Related papers: Physical Zero-Knowledge Proof for Numberlink Puzzl…
This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class…
In the thesis we focus on designing an authentication system to authenticate users over a network with a username and a password. The system uses the zero-knowledge proof (ZKP) system as a password verification mechanism. The ZKP protocol…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
We study the Short Path Packing problem which asks, given a graph $G$, integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$ pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The problem has…
We present an agnostic signal reconstruction method for zero-knowledge one-way communication channels in which a receiver aims to interpret a message sent by an unknown source about which no prior knowledge is available and to which no…
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s_0,t_0), ...,(s_k,t_k), whether there are k+1 pairwise disjoint paths P_0, ...,P_k, such that P_i connects s_i to t_i. Robertson and Seymour have proven that…
The syndrome decoding problem is one of the NP-complete problems lying at the foundation of code-based cryptography. The variant thereof where the distance between vectors is measured with respect to the Lee metric, rather than the more…
For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the…
The problem of $A$ privately transmitting information to $B$ by a public announcement overheard by an eavesdropper $C$ is considered. To do so by a deterministic protocol, their inputs must be correlated. Dependent inputs are represented…
In the context of cloud computing, services are held on cloud servers, where the clients send their data to the server and obtain the results returned by server. However, the computation, data and results are prone to tampering due to the…
A deadlock occurs in a network when two or more items prevent each other from moving and are stalled. In a general model, items are stored at vertices and each vertex $v$ has a buffer with $b(v)$ slots. Given a route for each item toward…
A non-interactive ZK (NIZK) proof enables verification of NP statements without revealing secrets about them. However, an adversary that obtains a NIZK proof may be able to clone this proof and distribute arbitrarily many copies of it to…
In this document we define a method of proof that we call proof by dichotomy. Its field of application is any proposition on the set of natural numbers N. It consists in the repetition of a step. A step proves the proposition for half of…
When shuffling a deck of cards, one probably wants to make sure it is thoroughly shuffled. A way to do this is by sifting through the cards to ensure that no adjacent cards are the same number, because surely this is a poorly shuffled deck.…
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrary planar graph to index the decomposition. We prove that…
In a proof of knowledge (PoK), a verifier becomes convinced that a prover possesses privileged information. In combination with zero-knowledge proof systems, PoKs play an important role in security protocols such as in digital signatures…
Zero-Knowledge (ZK) proof systems are cryptographic protocols that can (with overwhelming probability) demonstrate that the pair $(X, W)$ is in a relation $R$ without revealing information about the private input $W$. This membership…
What is the funniest number in cryptography (Episode 2)? 0 [1]. The reason is that $\forall x, x \cdot 0 = 0$, i.e., the equation is satisfied no matter what $x$ is. We'll use zero to attack zero-knowledge proof (ZKP). In particular, we'll…
Many seminal results in Interactive Proofs (IPs) use algebraic techniques based on low-degree polynomials, the study of which is pervasive in theoretical computer science. Unfortunately, known methods for endowing such proofs with zero…