# Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis

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## Abstract

**:**

## 1. Introduction

- Secure certificateless authentication scheme: According to our design, a certificateless cryptography mechanism is applied so as to provide improved security assurance. BS and UE itself generate the partial private key respectively so as to prevent the key escrow problem of identity-based encryption. Moreover, conditional privacy-preserving authentication (CPPA) is deployed. That is, the user anonymity is provided through the entire authentication session, preventing illegal tracing towards particular UEs, while the valid identity-related information is recorded in BS side in the preliminary registration phase. Hence the tracking and revocation towards malicious UEs can be conducted by trustworthy authority. Additionally, bilinear pairing is adopted in order for advanced security properties.
- Efficient Group key distribution with updating mechanism: During the authentication process, the allocated group key computed by BS will be delivered to all legitimate UEs through one broadcasting operation, which drastically alleviates the communication cost compared with conventional one-to-one key distribution. Note that only the authentic UEs have the capability of deriving the valid group key. Therefore, the designed key updating mechanism only require small modification in the BS side, while the decrypting information in the UEs side remains constant as soon as the UEs are validated. Similarly, fast UE revocation process can be operated by BS without extensive computation.
- Continuous authentication strategy adopting smartphone sensor behavior analysis: The unique user behavioral data acquired by accelerometer and gyroscope sensors in smart phone (UE) is processed and characterized by time and frequency domain features. Subsequently, appropriate activity recognition implementation is conducted, where the individual behavior profile is evaluated with the pre-defined biometric parameter to reveal the real-time personal activity level. In this case, continuous authentication is performed with the adopted biometric parameter periodically. Security analysis demonstrates that the proposed scheme is able to provide adequate security assurance. Moreover, performance analysis proves that the proposed design is efficient compared with the state-of-the-art authentication schemes. To the best of our knowledge, we are the first to design the D2D authenticating and key distributing method with biometric continuous authentication. Potential scenarios include disaster rescue and medical aid in harsh environment.

## 2. Related Works

## 3. Preliminaries and Model Definitions

#### 3.1. Bilinear Pairing

- Bilinearity: $\forall {g}_{1}\in {\mathbb{G}}_{1}$, $\forall {g}_{2}\in {\mathbb{G}}_{2}$, $\forall a,b\in \mathbb{Z}$, there is $\widehat{e}({{g}_{1}}^{a},{{g}_{2}}^{b})=\widehat{e}{({g}_{1},{g}_{2})}^{ab}$.
- Non-degeneracy: $\exists {g}_{1}\in {\mathbb{G}}_{1}$, $\exists {g}_{2}\in {\mathbb{G}}_{2}$, there is $\widehat{e}({g}_{1},{g}_{2})\ne 1$.
- Computability: $\forall {g}_{1}\in {\mathbb{G}}_{1}$, $\forall {g}_{2}\in {\mathbb{G}}_{2}$, there exists an efficient algorithm so that $\widehat{e}({g}_{1},{g}_{2})$ can be calculated.

**Definition 1**(Decisional Bilinear Diffie-Hellman (DBDH) Problem)

**.**

#### 3.2. Hash Function

- Given a input message x of arbitrary length, the message digest of a fixed length output $h\left(x\right)$ can be calculated accordingly.
- Given y, it is difficult to calculate the value of $x={h}^{-1}\left(y\right)$.
- Given x, it is computationally infeasible to find ${x}^{\prime}\ne x$ such that $h\left({x}^{\prime}\right)=h\left(x\right)$.

