# Secure Authentication in the Smart Grid

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## Abstract

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## 1. Introduction

#### 1.1. Our Contribution

- We propose the first independent security analysis of LLAKEP in various scenarios with varying access to the adversary. Our security analysis demonstrates important security issues in this protocol.
- In terms of efficiency, we show that this protocol could be designed more efficiently and propose a promising solution to address this flaw.
- We propose the LLAKEP${}^{+}$ protocol as an improved protocol that uses the same set of cryptographic primitives as the LLAKEP protocol.
- We carefully evaluate the security of the proposed protocol both informally and formally using a real or random model and confirm its security using the Scyther tool. We also evaluate the security of the proposed protocol and compare it with the state of the art, which shows that the proposed protocol has a low communication cost and a comparable computation cost.

#### 1.2. Paper Organization

## 2. Preliminaries

#### 2.1. Notation

#### 2.2. Elliptic Curve Cryptography

#### 2.3. System Model

#### 2.4. LLAKEP Description

#### 2.5. Initialization

#### 2.6. User Registration

#### 2.7. Authenticated Key Agreement

- The EBR user enters its $I{D}_{EBR}$ and $P{W}_{EBR}$ on the smart glass. MC computes $HIP={H}_{2}(I{D}_{EBR}\parallel P{W}_{EBR})$, ${a}_{MC}=HIP\oplus v$, and verifies whether $C\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel P{W}_{EBR}\parallel {a}_{MC})$. Assuming that verification was successful, MC generates a random number ${r}_{MC}$ and computes ${U}_{EBR}={r}_{MC}+s{k}_{EBR},R={r}_{MC}\xb7p{k}_{BSS},CI{D}_{EBR}={l}^{\prime}\oplus HIP={H}_{1}\left(s{k}_{BSS}\right)\oplus {H}_{2}(s{k}_{BSS}\parallel I{D}_{EBR})$ and $Aut{h}_{EBR}={H}_{2}(I{D}_{EBR}\parallel R\parallel CI{D}_{EBR}\parallel {T}_{MC})$, where ${T}_{MC}$ is the current timestamp. Next, using a public channel, EBR sends $\{Aut{h}_{EBR},$$CI{D}_{EBR},{U}_{EBR},{T}_{MC}\}$ to BSS.
- Once received the message, BSS verifies ${T}_{MC}$, calculates ${H}_{2}(s{k}_{BSS}\parallel I{D}_{EBR})=CI{D}_{EBR}\oplus $${H}_{1}\left(s{k}_{BSS}\right)$ and ${R}_{EBR}={U}_{EBR}\xb7G-p{k}_{EBR}={r}_{MC}\xb7G$ and ${R}^{*}=s{k}_{BSS}\xb7{R}_{EBR}$ and verifies whether $Aut{h}_{EBR}\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel {R}^{*}\parallel CI{D}_{EBR}\parallel {T}_{MC})$. Next, it generates a random number ${r}_{BSS}$ and computes ${R}_{BSS}={r}_{BSS}\xb7G$, $S{K}_{BSS}={r}_{BSS}\xb7{R}_{EBR}$ and $Aut{h}_{BSS}={H}_{2}(I{D}_{EBR}\parallel {R}^{*}\parallel S{K}_{BSS}\parallel {T}_{BSS})$, where ${T}_{BSS}$ is the current timestamp. Next, using a public channel, BSS sends $\{Aut{h}_{BSS},{R}_{BSS},{T}_{BSS}\}$ to EBR.
- EBR verifies ${T}_{BSS}$, calculates $S{K}_{EBR}={r}_{MC}\xb7{R}_{BSS}$ and verifies whether $Aut{h}_{BSS}^{*}\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel R\parallel S{K}_{EBR}\parallel {T}_{BSS})$ to authenticate BSS. After successful authentication, EBR calculates $sk=kdf(I{D}_{EBR}\parallel S{K}_{EBR}\parallel {T}_{MC}\parallel {T}_{BSS})$ and $Aut{h}_{EB}={H}_{2}(I{D}_{EBR}\parallel R\parallel sk\parallel {T}_{MC}^{\prime})$, where ${T}_{MC}^{\prime}$ is the current timestamp. Next, using a public channel, EBR sends $\{Aut{h}_{EB},{T}_{MC}^{\prime}\}$ to BSS.
- BSS verifies ${T}_{MC}^{\prime}$ and computes $s{k}^{\prime}=kdf(I{D}_{EBR}\parallel S{K}_{BSS}\parallel {T}_{MC}\parallel {T}_{BSS})$ and checks whether $Aut{h}_{EB}\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel {R}^{*}\parallel s{k}^{\prime}\parallel {T}_{MC}^{\prime})$ to authenticate EBR and store the session key $s{k}^{\prime}$, which is used for secure communication between EBR and BSS.

