Related papers: A Zero-Knowledge PCP Theorem
We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the…
We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool,…
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness…
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…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…
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…
In this paper, we show that the zero-knowledge construction for Hamiltonian cycle remains secure against quantum adversaries in the relativistic setting. Our main technical contribution is a tool for studying the action of consecutive…
In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research…
I present a single algorithm which solves the clique problems, "What is the largest size clique?", "What are all the maximal cliques?" and the decision problem, "Does a clique of size k exist?" for any given graph in polynomial time. The…
Privacy concerns in machine learning systems have grown significantly with the increasing reliance on sensitive user data for training large-scale models. This paper introduces a novel framework combining Probably Approximately Correct…
Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $\gamma>0$ such that any subset of $\mathbb{F}_q$ of size at least $q^{1-\gamma}$ contains a nontrivial…
Continual Learning (CL) is essential for enabling self-evolving large language models (LLMs) to adapt and remain effective amid rapid knowledge growth. Yet, despite its importance, little attention has been given to establishing statistical…
Relativistic cryptography is a proposal for achieving unconditional security that exploits the fact that no information carrier can travel faster than the speed of light. It is based on space-time constraints but doesn't require quantum…
We study Bayesian persuasion under approximate best response, where the receiver may choose any action that is not too much suboptimal given their posterior belief upon receiving the signal. We focus on the computational aspects of the…
An undirected graph $G$ is known to both the prover $P$ and the verifier $V$, but only $P$ knows a subgraph $H$ of $G$. Without revealing any information about $H$, $P$ wants to convince $V$ that $H$ is a connected spanning subgraph of $G$,…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
For a NIP theory $T$, a sufficiently saturated model $\mathfrak{C}$ of $T$, and an invariant (over some small subset of $\mathfrak{C}$) global type $p$, we prove that there exists a finest relatively type-definable over a small set of…