Related papers: Duffing oscillator and elliptic curve cryptography
Quantum cryptography is reviewed, first using entanglement both for the intuition and for the experimental realizations. Next, the implementation is simplified in several steps until it becomes practical. At this point entanglement has…
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
In cryptography, encryption is the process of obscuring information to make it unreadable without special knowledge. This is usually done for secrecy, and typically for confidential communications. Encryption can also be used for…
Local differential privacy is a widely studied restriction on distributed algorithms that collect aggregates about sensitive user data, and is now deployed in several large systems. We initiate a systematic study of a fundamental limitation…
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…
Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena.…
Existing large-scale optimization schemes are challenged by both scalability and cyber-security. With the favorable scalability, adaptability, and flexibility, decentralized and distributed optimization paradigms are widely adopted in…
We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that…
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several…
Like all of quantum information theory, quantum cryptography is traditionally based on two level quantum systems. In this letter, a new protocol for quantum key distribution based on higher dimensional systems is presented. An experimental…
One-way functions are widely used for encrypting the secret in public key cryptography, although they are regarded as plausibly one-way but have not been proven so. Here we discuss the public key cryptosystem based on the system of higher…
Assume $X$ is a variety for which the elliptic stable envelope exists. In this note we construct natural $q$-difference equations from the elliptic stable envelope of $X$. In examples, these equations coincide with the quantum difference…
In 2004, Muzereau et al. showed how to use a reduction algorithm of the discrete logarithm problem to Diffie-Hellman problem in order to estimate lower bound on Diffie-Hellman problem on elliptic curves. They presented their estimates for…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a…
We consider the problem of learned transform compression where we learn both, the transform as well as the probability distribution over the discrete codes. We utilize a soft relaxation of the quantization operation to allow for…
The recently introduced approach for Encrypted Image Folding is generalized to make it Self Contained. The goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery. The need for…
Encrypted computation opens up promising avenues across a plethora of application domains, including machine learning, health-care, finance, and control. Arithmetic homomorphic encryption, in particular, is a natural fit for cloud-based…