#### 2.8. Password Change

## 3. On the Security of LLAKEP

#### 3.1. Insider Adversary

#### 3.1.1. Traceability and Anonymity

#### 3.1.2. Known Session-Specific Temporary Information Attack

#### 3.1.3. Impersonation Attack after a Successful KSTI Attack

- The adversary generates a random number ${r}_{adv}$ and computes ${U}_{EBR}={r}_{adv}+s{k}_{EBR}$, ${R}_{adv}={r}_{adv}\xb7p{k}_{BSS}$ and $Aut{h}_{EBR}={H}_{2}(I{D}_{EBR}\parallel R\parallel CI{D}_{EBR}\parallel {T}_{adv})$, where ${T}_{adv}$ is the current timestamp. Next, using a public channel, the adversary sends $\{Aut{h}_{EBR},CI{D}_{EBR},{U}_{EBR},{T}_{MC}\}$ to BSS.
- Obviously ${T}_{MC}$ and $Aut{h}_{EBR}$ are accepted by $BSS$ and ${R}_{adv}={r}_{adv}\xb7p{k}_{BSS}$ is extracted by BSS from the received ${U}_{EBR}={r}_{adv}+s{k}_{EBR}$. Next, it generates a random number ${r}_{BSS}$ and computes ${R}_{BSS}={r}_{BSS}\xb7G$, $S{K}_{BSS}={r}_{BSS}\xb7{R}_{avd}$ and $Aut{h}_{BSS}={H}_{2}(I{D}_{EBR}\parallel {R}_{adv}\parallel S{K}_{BSS}\parallel {T}_{BSS})$ and sends $\{Aut{h}_{BSS},{R}_{BSS},{T}_{BSS}\}$ to EBR (impersonated by the adversary).
- The adversary calculates $S{K}_{adv}={r}_{adv}\xb7{R}_{BSS}$, $sk=kdf(I{D}_{EBR}\parallel S{K}_{adv}\parallel {T}_{adv}\parallel {T}_{BSS})$ and $Aut{h}_{ad}={H}_{2}(I{D}_{EBR}\parallel {R}_{adv}\parallel S{K}_{adv}\parallel {T}_{adv}^{\prime})$, where ${T}_{adv}^{\prime}$ is the current timestamp. Next, using a public channel, the adversary sends $\{Aut{h}_{ad},{T}_{adv}^{\prime}\}$ to BSS.
- BSS verifies ${T}_{adv}^{\prime}$, calculates $s{k}^{\prime}=kdf(I{D}_{EBR}\parallel S{K}_{BSS}\parallel {T}_{MC}\parallel {T}_{BSS})$ and verifies whether $Aut{h}_{ad}\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel {R}_{adv}\parallel s{k}^{\prime}\parallel {T}_{MC}^{\prime})$ to authenticate EBR/adversary and store the session key $s{k}^{\prime}$, which is used for the secure communication between EBR/adversary and BSS.