#### 3.3. Notations

#### 3.4. System Model

#### 3.5. Network Assumptions

## 4. Proposed Secure Certificateless Group Authentication Scheme for D2D Communication

#### 4.1. Offline Registration Phase

#### 4.2. Authentication Phase

#### 4.3. Group Key Distribution Phase

#### 4.4. Group Key Updating Strategy

## 5. Proposed Continuous Authentication Method

#### 5.1. Sensor Data Preprocessing

#### 5.2. Feature Extraction

- $Max\left(x\right)$ and $Min\left(x\right)$: The maximum and minimum value of input x.
- $\mu \left(x\right)$: The mean value defined as:$$\mu \left(x\right)=\frac{1}{n}\sum _{i=1}^{n}{x}_{i}$$
- $\sigma \left(x\right)$: The overall standard deviation defined as:$$\sigma \left(x\right)=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{({x}_{i}-\mu )}^{2}}$$
- $\gamma \left(x\right)$: The skewness of x defined as:$$\gamma \left(x\right)=\frac{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}}{({x}_{i}-\mu )}^{3}}{{\left(\frac{1}{n}{\displaystyle \sum _{i=1}^{n}}{({x}_{i}-\mu )}^{2}\right)}^{\frac{3}{2}}}$$
- $\kappa \left(x\right)$: The kurtosis of x defined as:$$\kappa \left(x\right)=\frac{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}}{({x}_{i}-\mu )}^{4}}{{\left(\frac{1}{n}{\displaystyle \sum _{i=1}^{n}}{({x}_{i}-\mu )}^{2}\right)}^{2}}$$
- ${\rho}_{X,Y}$: The correlation between each pair of axes of the sensor data:$$\left\{\begin{array}{c}{\rho}_{X,Y}=\frac{\mathrm{cov}(X,Y)}{{\sigma}_{X}{\sigma}_{Y}}\hfill \\ \mathrm{cov}(X,Y)=\frac{1}{n}\sum _{i=1}^{n}({x}_{i}-{\mu}_{X})({y}_{i}-{\mu}_{Y})\hfill \end{array}\right.$$
- $IQR\left(x\right)$: Interquartile range of input x.
- $FFT\left(x\right)$: Frequency domain feature of input x.

#### 5.3. Classification and Authentication Design

## 6. Security Analysis

#### 6.1. Resistance to Forgery Against Adaptive Chosen Message Attack

**Definition**

**2**

**.**Let $\mathcal{A}$ be a probabilistic polynomial time Turing machine, given only the public data as an input. Within a certain time bound $\mathcal{T}$, if $\mathcal{A}$ can produce, with non-negligible probability, a valid signature $(m,{\sigma}_{1},h,{\sigma}_{2})$, where the tuple $({\sigma}_{1},h,{\sigma}_{2})$ can be simulated without knowing the secret key. In this case, with an indistinguishable distribution probability, there is another machine which has control over the machine obtained from $\mathcal{A}$ replacing interaction with the signer by simulation and produces two valid signatures $(m,{\sigma}_{1},h,{\sigma}_{2})$ and $(m,{\sigma}_{1},{h}^{\prime},{\sigma}_{2}^{\prime})$ such that $h\ne {h}^{\prime}$.

