Related papers: An Improved Physical ZKP for Nonogram and Nonogram…
We study the problem of colouring visibility graphs of polygons. In particular, for visibility graphs of simple polygons, we provide a polynomial algorithm for 4-colouring, and prove that the 5-colourability question is already NP-complete…
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,…
A {\em hole} is a chordless cycle of length at least four. A hole is {\em even} (resp. {\em odd}) if it contains an even (resp. odd) number of vertices. A \emph{cap} is a graph induced by a hole with an additional vertex that is adjacent to…
The Decodoku project seeks to let users get hands-on with cutting-edge quantum research through a set of simple puzzle games. The design of these games is explicitly based on the problem of decoding qudit variants of surface codes. This…
In this study, we introduce a novel zero-knowledge identification scheme based on the hardness of the subgroup distance problem in the Hamming metric. The proposed protocol, named Subgroup Distance Zero Knowledge Proof (SDZKP), employs a…
We present the first constructions of single-prover proof systems that achieve perfect zero knowledge (PZK) for languages beyond NP, under no intractability assumptions: 1. The complexity class #P has PZK proofs in the model of Interactive…
We study a combinatorial coloring game between two players, Spoiler and Algorithm, who alternate turns. First, Spoiler places a new token at a vertex in $G$, and Algorithm responds by assigning a color to the new token. Algorithm must…
Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide…
We consider the following game, played on a $k$-uniform hypergraph $H$. There are $q$ colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to…
In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability…
In the Nikoli pencil-and-paper game Double Choco, a puzzle consists of an m $\times$ n grid of cells of white or gray color, separated by dotted lines where each cell possibly contains an integer. The goal is to partition the grid into…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
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…
For an integer $r$, the graph $P_6+rP_3$ has $r+1$ components, one of which is a path on $6$ vertices, and each of the others is a path on $3$ vertices. In this paper we provide a polynomial-time algorithm to test if a graph with no induced…
In database applications involving sensitive data, the dual imperatives of data confidentiality and provable query processing are important. This paper introduces PoneglyphDB, a database system that leverages non-interactive zero-knowledge…
In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint…
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed…
In this paper we have given a unified graph coloring algorithm for planar graphs. The problems that have been considered in this context respectively, are vertex, edge, total and entire colorings of the planar graphs. The main tool in the…
This paper investigates the feasibility of achieving zero-knowledge verifiability for graph databases, enabling database owners to cryptographically prove the query execution correctness without disclosing the underlying data. Although…
Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the…