Non-Malleable Commitments Using Goldreich-Levin List Decoding

We give the first construction of three-round non-malleable commitments from the almost minimal assumption of injective one-way functions. Combined with the lower bound of Pass (TCC 2013), our result is almost the best possible w.r.t. standard polynomial-time hardness assumptions (at least w.r.t. black-box reductions). Our results rely on a novel technique which we call bidirectional Goldreich-Levin extraction. Along the way, we also obtain the first rewind secure delayed-input witness indistinguishable (WI) proofs from only injective one-way functions. We also obtain the first construction of a distributionally extractable commitment scheme from injective one-way functions. We believe both of these to be of independent interest. In particular, as a direct corollary of our rewind secure WI construction, we are able to obtain a construction of 3-round promise zero-knowledge from only injective one-way functions

Reusable Designated-Verifier NIZKs for all NP from CDH

Non-interactive zero-knowledge proofs (NIZKs) are a fundamental cryptographic primitive. Despite a long history of research, we only know how to construct NIZKs under a few select assumptions, such as the hardness of factoring or using bilinear maps. Notably, there are no known constructions based on either the computational or decisional Diffie-Hellman (CDH/DDH) assumption without relying on a bilinear map. In this paper, we study a relaxation of NIZKs in the designated verifier setting (DV-NIZK), in which the public common-reference string is generated together with a secret key that is given to the verifier in order to verify proofs. In this setting, we distinguish between one-time and reusable schemes, depending on whether they can be used to prove only a single statement or arbitrarily many statements. For reusable schemes, the main difficulty is to ensure that soundness continues to hold even when the malicious prover learns whether various proofs are accepted or rejected by the verifier. One-time DV-NIZKs are known to exist for general NP statements assuming only public-key encryption. However, prior to this work, we did not have any construction of reusable DV-NIZKs for general NP statements from any assumption under which we didn\u27t already also have standard NIZKs. In this work, we construct reusable DV-NIZKs for general NP statements under the CDH assumption, without requiring a bilinear map. Our construction is based on the hidden-bits paradigm, which was previously used to construct standard NIZKs. We define a cryptographic primitive called a hidden-bits generator (HBG), along with a designated-verifier variant (DV-HBG), which modularly abstract out how to use this paradigm to get both standard NIZKs and reusable DV-NIZKs. We construct a DV-HBG scheme under the CDH assumption by relying on techniques from the Cramer-Shoup hash-proof system, and this yields our reusable DV-NIZK for general NP statements under CDH. We also consider a strengthening of DV-NIZKs to the malicious designated-verifier setting (MDV-NIZK) where the setup consists of an honestly generated common random string and the verifier then gets to choose his own (potentially malicious) public/secret key pair to generate/verify proofs. We construct MDV-NIZKs under the ``one-more CDH\u27\u27 assumption without relying on bilinear maps

Predictable arguments of knowledge

We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK). Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality. We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography

An efficient quantum parallel repetition theorem and applications

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled to an equivalent $3$-message argument system, mirroring the transformation for quantum proof systems [KW00, KKMV07]. As immediate applications, we show how to derive hardness amplification theorems for quantum bit commitment schemes (answering a question of Yan [Yan22]), EFI pairs (answering a question of Brakerski, Canetti, and Qian [BCQ23]), public-key quantum money schemes (answering a question of Aaronson and Christiano [AC13]), and quantum zero-knowledge argument systems. We also derive an XOR lemma [Yao82] for quantum predicates as a corollary

Cryptography based on the Hardness of Decoding

This thesis provides progress in the fields of for lattice and coding based cryptography. The first contribution consists of constructions of IND-CCA2 secure public key cryptosystems from both the McEliece and the low noise learning parity with noise assumption. The second contribution is a novel instantiation of the lattice-based learning with errors problem which uses uniform errors

Composable Security in the Tamper Proof Hardware Model under Minimal Complexity

We put forth a new formulation of tamper-proof hardware in the Global Universal Composable (GUC) framework introduced by Canetti et al. in TCC 2007. Almost all of the previous works rely on the formulation by Katz in Eurocrypt 2007 and this formulation does not fully capture tokens in a concurrent setting. We address these shortcomings by relying on the GUC framework where we make the following contributions: (1) We construct secure Two-Party Computation (2PC) protocols for general functionalities with optimal round complexity and computational assumptions using stateless tokens. More precisely, we show how to realize arbitrary functionalities with GUC security in two rounds under the minimal assumption of One-Way Functions (OWFs). Moreover, our construction relies on the underlying function in a black-box way. As a corollary, we obtain feasibility of Multi-Party Computation (MPC) with GUC-security under the minimal assumption of OWFs. As an independent contribution, we identify an issue with a claim in a previous work by Goyal, Ishai, Sahai, Venkatesan and Wadia in TCC 2010 regarding the feasibility of UC-secure computation with stateless tokens assuming collision-resistant hash-functions (and the extension based only on one-way functions). (2) We then construct a 3-round MPC protocol to securely realize arbitrary functionalities with GUC-security starting from any semi-honest secure MPC protocol. For this construction, we require the so-called one-many commit-and-prove primitive introduced in the original work of Canetti, Lindell, Ostrovsky and Sahai in STOC 2002 that is round-efficient and black-box in the underlying commitment. Using specially designed ``input-delayed\u27\u27 protocols we realize this primitive (with a 3-round protocol in our framework) using stateless tokens and one-way functions (where the underlying one-way function is used in a black-box way)

