This opens interesting directions for the design of cryptographic protocols leveraging on blockchain technology.

We introduce the corrupted token model. This model generalizes the tamper-proof token model proposed by Katz (EUROCRYPT ’07) relaxing the trust assumption on the honest behavior of tokens. Our model is motivated by the real-world practice of outsourcing hardware production to possibly corrupted manufacturers. We capture the malicious behavior of token manufacturers by allowing the adversary to corrupt the tokens of honest players at the time of their creation.We show that under minimal complexity assumptions, i.e., the existence of one-way functions, it is possible to UC-securely realize (a variant of) the tamper-proof token functionality of Katz in the corrupted token model with n stateless tokens assuming that the adversary corrupts at most $$n-1$$ of them (for any $$n>0$$). We apply this result to existing multi-party protocols in Katz’s model to achieve UC-secure MPC in the corrupted token model assuming only the existence of one-way functions. Finally, we show how to obtain the above results using tokens of small size that take only short inputs. The technique in this result can also be used to improve the assumption of UC-secure hardware obfuscation recently proposed by Nayak et al. (NDSS ’17). While their construction requires the existence of collision-resistant hash functions, we can obtain the same result from only one-way functions. Moreover using our main result we can improve the trust assumption on the tokens as well.

We revisit the problem of universally composable (UC) secure multiparty computation in the stateless hardware token model. We construct a three round multi-party computation protocol for general functions based on one-way functions where each party sends two tokens to every other party. Relaxing to the two-party case, we also construct a two round protocol based on one-way functions where each party sends a single token to the other party, and at the end of the protocol, both parties learn the output.One of the key components in the above constructions is a new two-round oblivious transfer protocol based on one-way functions using only one token, which can be reused an unbounded polynomial number of times. All prior constructions required either stronger complexity assumptions, or larger number of rounds, or a larger number of tokens.

At ICS 2010, Dziembowski, Pietrzak and Wichs introduced the notion of non-malleable codes, a weaker form of error-correcting codes guaranteeing that the decoding of a tampered codeword either corresponds to the original message or to an unrelated value. The last few years established non-malleable codes as one of the recently invented cryptographic primitives with the highest impact and potential, with very challenging open problems and applications.In this work, we focus on so-called continuously non-malleable codes in the split-state model, as proposed by Faust et al. (TCC 2014), where a codeword is made of two shares and an adaptive adversary makes a polynomial number of attempts in order to tamper the target codeword, where each attempt is allowed to modify the two shares independently (yet arbitrarily). Achieving continuous non-malleability in the split-state model has been so far very hard. Indeed, the only known constructions require strong setup assumptions (i.e., the existence of a common reference string) and strong complexity-theoretic assumptions (i.e., the existence of non-interactive zero-knowledge proofs and collision-resistant hash functions).As our main result, we construct a continuously non-malleable code in the split-state model without setup assumptions, requiring only one-to-one one-way functions (i.e., essentially optimal computational assumptions). Our result introduces several new ideas that make progress towards understanding continuous non-malleability, and shows interesting connections with protocol-design and proof-approach techniques used in other contexts (e.g., look-ahead simulation in zero-knowledge proofs, non-malleable commitments, and leakage resilience).

The notion of non-interactive secure computation (NISC) first introduced in the work of Ishai et al. [EUROCRYPT 2011] studies the following problem: Suppose a receiver R wishes to publish an encryption of her secret input y so that any sender S with input x can then send a message m that reveals f(x, y) to R (for some function f). Here, m can be viewed as an encryption of f(x, y) that can be decrypted by R. NISC requires security against both malicious senders and receivers, and also requires the receiver’s message to be reusable across multiple computations (w.r.t. a fixed input of the receiver).All previous solutions to this problem necessarily rely upon OT (or specific number-theoretic assumptions) even in the common reference string model or the random oracle model or to achieve weaker notions of security such as super-polynomial-time simulation.In this work, we construct a NISC protocol based on the minimal assumption of one way functions, in the stateless hardware token model. Our construction achieves UC security and requires a single token sent by the receiver to the sender.