Wireless Communications and Mobile Computing

Volume 2018, Article ID 7209475, 9 pages

https://doi.org/10.1155/2018/7209475

## A Fog Computing Security: 2-Adic Complexity of Balanced Sequences

The Information Security Department, The First Research Institute of the Ministry of Public Security of P.R.C., Beijing 100084, China

Correspondence should be addressed to Wang Hui-Juan; moc.361@904jhw

Received 9 January 2018; Accepted 5 March 2018; Published 9 September 2018

Academic Editor: Fuhong Lin

Copyright © 2018 Wang Hui-Juan and Jiang Yong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In the fog computing environment, the periodic sequence can provide sufficient authentication code and also reduce the power consumption in the verification. But the periodic sequence faces a known full-cycle attack threat in fog computing. This paper studies the 2-adic complexity attack ability of the periodic balance sequence in the fog computing environment. It uses the exponential function as a new approach to study the 2-adic properties of periodic balance sequence and presents that the 2-adic complexity of the periodic balanced sequence is not an attacking threat when used in fog computing.

#### 1. Introduction

Fog computing is a decentralized computing architecture compared to cloud computing and is currently used primarily for mobile and portable devices. Due to the current proliferation of IoT devices, the main advantage of fog computing is the ability to quickly provide scalable, decentralized solutions. Between data sources and cloud infrastructure, fog computing mainly processes and stores data. Fog computing can improve computational performance by reducing the amount of processing and storage that extra data consumes. Fog computing has real-time responsiveness and offers a cost-effective, flexible deployment of hardware and software in computing system deployments. Fog platform also faces a lot of network security issues. Such as code injection attacks (such as SQL injection), session and cookie hijacking (posing as legitimate users), illegal direct data access unsafe references, malicious redirect and driver attacks, web attacks, and other cyberattacks. Due to the relatively small computing resources (memory, processing, and storage) of the fog computing system, there is no security protection that can consume a large amount of secure authentication storage as cloud computing does. Fog computing should be defined for a broader range of ubiquitous connected devices, which requires the fog server to generate a large number of security codes at one time and a relatively low computational load during verification. For secure communications and authentication, stream ciphers are recognized as fast certification, which require less computation and storage capacity. AES-based cipher type mentioned in [1] is an encryption algorithm which is suitable for fog platforms. But fog calculation of data encryption security needs to consider stream cipher antiattack performance. In the fog computing environment using stream ciphers, the security verification and data transmission should be considered between the length of the password and the verification algorithm. The safety of some fog calculations strongly depends on the security of the sequence itself by weakening the verification algorithm. In this case, the fog server will distribute a large amount of security codes, and it is easier for an attacker to collect large numbers of plain-texts and cipher-texts so that he may filter out full-period encrypted sequences. Currently, there are many attacks on the known periodic sequences in which a common one is the 2-adic complexity attack.

For cryptographic applications, a good pseudorandom generator must be infeasible to find the corresponding initial state. Hence many modern stream ciphers are designed by combining the output sequences in various nonlinear ways. Goresky and Klapper first introduced feedback with carry shift registers (FCSRs) as shown in Figure 1, which are a class of nonlinear sequence generators by [2], and used the arithmetic in the 2-adic number to analyze this stream generator. For the security of the stream, rational approximation algorithm given in [2] is an important adaptive synthesizing algorithm against FCSRs, as shown in Algorithm 1, by which if a key-stream can be generated by a short FCSR, then this FCSR can be efficiently determined from a small subsequence of the key-stream. Therefore, the rational approximation algorithm sets up a new measure of key-stream security and is referred to as 2-adic complexity. For the properties of FCSRs, it is well known that any strictly periodic sequence can be generated by an FCSR. Then any binary sequence with low 2-adic complexity is insecure for cryptographic applications. Although some properties of 2-adic complexity had been proven, such as the expected value and variance of 2-adic complexities of periodic binary sequences and the 2-adic complexity of -sequence, the 2-adic complexity of binary sequences has not been quite clear. This paper studies one function of periodic balance sequence which can against the 2-adic complexity attack in the fog computing environment.