A New Approach to Efficient Non-Malleable Zero-Knowledge

Non-malleable zero-knowledge, originally introduced in the context of man-in-the-middle attacks, serves as an important building block to protect against concurrent attacks where different protocols may coexist and interleave. While this primitive admits almost optimal constructions in the plain model, they are several orders of magnitude slower in practice than standalone zero-knowledge. This is in sharp contrast to non-malleable commitments where practical constructions (under the DDH assumption) have been known for a while. We present a new approach for constructing efficient non-malleable zero-knowledge for all languages in NP, based on a new primitive called instance-based non-malleable commitment (IB-NMC). We show how to construct practical IB-NMC by leveraging the fact that simulators of sub-linear zero-knowledge protocols can be much faster than the honest prover algorithm. With an efficient implementation of IB-NMC, our approach yields the first general-purpose non-malleable zero-knowledge protocol that achieves practical efficiency in the plain model. All of our protocols can be instantiated from symmetric primitives such as block-ciphers and hash functions, have reasonable efficiency in practice, and are general-purpose. Our techniques also yield the first efficient non-malleable commitment scheme without public-key assumptions

Non-Malleable Codes Against Bounded Polynomial Time Tampering

We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) model and requires the assumptions that (1) $\mathbf{E}$ is hard for $\mathbf{NP}$ circuits of some exponential $2^{\beta n}$ ($\beta>0$) size (widely used in the derandomization literature), (2) sub-exponential trapdoor permutations exist, and (3) $\mathbf{P}$ certificates with sub-exponential soundness exist. While it is impossible to construct NMC secure against arbitrary polynomial-time tampering (Dziembowski, Pietrzak, Wichs, ICS \u2710), the existence of NMC secure against $O(n^c)$-time tampering functions (for any fixed $c$), was shown (Cheraghchi and Guruswami, ITCS \u2714) via a probabilistic construction. An explicit construction was given (Faust, Mukherjee, Venturi, Wichs, Eurocrypt \u2714) assuming an untamperable CRS with length longer than the runtime of the tampering function. In this work, we show that under computational assumptions, we can bypass these limitations. Specifically, under the assumptions listed above, we obtain non-malleable codes in the plain model against $O(n^c)$-time tampering functions (for any fixed $c$), with codeword length independent of the tampering time bound. Our new construction of NMC draws a connection with non-interactive non-malleable commitments. In fact, we show that in the NMC setting, it suffices to have a much weaker notion called quasi non-malleable commitments---these are non-interactive, non-malleable commitments in the plain model, in which the adversary runs in $O(n^c)$-time, whereas the honest parties may run in longer (polynomial) time. We then construct a 4-tag quasi non-malleable commitment from any sub-exponential OWF and the assumption that $\mathbf{E}$ is hard for some exponential size $\mathbf{NP}$-circuits, and use tag amplification techniques to support an exponential number of tags

On Non-uniform Security for Black-box Non-Interactive CCA Commitments

We obtain a black-box construction of non-interactive CCA commitments against non-uniform adversaries. This makes black-box use of an appropriate base commitment scheme for small tag spaces, variants of sub-exponential hinting PRG (Koppula and Waters, Crypto 2019) and variants of keyless sub-exponentially collision-resistant hash function with security against non-uniform adversaries (Bitansky, Kalai and Paneth, STOC 2018 and Bitansky and Lin, TCC 2018). All prior works on non-interactive non-malleable or CCA commitments without setup first construct a base scheme for a relatively small identity/tag space, and then build a tag amplification compiler to obtain commitments for an exponential-sized space of identities. Prior black-box constructions either add multiple rounds of interaction (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) or only achieve security against uniform adversaries (Garg, Khurana, Lu and Waters, Eurocrypt 2021). Our key technical contribution is a novel tag amplification compiler for CCA commitments that replaces the non-interactive proof of consistency required in prior work. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA2 (chosen commitment attack) security. In addition to only making black-box use of the base scheme, our construction replaces sub-exponential NIWIs with sub-exponential hinting PRGs, which can be obtained based on assumptions such as (sub-exponential) CDH or LWE