Related papers: Higher Order Differentiation over Finite Fields wi…
Adversarial examples have revealed the vulnerability of deep learning models and raised serious concerns about information security. The transfer-based attack is a hot topic in black-box attacks that are practical to real-world scenarios…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
Machine learning based data-driven technologies have shown impressive performances in a variety of application domains. Most enterprises use data from multiple sources to provide quality applications. The reliability of the external data…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
Deep Neural Networks (DNNs) are well-known to be vulnerable to Adversarial Examples (AEs). A large amount of efforts have been spent to launch and heat the arms race between the attackers and defenders. Recently, advanced gradient-based…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
Although local differential privacy (LDP) protects individual users' data from inference by an untrusted data curator, recent studies show that an attacker can launch a data poisoning attack from the user side to inject carefully-crafted…
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in the ring of differential polynomials over a differential…
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher…
In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful:…
Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to construct…
The notion of Local Differential Privacy (LDP) enables users to answer sensitive questions while preserving their privacy. The basic LDP frequent oracle protocol enables the aggregator to estimate the frequency of any value. But when the…
Federated Learning (FL) has emerged as a promising privacy-preserving collaborative model training paradigm without sharing raw data. However, recent studies have revealed that private information can still be leaked through shared gradient…
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…
The previous study has shown that universal adversarial attacks can fool deep neural networks over a large set of input images with a single human-invisible perturbation. However, current methods for universal adversarial attacks are based…
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of…
In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference…
Graph Neural Networks (GNNs) are vital in data science but are increasingly susceptible to adversarial attacks. To help researchers develop more robust GNN models, it's essential to focus on designing strong attack models as foundational…
In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of…