# Blockchain Enabled Anonymous Privacy-Preserving Authentication Scheme for Internet of Health Things

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## Abstract

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## 1. Introduction

- Development of an authentication scheme that guarantees efficient anonymous authentication for patients and medical staff, where confidential biological information is accessed only by authenticated doctors or patients.
- Development of an authentication scheme that guarantees integrity and data confidentiality of both the confidential biological information and medical prescription of patients and doctors from attackers.
- Development of an authentication scheme that guarantees an efficient revoking mechanism for malicious misbehaving of medical staff in the IoHT wireless body area network.
- Development of an efficient authentication handover that enables avoiding re-authentication of the patients when new doctors start their health monitoring process.

## 2. Related Works

## 3. Development Methods of the Proposed Authentication Scheme

#### 3.1. Elliptic Curve Cryptography

#### 3.2. Bilinear Pairing

- (1)
- Bilinearity: for any $A,B,C\in {G}_{1}$, $e\left(A,B+C\right)=e\left(A,B\right)e\left(A,C\right)$ and $e\left(A+B,C\right)=e\left(A,C\right)e\left(B,C\right)$.
- (2)
- Non-degeneracy: for non-identify points $P,Q\in {G}_{1}$, $e\left(P,Q\right)\ne {1}_{{G}_{T}}$, where ${1}_{{G}_{T}}$ is the identity point of ${G}_{T}$.
- (3)
- Computability: for any two points $P,Q\in {G}_{1}$, there exists a polynomial time algorithm to determine the value of $e\left(P,Q\right)$.

#### 3.3. Blockchain Technology

#### 3.4. System Model

#### 3.5. Security Objectives

- Ensuring message integrity and authentication: the confidential biological sensitive data of the patient or the medical prescription of the doctor should be integrity preserved. The possibility of forging or modifying the information by the intruder should be eliminated.
- Ensuring nonrepudiation: only authenticated end users are allowed to participate in the data transfer over the IoHT network. There must be no possibility for the registered users to deny the message transmission once it is sent.
- Ensuring anonymity and privacy: the real identity of the end users should be preserved during the transfer of confidential data. Moreover, the private confidential information of the end users should be preserved.
- Ensuring unlinkability: there should not be any correlation between the subsequent information sent between the end users.
- Ensuring revocation and traceability: if any mishap occurs in the network and the end user is trying to send fake information, the real identity of the end user should be traced immediately and revoked from the IoHT network.

## 4. Description of the Proposed Authentication Scheme

Algorithm 1: Flow diagram of registration, key generation and authentication of patient. | |

part 1: the anonymous authentication of patient | |

Initialization:1. Elliptic curve of finite field:${y}^{2}={x}^{3}+ax+bmodq$ | |

2. Points on the curve:$X$ | |

3. Random numbers$a,b\in {Z}_{q}^{*}$ | |

4. Public parameter of TE:$\alpha =aX$ | |

5. Authentication parameter of TE:$\beta =bX$ | |

6. Hash function generation:$H:\left\{0,1\right\}\to {Z}_{q}^{*}$ | |

7. Public parameters:$(\alpha $,$\beta $,$H,X,e\left(X,X\right),q)$ | |

Patient’s registration: | |

8. TE chooses${\rho}_{i},k\in {Z}_{q}^{*}$ | |

calculate$VI{D}_{{p}_{i}}={\rho}_{i}\left(a+b\right)$ | |

calculate$FI{D}_{{p}_{i}}\in {Z}_{q}^{*}$ | |

9. $\left({\rho}_{i},VI{D}_{{p}_{i}},FI{D}_{{p}_{i}},{x}_{1},{x}_{3}\right)$ Patient | |

10. $\left(FI{D}_{{p}_{i}},Z\right)$ Blockchain where $Z=e{\left(X,X\right)}^{{\rho}_{i}}$ | |

Doctor’s registration: | |

11. $TE$ chooses ${c}_{i},x\in {Z}_{q}^{*}$ | |

calculate$VI{D}_{di}=\left(\frac{1}{a+b}\right)X$ | |

calculate$FI{D}_{di}$ $\in {Z}_{q}^{*}$ | |

12. $\left(VI{D}_{di},FI{D}_{di},x,{y}_{3},{y}_{5},{y}_{6},{y}_{7}\right)$ Doctor | |

Patient’s key generation: | |

13. secret key is$S{k}_{{p}_{i}}={x}_{3}+H({x}_{1}|\left|FI{D}_{{p}_{i}}\right){\rho}_{i}$ | |

14. public validation key is$P{k}_{{p}_{i}}=S{k}_{{p}_{i}}.X$ | |

Doctor’s key generation: | |

15. $secretkeyisS{k}_{{d}_{i}}={y}_{5}+H({y}_{1}|\left|FI{D}_{{d}_{i}}\right)x$ | |