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Setup Phase.**${\mathcal{B}}_{1}$ chooses the bilinear group $(\mathcal{P},\mathbb{G},{\mathbb{G}}_{\mathcal{S}},\widehat{e})$ of prime order $\mathcal{P}$, as well as the generator $g,w\in \mathbb{G}$. Thereafter, ${\mathcal{B}}_{1}$ randomly chooses the system master key $mk\in {\mathbb{Z}}_{\mathcal{P}}$ and computes $PK={g}^{mk}$ accordingly. The public parameters $(\mathcal{P},\mathbb{G},{\mathbb{G}}_{\mathcal{S}},\widehat{e},g,w,PK,{H}_{1},{H}_{2},{H}_{3},{H}_{4})$ are delivered to ${\mathcal{A}}_{1}$, where ${H}_{1}$, ${H}_{2}$, and ${H}_{3}$ are defined as random oracles controlled by ${\mathcal{B}}_{1}$. Similarly, ${H}_{4}$ is defined as the anti-collision hash function. Note that the system master key $mk$ is kept secret from the adversary ${\mathcal{A}}_{1}$.**Query Phase.**${\mathcal{A}}_{1}$ adaptively issues the following queries:- -
- ${H}_{1}$ hash Query: Assume that ${\mathcal{A}}_{1}$ does not has the ability to calculate the hash function ${H}_{1}(.)$. The response to ${H}_{1}$ hash Query can be simulated by maintaining a list $Lis{t}_{{H}_{1}}$ initialized to be empty. When the adversary ${\mathcal{A}}_{1}$ invokes the ${H}_{1}$ hash Query with input values $ID$, ${\mathcal{B}}_{1}$ will then check whether the parameter $ID$ exists in the hash list $Lis{t}_{{H}_{1}}$. If the tuple $(ID,\zeta )$ has already been stored in $Lis{t}_{{H}_{1}}$, ${\mathcal{B}}_{1}$ outputs $\zeta ={H}_{1}\left(ID\right)$ to ${\mathcal{A}}_{1}$. Otherwise, ${\mathcal{B}}_{1}$ chooses random $\zeta \in {\mathbb{Z}}_{\mathcal{P}}$ and forwards it to ${\mathcal{A}}_{1}$. The new tuple $(I{D}_{i},\zeta )$ will be subsequently added to $Lis{t}_{{H}_{1}}$.
- -
- ${H}_{2}$ hash Query: Assume that ${\mathcal{A}}_{1}$ does not has the ability to calculate the hash function ${H}_{2}(.)$. The response to ${H}_{2}$ hash Query can be simulated by maintaining a list $Lis{t}_{{H}_{2}}$ initialized to be empty. When the adversary ${\mathcal{A}}_{1}$ invokes the ${H}_{2}$ hash Query with input values $(Tid,\mathcal{T},\eta )$, ${\mathcal{B}}_{1}$ will then check whether the record $(Tid,\mathcal{T},\eta )$ exists in the hash list $Lis{t}_{{H}_{2}}$. If the tuple $(Auth,Tid,\mathcal{T},\eta )$ has already been stored in $Lis{t}_{{H}_{2}}$, ${\mathcal{B}}_{1}$ outputs $Auth={H}_{2}(Tid,\mathcal{T},\eta )$ to ${\mathcal{A}}_{1}$. Otherwise, ${\mathcal{B}}_{1}$ chooses random $Auth\in {\mathbb{Z}}_{\mathcal{P}}$ and forwards it to ${\mathcal{A}}_{1}$. The new tuple $(Auth,Tid,\mathcal{T},\eta )$ will be subsequently added to $Lis{t}_{{H}_{2}}$.
- -
- ${H}_{3}$ hash Query: Assume that ${\mathcal{A}}_{1}$ does not has the ability to calculate the hash function ${H}_{3}(.)$. The response to ${H}_{3}$ hash Query can be simulated by maintaining a list $Lis{t}_{{H}_{3}}$ initialized to be empty. When the adversary ${\mathcal{A}}_{1}$ invokes the ${H}_{3}$ hash Query with input values $(\rho ,\eta )$, ${\mathcal{B}}_{1}$ will then check whether the record $(\phi ,\rho ,\eta )$ exists in the hash list $Lis{t}_{{H}_{3}}$. If the tuple $(\phi ,\rho ,\eta )$ has already been stored in $Lis{t}_{{H}_{3}}$, ${\mathcal{B}}_{1}$ outputs $\phi ={H}_{3}(\rho ,\eta )$ to ${\mathcal{A}}_{1}$. Otherwise, ${\mathcal{B}}_{1}$ chooses random $\phi \in {\mathbb{Z}}_{\mathcal{P}}$ and forwards it to ${\mathcal{A}}_{1}$. The new tuple $(\phi ,\rho ,\eta )$ will be subsequently added to $Lis{t}_{{H}_{3}}$.
- -
- Extraction Query: Upon the Extract Query with $ID$ is made to ${\mathcal{B}}_{1}$, ${\mathcal{B}}_{1}$ conducts ${H}_{1}$ hash Query on the input $ID$ and outputs the corresponding tuple $(ID,\zeta )$. Note that the tuple $(ID,\zeta )$ has already recorded in $Lis{t}_{{H}_{1}}$. ${\mathcal{B}}_{1}$ randomly selects $X,r\in {\mathbb{Z}}_{\mathbb{P}}$ and computes $\mathcal{U}=X{\zeta}^{r}$ and $\mathcal{V}=\widehat{e}{(\zeta ,{g}^{-r})}^{mk}$ adopting the acquired $\zeta $ and previously stored $mk$. The calculated tuple $(\mathcal{U},\mathcal{V})$ will be sent to ${\mathcal{A}}_{1}$.