#### 3.2. Key Compromised Impersonation Attack

- The EBR user enters its $I{D}_{EBR}$ and $P{W}_{EBR}$ on the smart glass. MC verifies them, generates a random number ${r}_{MC}$ and computes ${U}_{EBR}={r}_{MC}+s{k}_{EBR},R={r}_{MC}\xb7p{k}_{BSS},CI{D}_{EBR}={l}^{\prime}\oplus HIP={H}_{1}\left(s{k}_{BSS}\right)\oplus {H}_{2}(s{k}_{BSS}\parallel I{D}_{EBR})$ and $Aut{h}_{EBR}=$${H}_{2}(I{D}_{EBR}\parallel R\parallel CI{D}_{EBR}\parallel {T}_{MC})$ and sends $\{Aut{h}_{EBR},CI{D}_{EBR},{U}_{EBR},{T}_{MC}\}$ to BSS.
- The adversary extracts ${r}_{MC}={U}_{EBR}-s{k}_{EBR}$, computes ${R}_{EBR}={r}_{MC}\xb7G$ and ${R}^{*}={r}_{MC}\xb7p{k}_{BSS}$, generates a random number ${r}_{adv}$, computes ${R}_{adv}={r}_{adv}\xb7G$, $S{K}_{adv}={r}_{adv}\xb7{R}_{EBR}$ and $Aut{h}_{adv}={H}_{2}(I{D}_{EBR}\parallel R\parallel S{K}_{adv}\parallel {T}_{adv})$ and sends $\{Aut{h}_{adv},{R}_{adv},{T}_{adv}\}$ to EBR.
- EBR verifies ${T}_{adv}$, calculates $S{K}_{EBR}={r}_{MC}\xb7{R}_{adv}$ and verifies whether $Aut{h}_{adv}^{*}\stackrel{?}{=}{H}_{2}(I{D}_{EBR}\parallel R\parallel S{K}_{EBR}\parallel {T}_{adv})$ to authenticate BSS/adversary which authenticates.

#### 3.3. The Lack of Perfect Forward Secrecy

#### 3.4. A Note on the LLAKEP Efficiency

## 4. LLAKEP${}^{+}$ Description

#### 4.1. Initialization

#### 4.2. User Registration

#### 4.3. Authenticated Key Agreement

- The EBR user enters its $I{D}_{EBR}$ and $P{W}_{EBR}$ on the smart glass. MC computes $({a}_{MC}\parallel s\parallel r)=$${H}^{e}(I{D}_{EBR}\parallel P{W}_{EBR})\oplus d$, and $HID=H(I{D}_{EBR}\parallel {a}_{MC})$ and verifies whether $v\stackrel{?}{=}H(s\parallel r\parallel H(I{D}_{EBR}\parallel P{W}_{EBR})\parallel {a}_{MC})$ to accept the login. If the verification was successful, MC obtains the current time ${T}_{MC}$, generates a random number ${k}_{MC}\in [1,n-1]$ and calculates ${R}_{EBR}={k}_{MC}\xb7G$ and $Aut{h}_{EBR}=HID\oplus H({k}_{MC}\xb7p{k}_{BSS}\parallel {T}_{MC})$. Then, it sends $({R}_{EBR},{T}_{MC},Aut{h}_{EBR})$ to BSS over a public channel.
- BSS validates ${T}_{MC}$ after receiving the message and calculates $HID=Aut{h}_{EBR}\oplus H(s{k}_{BSS}\xb7{R}_{EBR}\parallel {T}_{MC})$. If it detects the extracted $HID$ in its database, BSS generates a random number ${k}_{BSS}\in [1,n-1]$ and calculates ${R}_{BSS}={k}_{BSS}\xb7G$, the temporary session key $sk=H({k}_{BSS}\xb7{R}_{EBR}\parallel {k}_{BSS}\xb7p{k}_{EBR}\parallel s{k}_{BSS}\xb7{R}_{EBR})$ and $Aut{h}_{BSS}=H({R}_{BSS}\parallel {T}_{MC}\parallel sk)$. Then, it sends $({R}_{BSS},Aut{h}_{BSS})$ to EBR over a public channel.
- EBR computes the session key, after receiving the message, $sk=H({k}_{MC}\xb7{R}_{BSS}\parallel s{k}_{EBR}\xb7{R}_{EBR}\parallel {k}_{MC}\xb7p{k}_{BSS})$ and verifies whether $Aut{h}_{BSS}\stackrel{?}{=}H({R}_{BSS}\parallel {T}_{MC}\parallel sk)$ to authenticate BSS. If BSS has been authenticated, EBR returns ${V}_{EBR}=H(sk\parallel {T}_{MC}\parallel HID)$ to BSS.
- BSS verifies the received ${V}_{EBR}$ to authenticate EBR and also confirm the shared session key.

