Related papers: Post-quantum hash functions using $\mathrm{SL}_n(\…
The long-term security of public blockchains strictly depends on the hardness assumptions of the underlying digital signature schemes. In the current scenario, most deployed cryptocurrencies and blockchain platforms rely on elliptic-curve…
Pebble games were originally formulated to study time-space tradeoffs in computation, modeled by games played on directed acyclic graphs (DAGs). Close connections between pebbling and cryptography have been known for decades. A series of…
Take $S \subset \mathrm{SL}_2(\mathbb{Z}) \times \mathrm{SL}_2(\mathbb{Z})\times \mathrm{SL}_2(\mathbb{Z})$ be finite symmetric and assume $S$ generates a group $G$ which is Zariski-dense in $\mathrm{SL}_2 \times \mathrm{SL}_2\times…
In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes.…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
Image hash codes are produced by binarizing the embeddings of convolutional neural networks (CNN) trained for either classification or retrieval. While proxy embeddings achieve good performance on both tasks, they are non-trivial to…
Collision-resistant cryptographic hash functions (CRHs) are crucial for security, particularly for message authentication in Zero-knowledge Proof (ZKP) applications. However, traditional CRHs like SHA-2 or SHA-3, while optimized for CPUs,…
Security of information transmitted through the Internet is an international concern. This security is guaranteed by tools like hash functions. However, as security flaws have been recently identified in the current standard in this domain,…
Shor's and Grover's algorithms' efficiency and the advancement of quantum computers imply that the cryptography used until now to protect one's privacy is potentially vulnerable to retrospective decryption, also known as \emph{harvest now,…
Starting from the one-way group action framework of Brassard and Yung (Crypto '90), we revisit building cryptography based on group actions. Several previous candidates for one-way group actions no longer stand, due to progress both on…
In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem…
We use Margulis' construction together with lattice counting arguments to build Cayley graphs on $\mathrm{SL}_{2}\left(\mathbb{F}_{p}\right),\;p\to\infty$ which are d-regular graphs with girth…
We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for…
The construction of perfect hash functions is a well-studied topic. In this paper, this concept is generalized with the following definition. We say that a family of functions from $[n]$ to $[k]$ is a $\delta$-balanced $(n,k)$-family of…
Randomized algorithms are often enjoyed for their simplicity, but the hash functions employed to yield the desired probabilistic guarantees are often too complicated to be practical. Here we survey recent results on how simple hashing…
Locality-sensitive hashing (LSH) is an important tool for managing high-dimensional noisy or uncertain data, for example in connection with data cleaning (similarity join) and noise-robust search (similarity search). However, for a number…
We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter,…
Property-preserving hash functions allow for compressing long inputs $x_0$ and $x_1$ into short hashes $h(x_0)$ and $h(x_1)$ in a manner that allows for computing a predicate $P(x_0, x_1)$ given only the two hash values without having…