#### 6.2. Resistance to Replay Attack

#### 6.3. Provision to Identity Privacy Preserving

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

#### 6.4. Session Key Establishment

**Theorem**

**3.**

**Proof**

**of**

**Theorem**

**3.**

#### 6.5. Certificateless Authentication

**Theorem**

**4.**

**Proof**

**of**

**Theorem**

**4.**

#### 6.6. Continuous Authentication

#### 6.7. Comparison on Security Properties

## 7. Performance Analysis

#### 7.1. Storage Overhead

#### 7.2. Computation Cost

#### 7.3. Communication Cost

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Parameters | Description |
---|---|

SN, UE | Service network, user entity |

$\mathbb{G}$,${\mathbb{G}}_{\mathcal{S}}$ | Cyclic multiplicative group |

g, w | Generator of $\mathbb{G}$ |

$I{D}_{i}$ | Unique identity of UE i |

$mk$ | System master key |

${X}_{i}$ | HC and ${\mathrm{PC}}_{i}$ partial private key generated by SN |

${\vartheta}_{i}$ | Partial private key generated by UE itself |

$\left\{{a}_{0},{a}_{1},\cdots ,{a}_{t-1}\right\}$ | Coefficients of function $f\left(x\right)$ |

$PK$ | SN public key |

${H}_{1}$, ${H}_{2}$, ${H}_{3}$, ${H}_{4}$ | Secure hash functions |

$\gamma $ | Group key generated by SN |

$TS$ | Current time stamps |

m | Message to be transmitted |

t | Number of participating UEs |

Scheme | SeDS [19] | LRSA [32] | GRAAD [12] | PPAKA [9] | Our Scheme |
---|---|---|---|---|---|

Forgery Attack Resistance | √ | √ | √ | √ | √ |

Replay Attack Resistance | √ | √ | √ | √ | √ |

Provision to Identity Privacy Preserving | √ | √ | √ | √ | √ |

Session Key Establishment | √ | √ | √ | √ | √ |

Certificateless Authentication | × | × | √ | × | √ |

Dynamic Key Updating | √ | √ | × | √ | √ |

Continuous Authentication | × | × | × | × | √ |

Scheme | SeDS [19] | LRSA [32] | GRAAD [12] | PPAKA [9] | Our Scheme |
---|---|---|---|---|---|

Storage (UE) | 2816 bits | 3040 bits | 3488 bits | 4704+$192t$ bits | 2304+$16t$ bits |

Scheme | SeDS [19] | LRSA [32] | GRAAD [12] | PPAKA [9] | Our Scheme |
---|---|---|---|---|---|

Computation cost (SN) | $2e$+$3Ex$+$Dec$+$3H$ | $6tp$+$6tH$+$2tM$ | $2te$+$7tH$+$tEnc$+$tDec$ | $(t+1)Ex$+$tH$ | $3te$+$(4t+1)Ex$+$(2t+1)H$+$2tM$ |

Computation cost (UE) | $4p$+$5Ex$+$2Enc$+$2H$ | $8p$+$7H$+$2D$+M | $3p$+$8Ex$+$14H$+$2M$ | $3Ex$+$(t+4)H$+$(2t-1)M$ | $3e$+$Ex$+$2H$+$2M$ |

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## Share and Cite

**MDPI and ACS Style**

Tan, H.; Song, Y.; Xuan, S.; Pan, S.; Chung, I.
Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis. *Symmetry* **2019**, *11*, 969.
https://doi.org/10.3390/sym11080969

**AMA Style**

Tan H, Song Y, Xuan S, Pan S, Chung I.
Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis. *Symmetry*. 2019; 11(8):969.
https://doi.org/10.3390/sym11080969

**Chicago/Turabian Style**

Tan, Haowen, Yuanzhao Song, Shichang Xuan, Sungbum Pan, and Ilyong Chung.
2019. "Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis" *Symmetry* 11, no. 8: 969.
https://doi.org/10.3390/sym11080969