16. public validation key is $P{k}_{{d}_{i}}=S{k}_{{d}_{i}}.X$ | |

Anonymous authentication of Patient: | |

Patient | Doctor |

17. ${\rho}_{i}X$ | $FI{D}_{di}X$ |

18. $FI{D}_{di}X$ | ${\rho}_{i}X$ |

19. $f=FI{D}_{di}X.{\rho}_{i}$ | $f={\rho}_{i}X.FI{D}_{di}$ |

20. ${f}_{1}=VI{D}_{{p}_{i}}\u2a01H\left(f\right)$ | $VI{D}_{{p}_{i}}={f}_{1}\u2a01H\left(f\right)$ |

21. | Verifies$e\left(VI{D}_{{p}_{i}}X,VI{D}_{{d}_{i}}\right)=Z$ |

22. | $AA=\left(FI{D}_{{p}_{i}},FI{D}_{{d}_{i}},H\left(FI{D}_{{p}_{i}},FI{D}_{{d}_{i}}\right)\right)$ |

23_{.} $FI{D}_{{d}_{i}}=VI{D}_{{p}_{i}}\u2a01{f}_{2}$ | ${f}_{2}=VI{D}_{{p}_{i}}\u2a01FI{D}_{{d}_{i}}$ |

Algorithm 2: Anonymous authentication of doctor and handover authentication. | ||

part 2: the anonymous authentication of the doctor | ||

Doctor | Patient | |

1. | Reception of parameters: $VI{D}_{di},FI{D}_{di},{c}_{i},x,b,{y}_{3},{y}_{5},{y}_{6},{y}_{7}$ | |

2. | ${l}_{1}=FI{D}_{{d}_{i}}\u2a01{y}_{7}$ | |

3. | ${l}_{2}=VI{D}_{{p}_{i}}\u2a01{y}_{6}$ | |

4. | ${l}_{1},{l}_{2},{c}_{i}$ | |

5. | ${y}_{6}=VI{D}_{{p}_{i}}\u2a01{l}_{2}$ | |

6. | ${y}_{7}=FI{D}_{{d}_{i}}\u2a01{l}_{1}$ | |

7. | Verifies${y}_{6}X=\left({y}_{1}+{y}_{6}\beta \right)$ | |

Transfer of biotic information from the patient to the doctor | ||

Patient | Doctor | |

8. | ${t}_{1},{t}_{2}$ $\in {Z}_{q}^{*}$ | |

9. | ${u}_{1}={t}_{1}\left(P{k}_{{p}_{i}}+H\left(\omega \right)X\right)$ | |

10. | ${v}_{1}=H({g}^{{t}_{1}}||P{k}_{{d}_{i}})$ | |

11. | ${m}_{1}={t}_{2}X$ | |

12. | ${m}_{2}={\left[S{k}_{{p}_{i}}+H\left(\omega \right)\right]}^{-1}X-{t}_{2}P{k}_{{d}_{i}}$ | |

13. | $\left({u}_{1},{v}_{1}\right)$,${m}_{1}$ and ${m}_{2}$ | |

14. | Verifies$e\left({u}_{1},S{k}_{{d}_{i}}{m}_{1}+{m}_{2}\right)={g}^{{t}_{1}}$ | |

Transfer of medical prescription from the doctor to patient | ||

Doctor | Patient | |

15. | ${t}_{3},{t}_{4}$ $\in {Z}_{q}^{*}$ | |

16. | ${u}_{2}={t}_{3}\left(P{k}_{{d}_{i}}+H\left({\omega}^{\prime}\right)X\right)$ | |

17. | ${v}_{2}=H({g}^{{t}_{3}}||P{k}_{{p}_{i}})$ | |

18. | ${m}_{3}={t}_{4}X$ | |

19. | ${m}_{4}={\left[S{k}_{{d}_{i}}+H\left({\omega}^{\prime}\right)\right]}^{-1}X-{t}_{4}P{k}_{{p}_{i}}$ | |

20. | $\left({u}_{2},{v}_{2}\right)$, ${m}_{3}$ and ${m}_{4}$ | |

21. | Verifies$e\left({u}_{2},S{k}_{{p}_{i}}{m}_{3}+{m}_{4}\right)={g}^{{t}_{3}}$ | |

Handover authentication | ||

Current doctor | Next doctor(s) | |

22. | ${d}_{1},{d}_{2},{d}_{3}\in {Z}_{q}^{*}$ | |

23. | ${D}_{1}={d}_{1}\alpha $, ${D}_{2}={d}_{2}\alpha $, ${D}_{3}={D}_{1}+{D}_{2}$, ${D}_{4}={d}_{3}\alpha $,${D}_{5}={D}_{3}+{D}_{4}$ | |

24. | ${Q}_{i}={\partial}_{i}\left({d}_{1}+{d}_{2}+{d}_{3}\right)modq$where${\partial}_{i}=H\left(\omega \times {D}_{4}\right)$ | |

25. | $\sigma =\left({D}_{4},\omega \right)$ | |

26. | $\left({Q}_{i},TS,\omega ,\sigma ,{D}_{3},FI{D}_{pi}\right)$ | ${\partial}_{i}=H\left(\omega \times {D}_{4}\right)$ |

