相关论文: Mapping the Discrete Logarithm
Counting graph homomorphisms and its generalizations such as the Counting Constraint Satisfaction Problem (CSP), its variations, and counting problems in general have been intensively studied since the pioneering work of Valiant. While the…
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
The algebraic structure of the group generated by the encryption functions of a block cipher depends on the key schedule algorithm used for generating the round keys. For such a reason, in general, studying this group does not appear to be…
In this work, we study the applications of differential privacy (DP) in the context of graph-structured data. We discuss the formulations of DP applicable to the publication of graphs and their associated statistics as well as machine…
For a prime number $p>2$, we explain the construction of the difference divisors on the unitary Rapoport-Zink spaces of hyperspecial level and the GSpin Rapoport-Zink spaces of hyperspecial level associated to a minuscule cocharacter $\mu$…
Biggs proposed the sandpile group of certain modified wheel graphs for cryptosystems relying on the difficulty of the discrete logarithm problem. Blackburn and independently Shokrieh showed that the discrete logarithm problem is efficiently…
Recently, Ko\c{c} proposed a neat and efficient algorithm for computing \[ x = a^{-1} \pmod {p^k} \] for a prime $p$ based on the exact solution of linear equations using $p$-adic expansions. The algorithm requires only addition and right…
In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's…
A graph $G$ is called self-ordered (a.k.a asymmetric) if the identity permutation is its only automorphism. Equivalently, there is a unique isomorphism from $G$ to any graph that is isomorphic to $G$. We say that $G=(V,E)$ is robustly…
Differential calculus on discrete spaces is studied in the manner of non-commutative geometry by representing the differential calculus by an operator algebra on a suitable Krein space. The discrete analogue of a (pseudo-)Riemannian metric…
Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…
Monadic stability and the more general monadic dependence (or NIP) are tameness conditions for classes of logical structures, studied in the 80's in Shelah's classification program in model theory. They recently emerged in algorithmic and…
Cross-modal hashing enables efficient retrieval by encoding images and text into compact binary codes. State-of-the-art methods rely on semantic similarity graphs derived from user interactions for supervision, yet these graphs encode…
Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
In this paper we consider the description of homomorphic and fully homomorphic ciphers in the $p$-adic model of encryption. This model describes a wide class of ciphers, but certainly not all. Homomorphic and fully homomorphic ciphers are…