Related papers: Perfect Zero-Knowledge PCPs for #P
Zero-Knowledge Proofs (ZKPs) have emerged as an important cryptographic technique allowing one party (prover) to prove the correctness of a statement to some other party (verifier) and nothing else. ZKPs give rise to user's privacy in many…
Zero-knowledge proofs are an essential building block in many privacy-preserving systems. However, implementing these proofs is tedious and error-prone. In this paper, we present zksk, a well-documented Python library for defining and…
In last years, there has been an increasing effort to leverage Distributed Ledger Technology (DLT), including blockchain. One of the main topics of interest, given its importance, is the research and development of privacy mechanisms, as…
Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an…
Constraint Programming (CP) is a powerful paradigm for solving combinatorial problems, yet translating natural language problem descriptions into executable models remains a significant bottleneck. While Large Language Models (LLMs) show…
In their recent breakthrough result, Slofstra and the second author show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE (STOC'24). We build on their result to show that there exists a succinct two-player…
Zero-knowledge proofs (ZKPs) are an emerging technology that has become the solution to efficiently provide security and privacy along with the transparency requirement of blockchains. ZKPs are usually expressed by means of arithmetic…
Zero-knowledge proofs (zk-Proofs) are communication protocols by which a prover can demonstrate to a verifier that it possesses a solution to a given public problem without revealing the content of the solution. Arbitrary computations can…
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical…
While the amount of data produced and accumulated continues to advance at unprecedented rates, protection and concealment of data increase its prominence as a field of scientific study that requires more action. It is essential to protect…
Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving…
We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment $x \in \{0,1\}^n$ to a CNF formula $\varphi$ is shared between two parties, where Alice knows $x_1, \dots, x_{n/2}$, Bob knows…
A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e.,…
Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box,…
All known proofs of the PCP theorem rely on multiple "composition" steps, where PCPs over large alphabets are turned into PCPs over much smaller alphabets at a (relatively) small price in the soundness error of the PCP. Algebraic proofs,…
We show that every language in NP has a PCP verifier that tosses $O(\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\text{poly}(n)$, while making at most $O(\text{poly}\log\log n)$ queries into a proof…
Ensuring the integrity of business processes without disclosing confidential business information is a major challenge in inter-organizational processes. This paper introduces a zero-knowledge proof (ZKP)-based approach for the verifiable…
We study the role of perfect completeness in probabilistically checkable proof systems (PCPs) and give a new way to transform a PCP with imperfect completeness to a PCP with perfect completeness when the initial gap is a constant. In…
The traditional definition of quantum zero-knowledge stipulates that the knowledge gained by any quantum polynomial-time verifier in an interactive protocol can be simulated by a quantum polynomial-time algorithm. One drawback of this…
This article introduces PnCP, a MATLAB toolbox for constructing positive maps which are not completely positive. We survey optimization and sum of squares relaxation techniques to find the most numerically efficient methods for this…