We introduce the definition ofm-to-1 mappings between two finite sets, which unifies and generalizes the definitions of 2-to-1 andn-to-1 mappings in recent literature. We also characterize thesem-to-1 mappings in terms of the generalized local criterion and thus provide three generic constructions ofm-to-1 mappings, which unify and generalize the previous known constructions. Using these constructions, the problem whetherxrh(xs) ism-to-1 on the multiplicative groupF∗qis converted into that whether an associated polynomialxr1h(x)s1ism2-to-1 on the order ℓ subgroupUℓ ofF∗q, wherem2=m/(r,s) and ℓ = (q− 1)/s. Furthermore, them2-to-1 property ofxr1h(x)s1onUℓ is studied in detail in five different cases. In addition, a recursive construction ofm-to-1 mappings fromm-to-1 mappings is proposed.

With continuous development of the Internet of Vehicles (IoV), intelligence is gradually becoming the mainstream trend of future transportation. However, the increasing number of vehicles and their high mobility also bring greater challenges to privacy and security. Most of the current authentication schemes in IoV focus on a single domain, ignoring the cross-domain requirements brought by high mobility. To address these issues better, we propose an efficient anonymous cross-domain authentication scheme EACAS based on elliptic curve cryptography within the certificate-less cryptography. We incorporate the secret sharing with digital signature to provide the trustworthy authentication for cross-domain vehicles, and the batch verification improves the efficiency of authentication. Besides, we also propose a hierarchical pseudonym method for multidomain scenarios, allowing vehicles to update pseudonyms at arbitrary locations and can be revealed. The formal security proof and analysis demonstrate the security characteristics, and the comprehensive performance evaluation shows the efficiency.

We consider the problem of intelligent and efficient task allocation mechanism in large-scale mobile edge computing (MEC), which can reduce delay and energy consumption in a parallel and distributed optimization. In this paper, we study the joint optimization model to consider cooperative task management mechanism among mobile terminals (MT), macro cell base station (MBS), and multiple small cell base station (SBS) for large-scale MEC applications. We propose a parallel multi-block Alternating Direction Method of Multipliers (ADMM) based method to model both requirements of low delay and low energy consumption in the MEC system which formulates the task allocation under those requirements as a nonlinear 0-1 integer programming problem. To solve the optimization problem, we develop an efficient combination of conjugate gradient, Newton and linear search techniques based algorithm with Logarithmic Smoothing (for global variables updating) and the Cyclic Block coordinate Gradient Projection (CBGP, for local variables updating) methods, which can guarantee convergence and reduce computational complexity with a good scalability. Numerical results demonstrate the effectiveness of the proposed mechanism and it can effectively reduce delay and energy consumption for a large-scale MEC system.

Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all PPs of degree ≤ 6 over finite fields Fq for all q and the inverses of all PPs of degree 7 over F2(n). The explicit inverse of a class of fifth degree PPs is the main result, which is obtained by using Lucas' theorem, some congruences of binomial coefficients, and a known formula for the inverses of PPs of finite fields.

Recently, the increase of different services makes the design of routing protocols more difficult in mobile ad hoc networks (MANETs), e.g., how to guarantee the QoS of different types of traffics flows in MANETs with resource constrained and malicious nodes. opportunistic routing (OR) can make full use of the broadcast characteristics of wireless channels to improve the performance of MANETs. In this paper, we propose a traffic-differentiated secure opportunistic routing from a game theoretic perspective, DSOR. In the proposed scheme, we use a novel method to calculate trust value, considering node's forwarding capability and the status of different types of flows. According to the resource status of the network, we propose a service price and resource price for the auction model, which is used to select optimal candidate forwarding sets. At the same time, the optimal bid price has been proved and a novel flow priority decision for transmission is presented, which is based on waiting time and requested time. The simulation results show that the network lifetime, packet delivery rate and delay of the DSOR are better than existing works.