Blockchain-Based Secure Outsourcing of Polynomial Multiplication and Its Application in Fully Homomorphic Encryption

The efficiency of fully homomorphic encryption has always affected its practicality. With the dawn of Internet of things, the demand for computation and encryption on resource-constrained devices is increasing. Complex cryptographic computing is a major burden for those devices, while outsourcing can provide great convenience for them. In this paper, we firstly propose a generic blockchain-based framework for secure computation outsourcing and then propose an algorithm for secure outsourcing of polynomial multiplication into the blockchain. Our algorithm for polynomial multiplication can reduce the local computation cost to O n . Previous work based on Fast Fourier Transform can only achieve O n log n for the local cost. Finally, we integrate the two secure outsourcing schemes for polynomial multiplication and modular exponentiation into the fully homomorphic encryption using hidden ideal lattice and get an outsourcing scheme of fully homomorphic encryption. Through security analysis, our schemes achieve the goals of privacy protection against passive attackers and cheating detection against active attackers. Experiments also demonstrate our schemes are more efficient in comparisons with the corresponding nonoutsourcing schemes.

Wireless Powered Mobile Edge Computing Systems: Simultaneous Time Allocation and Offloading Policies

To improve the computational power and limited battery capacity of mobile devices (MDs), wireless powered mobile edge computing (MEC) systems are gaining much importance. In this paper, we consider a wireless powered MEC system composed of one MD and a hybrid access point (HAP) attached to MEC. Our objective is to achieve a joint time allocation and offloading policy simultaneously. We propose a cost function that considers both the energy consumption and the time delay of an MD. The proposed algorithm, joint time allocation and offload policy (JTAOP), is used to train a neural network for reducing the complexity of our algorithm that depends on the resolution of time and the number of components in a task. The numerical results are compared with three benchmark schemes, namely, total local computation, total offloading and partial offloading. Simulations show that the proposed algorithm performs better in producing the minimum cost and energy consumption as compared to the considered benchmark schemes.

Local Levenberg-Marquardt Algorithm for Learning Feedforwad Neural Networks

This paper presents a local modification of the Levenberg-Marquardt algorithm (LM). First, the mathematical basics of the classic LM method are shown. The classic LM algorithm is very efficient for learning small neural networks. For bigger neural networks, whose computational complexity grows significantly, it makes this method practically inefficient. In order to overcome this limitation, local modification of the LM is introduced in this paper. The main goal of this paper is to develop a more complexity efficient modification of the LM method by using a local computation. The introduced modification has been tested on the following benchmarks: the function approximation and classification problems. The obtained results have been compared to the classic LM method performance. The paper shows that the local modification of the LM method significantly improves the algorithm’s performance for bigger networks. Several possible proposals for future works are suggested.

Developmental Incongruity as a Dynamical Representation of Heterochrony

The theory of heterochrony provides us with a generalized quantitative perspective on the dynamics of developmental trajectories. While useful, these linear developmental trajectories merely characterize changes in the speed and extent of growth in developmental time. One open problem in the literature involves how to characterize developmental trajectories for rare and incongruous modes of development. By combining nonlinear mathematical representations of development with models of gene expression networks (GRNs), the dynamics of growth given the plasticity and complexity of developmental timing are revealed. The approach presented here characterizes heterochrony as a dynamical system, while also proposing a computational motif in GRNs called triangular state machines (TSMs). TSMs enable local computation of phenotypic enhancement by producing nonlinear and potentially unexpected outputs. With a focus on developmental timing and a focus on sequential patterns of growth, formal techniques are developed to characterize delays and bifurcations in the developmental trajectory. More generally, growth is demonstrated using two conceptual models: a Galton board representing axial symmetry and a radial tree depicting differential growth. These techniques take into consideration the existence of multiple developmental genotypes operating in parallel, which ultimately characterize the exquisite phenotypic diversity observed in animal development.