Related papers: Higher Order Differentiation over Finite Fields wi…

We present a new, but simple, randomised order-preserving encryption (OPE) scheme based on the general approximate common divisor problem (GACDP). This appears to be the first OPE scheme to be based on a computational hardness primitive,…

The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…

The emergence of deep learning led to the broad usage of neural networks in the time series domain for various applications, including finance and medicine. While powerful, these models are prone to adversarial attacks: a benign targeted…

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol…

We consider the problem of designing and analyzing differentially private algorithms that can be implemented on {\em discrete} models of computation in {\em strict} polynomial time, motivated by known attacks on floating point…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

Gradient inversion attacks aim to reconstruct local training data from intermediate gradients exposed in the federated learning framework. Despite successful attacks, all previous methods, starting from reconstructing a single data point…

Deep neural networks are known to be vulnerable to adversarial perturbations, which are small and carefully crafted inputs that lead to incorrect predictions. In this paper, we propose DeepDefense, a novel defense framework that applies…

We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…

While deep neural networks have excellent results in many fields, they are susceptible to interference from attacking samples resulting in erroneous judgments. Feature-level attacks are one of the effective attack types, which targets the…

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

The existence of adversarial examples brings huge concern for people to apply Deep Neural Networks (DNNs) in safety-critical tasks. However, how to generate adversarial examples with categorical data is an important problem but lack of…

Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…

As AI-enabled cyber capabilities become more advanced, we propose "differential access" as a strategy to tilt the cybersecurity balance toward defense by shaping access to these capabilities. We introduce three possible approaches that form…

This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or…

Let $\mathbb{K}$ be a number field of degree $n$ over $\mathbb{Q}$. Let $\widehat{\mathbb{A}}$ be the set of integers of $\mathbb{K}$ which are primitive over $\mathbb{Q}$ and $I(\mathbb{K})$ be its index. Gunji and McQuillan defined the…

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We report on a recent implementation of Giesbrecht's algorithm for factoring polynomials in a skew-polynomial ring. We also discuss the equivalence between factoring polynomials in a skew-polynomial ring and decomposing $p^s$-polynomials…

Federated learning (FL) enables learning a global machine learning model from local data distributed among a set of participating workers. This makes it possible i) to train more accurate models due to learning from rich joint training…

Research in adversarial machine learning has shown how the performance of machine learning models can be seriously compromised by injecting even a small fraction of poisoning points into the training data. While the effects on model…