Internet of things (IoT) is a technology that can collect the data sensed by the devices for the further real-time services. Using the technique of cloud computing to assist IoT devices in data storing can eliminate the disadvantage of the constrained local storage and computing capability. However, the complex network environment makes cloud servers vulnerable to attacks, and adversaries pretend to be legal IoT clients trying to access the cloud server. Hence, it is necessary to provide a mechanism of mutual authentication for the cloud system to enhance the storage security. In this paper, a secure mutual authentication is proposed for cloud-assisted IoT. Note that the technique of chameleon hash signature is used to construct the authentication. Moreover, the proposed scheme can provide storage checking with the assist of a fully-trusted entity, which highly improves the checking fairness and efficiency. Security analysis proves that the proposed scheme in this paper is correct. Performance analysis demonstrates that the proposed scheme can be performed with high efficiency.
Citation: Dengzhi Liu, Zhimin Li, Chen Wang, Yongjun Ren. Enabling secure mutual authentication and storage checking in cloud-assisted IoT[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11034-11046. doi: 10.3934/mbe.2022514
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Internet of things (IoT) is a technology that can collect the data sensed by the devices for the further real-time services. Using the technique of cloud computing to assist IoT devices in data storing can eliminate the disadvantage of the constrained local storage and computing capability. However, the complex network environment makes cloud servers vulnerable to attacks, and adversaries pretend to be legal IoT clients trying to access the cloud server. Hence, it is necessary to provide a mechanism of mutual authentication for the cloud system to enhance the storage security. In this paper, a secure mutual authentication is proposed for cloud-assisted IoT. Note that the technique of chameleon hash signature is used to construct the authentication. Moreover, the proposed scheme can provide storage checking with the assist of a fully-trusted entity, which highly improves the checking fairness and efficiency. Security analysis proves that the proposed scheme in this paper is correct. Performance analysis demonstrates that the proposed scheme can be performed with high efficiency.
The definition of impulsive semi-dynamical system and its properties including the limit sets of orbits have been investigated [1,9]. The generalized planar impulsive dynamical semi-dynamical system can be described as follows
{dxdt=P(x,y),dydt=Q(x,y),(x,y)∉M,△x=a(x,y),△y=b(x,y),(x,y)∈M, | (1) |
where
I(z)=z+=(x+,y+)∈R2, x+=x+a(x,y), y+=y+b(x,y) |
and
Let
C+(z)={Π(z,t)|t∈R+} |
is called the positive orbit of
M+(z)=C+(z)∩M−{z}. |
Based on above notations, the definition of impulsive semi-dynamical system is defined as follows [1,9,23].
Definition 1.1. An planar impulsive semi-dynamic system
F(z,(0,ϵz))∩M=∅ and Π(z,(0,ϵz))∩M=∅. |
Definition 1.2. Let
1.
2. for each
It is clear that
Definition 1.3. Let
Denote the points of discontinuity of
Theorem 1.4. Let
In 2004 [2], the author pointed out some errors on Theorem 1.4, that is, it need not be continuous under the assumptions. And the main aspect concerned in the paper [2] is the continuality of
In the following we will provide an example to show this Theorem is not true for some special cases. Considering the following model with state-dependent feedback control
{dx(t)dt=ax(t)[1−x(t)K]−βx(t)y(t)1+ωx(t),dy(t)dt=ηβx(t)y(t)1+ωx(t)−δy(t),}x<ET,x(t+)=(1−θ)x(t),y(t+)=y(t)+τ,}x=ET. | (2) |
where
Define four curves as follows
L0:x=δηβ−δω; L1:y=rβ[1−xK](1+ωx); |
L2:x=ET; and L3:x=(1−θ)ET. |
The intersection points of two lines
yET=rβ[1−ETK](1+ωET), yθET=rβ[1−(1−θ)ETK](1+ω(1−θ)ET). |
Define the open set in
Ω={(x,y)|x>0,y>0,x<ET}⊂R2+={(x,y)|x≥0,y≥0}. | (3) |
In the following we assume that model (2) without impulsive effects exists an unstable focus
E∗=(xe,ye)=(δηβ−δω,rη(Kηβ−Kδω−δ)K(ηβ−δω)2), |
which means that model (2) without impulsive effects has a unique stable limit cycle (denoted by
In the following we show that model (2) defines an impulsive semi-dynamical system. From a biological point of view, we focus on the space
Further, we define the section
y+k+1=P(y+k)+τ=y(t1,t0,(1−θ)ET,y+k)+τ≐PM(y+k), and Φ(y+k)=t1. | (4) |
Now define the impulsive set
M={(x,y)| x=ET,0≤y≤YM}, | (5) |
which is a closed subset of
N=I(M)={(x+,y+)∈Ω| x+=(1−θ)ET,τ≤y+≤P(yθET)+τ}. | (6) |
Therefore,
According to the Definition 1.3 and topological structure of orbits of model (2) without impulsive effects, it is easy to see that
However, this is not true for case (C) shown in Fig. 2(C). In fact, for case (C) there exists a trajectory (denoted by
If we fixed all the parameter values as those shown in Fig. 3, then we can see that the continuities of the Poincaré map and the function
Theorem 2.1. Let
Note that the transversality condition in Theorem 2.1 may exclude the case (B) in Fig. 2(B). In fact, based on our example we can conclude that the function
Recently, impulsive semi-dynamical systems or state dependent feedback control systems arise from many important applications in life sciences including biological resource management programmes and chemostat cultures [5,6,10,12,17,18,19,20,21,22,24], diabetes mellitus and tumor control [8,13], vaccination strategies and epidemiological control [14,15], and neuroscience [3,4,7]. In those fields, the threshold policies such as
The above state-dependent feedback control strategies can be defined in broad terms in real biological problems, which are usually modeled by the impulsive semi-dynamical systems. The continuity of the function
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