#### 4.4. Password Change

## 5. Security and Cost Analysis of LLAKEP${}^{+}$

#### 5.1. Informal Security Analysis

#### 5.1.1. Replay Attack

#### 5.1.2. Impersonation Attack

#### 5.1.3. Traceability and Anonymity

#### 5.1.4. Secret Disclosure Attack

#### 5.1.5. Permanent De-Synchronization Attack

#### 5.1.6. Man-in-the-Middle Attack

#### 5.1.7. Stolen Smart Glass Attack

#### 5.1.8. Insider Adversary

#### 5.1.9. Perfect Forward Secrecy

#### 5.1.10. Known Session-Specific Temporary Information Attack

#### 5.1.11. Key Compromised Impersonation Attack

#### 5.2. Formal Security Evaluation

#### 5.2.1. Scyther

- Suppose that the long-term key is revealed to the adversary, what attack scenarios are the protocol vulnerable to?
- Assume the session key is exposed, what attack scenarios are the protocol vulnerable to?
- Suppose that the protocol state is exposed, what attack scenarios are the protocol vulnerable to?

#### 5.2.2. Formal Security Analysis in RoR Model

**Theorem 1.**

**Proof.**

#### 5.3. Cost Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IoT | Internet of Things |

EIoT | Energy Internet of Things |

IoD | Internet of Drones |

IIoT | Industrial Internet of Things |

IoV | Internet of Vehicles |

MIoT | Medical Internet of Things |

NVM | Non Volatile Memory |

IT | Information Technology |

EBR | Electric Bike Riders |

BSS | Battery Swap Station |

MC | Microprocessor Chip |

ECC | Elliptic Curve Cryptography |

KSTI | Known Session-specific Temporary Information |

KCI | Key Compromised Impersonation |

MitM | Man in the Middle Attack |

## Appendix A. SPDL Description of the Proposed Protocol

Listing A1: SPDL description of the proposed protocol. |

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**Figure 3.**Mutual authentication phase of LLAKEP scheme to share a session key between $EBR$ and $BSS$ [9].

**Figure 4.**Mutual authentication phase of LLAKEP${}^{+}$ scheme to share a session key between $EBR$ and $BSS$.

Symbol | Description |
---|---|

EBR | Electric bike riders |

BSS | Battery swap station |

MC | Microprocessor chip |

A | Adversary |

$I{D}_{EBR}$ | Identity of an electric bike rider EBR |

$P{W}_{EBR}$ | Password of an electric bike rider EBR |

$s{k}_{X}$ | Private key of X |

$p{k}_{X}$ | Public key of X |

$sk$ | Session key |

$E/{F}^{p}$ | An elliptic curve E over a prime finite field ${F}^{p}$ with p being a large prime |

n | Order of base point G |

${Z}^{n}$ | $1,2,\dots ,n-1$ |

$k\xb7G$ | Scalar multiplication on elliptic curves and G is a base point in $E/Fp$ |

$A\parallel B$ | Concatenation operation between strings A and B |

$A\oplus B$ | XOR operation between strings A and B |

$kdf(\xb7)$ | Key derivation function |

$H(\xb7)$ | A one-way hash function that generates digests |

Protocol | Primitives Call | Computations (ms) | Communication (bit) |
---|---|---|---|

[28] | $10\times {T}_{H}+8\times {T}_{em}$ | 17.831 | 1440 bits |

[29] | $5\times {T}_{H}+9\times {T}_{em}$ | 20.0455 | 1632 bits |

[30] | $11\times {T}_{H}+9\times {T}_{em}$ | 20.0593 | 1600 bits |

[31] | $8\times {T}_{H}+9\times {T}_{em}$ | 20.0524 | 1344 bits |

[9] | $12\times {T}_{H}+6\times {T}_{em}$ | 13.3836 | 1187 bits |

LLAKEP${}^{+}$ | $11\times {T}_{H}+8\times {T}_{em}$ | 17.8333 | 1152 bits |

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## Share and Cite

**MDPI and ACS Style**

Hosseinzadeh, M.; Ali Naqvi, R.; Safkhani, M.; Tightiz, L.; Majid Mehmood, R.
Secure Authentication in the Smart Grid. *Mathematics* **2023**, *11*, 176.
https://doi.org/10.3390/math11010176

**AMA Style**

Hosseinzadeh M, Ali Naqvi R, Safkhani M, Tightiz L, Majid Mehmood R.
Secure Authentication in the Smart Grid. *Mathematics*. 2023; 11(1):176.
https://doi.org/10.3390/math11010176

**Chicago/Turabian Style**

Hosseinzadeh, Mehdi, Rizwan Ali Naqvi, Masoumeh Safkhani, Lilia Tightiz, and Raja Majid Mehmood.
2023. "Secure Authentication in the Smart Grid" *Mathematics* 11, no. 1: 176.
https://doi.org/10.3390/math11010176