Round Optimal Black-Box “Commit-and-Prove”

We construct the first four-round non-malleable commitment scheme based solely on the black-box use of one-to-one one-way functions. Prior to our work, all non-malleable commitment schemes based on black-box use of polynomial-time cryptographic primitives require more than 16 rounds of interaction.A key tool for our construction is a proof system that satisfies a new definition of security that we call non-malleable zero-knowledge with respect to commitments. In a nutshell, such a proof system can be safely run in parallel with a (potentially interactive) commitment scheme. We provide an instantiation of this tool using the MPC-in-the-Head approach in combination with BMR.

Section: σ-Commitmentmentioning

confidence: 98%

Section: σ-Commitmentmentioning

confidence: 99%

Four-Round Black-Box Non-malleable Schemes from One-Way Permutations

Ciampi

Orsini

Siniscalchi

2022

“…, x ℓ as the output of a PRG, and remove complexity leveraging in the approach outlined above. It also may be possible to rely on black-box commit-and-prove sigma protocols (e.g., variants of the protocol in [KOS18]) to prove that commitments to pairs of strings share a common offset, thereby making our protocol blackbox and unconditionally secure in the QROM. We leave a formalization and detailed analysis of this approach, and more generally an exploration of one-message protocols in the QROM, to future work.…”

Section: Sender's Messagementioning

confidence: 99%

On the Round Complexity of Secure Quantum Computation

Bartusek

Coladangelo

Khurana³

et al. 2021

Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource.• First, we construct a one-shot (i.e., single message) string oblivious transfer (OT) protocol with random receiver bit in the shared EPR pairs model, assuming the (sub-exponential) hardness of LWE.Building on this, we show that secure teleportation through quantum channels is possible. Specifically, given the description of any quantum operation Q, a sender with (quantum) input ρ can send a single classical message that securely transmits Q(ρ) to a receiver. That is, we realize an ideal quantum channel that takes input ρ from the sender and provably delivers Q(ρ) to the receiver without revealing any other information. This immediately gives a number of applications in the shared EPR pairs model: (1) noninteractive secure computation of unidirectional classical randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a noninteractive zero-knowledge state synthesis protocol.

“…We implicitly use the CH-compiler but in a way, different from [CH20]. We focus on the important set-ting of commit-and-prove NIZK argument systems [Lip16,KOS18,Kiy20], i.e. languages of the form {Com(x 1 ), .…”

Section: Our Contributionmentioning

confidence: 99%

Efficient NIZKs for Algebraic Sets

Couteau¹,

Lipmaa²,

Parisella³

et al. 2021

Significantly extending the framework of (Couteau and Hartmann, Crypto 2020), we propose a general methodology to construct NIZKs for showing that an encrypted vector χ belongs to an algebraic set, i.e., is in the zero locus of an ideal I of a polynomial ring. In the case where I is principal, i.e., generated by a single polynomial F , we first construct a matrix that is a "quasideterminantal representation" of F and then a NIZK argument to show that F (χ) = 0. This leads to compact NIZKs for general computational structures, such as polynomial-size algebraic branching programs. We extend the framework to the case where I is non-principal, obtaining efficient NIZKs for R1CS, arithmetic constraint satisfaction systems, and thus for NP. As an independent result, we explicitly describe the corresponding language of ciphertexts as an algebraic language, with smaller parameters than in previous constructions that were based on the disjunction of algebraic languages. This results in an efficient GL-SPHF for algebraic branching programs.