27. | Verifies${Q}_{i}\alpha ={\partial}_{i}{D}_{5}$ |

#### 4.1. System Initialization

#### 4.2. Patient’s Registration

#### 4.3. Doctor’s Registration

#### 4.4. Patient’s Key Generation

**Proof of validation.**

#### 4.5. Doctor’s Key Generation

**Proof of validation.**

#### 4.6. Patient’s Anonymous Authentication

**Proof of validation.**

#### 4.7. Doctor’s Anonymous Authentication

**Proof of validation.**

#### 4.8. Transfer of Biotic Information from the Patient to the Doctor

**Proof of validation.**

#### 4.9. Transfer of Medical Prescription from the Doctor to Patient

**Proof of validation.**

#### 4.10. Handover Mechanism and Integrity Preservation

**Proof of validation.**

#### 4.11. Revocation

_{,}will not be allowed to proceed further in the IoHT network.

## 5. Security Analysis

#### 5.1. Impersonation Attack

#### 5.2. Bogus Message Attack

#### 5.3. Message Modification Attack

#### 5.4. Revocation Atack

#### 5.5. Non-Repudiation Attack

#### 5.6. Anonymity and Privacy-Preservation Attack

#### 5.7. Unlinkability Attack

#### 5.8. Sybil Attack

#### 5.9. Replay Attack

## 6. Performance Analysis

#### 6.1. Computational Overhead

#### 6.2. Communication Overhead

#### 6.3. Storage Cost

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Notations | Explanation |

$TE$ | Trusted entity |

$X$ | Point on the elliptic curve |

$q$ | Largest prime value |

$a,b$ | Random numbers of $TE$ |

$\alpha $ | Public parameter of $TE$ |

$\beta $ | Authentication parameter of $TE$ |

H: {0, 1}* | Hash function |

${p}_{i}$, $di$ | Patient and Doctor |

${\rho}_{i},k$ | Random numbers for patient chosen by $TE$ |

$VI{D}_{{p}_{i}}$ | Validation ID for the patient |

$FI{D}_{{p}_{i}}$ | Fake ID for the patient |

${c}_{i},x$ | Random numbers for doctor chosen by $TE$ |

$VI{D}_{di}$ | Validation ID for doctor |

$FI{D}_{di}$ | Fake ID for doctor |

$S{k}_{{p}_{i}}$ | Secret key for patient |

$P{k}_{{p}_{i}}$ | Public key for patient |

$S{k}_{{d}_{i}}$ | Secret key for doctor |

$P{k}_{{d}_{i}}$ | Public key for doctor |

$\omega $ | Confidential biological information of ${p}_{i}$ |

${t}_{1},{t}_{2}$ | Random numbers chosen by the patient |

$\left({u}_{1},{v}_{1}\right)\&\left({u}_{2},{v}_{2}\right)$ | Cipher texts |

${\omega}^{\prime}$ | Medical prescription of the doctor |

${t}_{3},{t}_{4}$,${d}_{1},{d}_{2},{d}_{3}$ | Random numbers chosen by the doctor |

$\sigma $ | Signature of a confidential biological message |

$TS$ | Timestamp |

${\omega}^{*}$ | Fake message |

$\oplus $ | Exclusive OR operation |

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Hardware Characteristics of the Simulation Server | Cryptographic Operation | Time Duration in Milliseconds (ms) |
---|---|---|

Processor: Core i7 RAM: 16 GB Frequency: 2.20 GHz Operating system: 64-bit Software: Cygwin with PBC library | One point multiplication $({T}_{m})$ | 2.226 |

One point addition $({T}_{a})$ | 0.001 | |

Exponential operation $({T}_{e})$ | 3.85 | |

Pairing operation $({T}_{p})$ | 2.91 | |

Hashing function $({T}_{h})$ | 0.0023 | |

Exclusive OR operation $({T}_{xor})$ | 0.001 |

Authentication Schemes | Authentication Time at the Patient Side (ms) | Authentication Time at Doctor Side (ms) |
---|---|---|

Liu et al. [49] | $n{T}_{p}+\left(n+1\right){T}_{h}+\left(2n+1\right){T}_{e}$ | $n{T}_{p}+\left(n+1\right){T}_{e}+n{T}_{h}$ |

Kumar et al. [44] | $(n+1){T}_{p}+\left(n+1\right){T}_{h}+\left(2n+1\right){T}_{m}$ | $n{T}_{p}+\left(2n+1\right){T}_{h}+\left(2n+1\right){T}_{m}$ |

Jegadeesan et al. [50] | $(n+1){T}_{p}+\left(n+1\right){T}_{h}+\left(n+1\right){T}_{m}$ | $(n+1){T}_{p}+n{T}_{h}+\left(n+1\right){T}_{m}$ |

Debiao et al. [51] | $(n+1){T}_{m}+\left(n+1\right){T}_{h}+n{T}_{p}+n{T}_{a}$ | $(n+1){T}_{m}+\left(2n+1\right){T}_{h}+n{T}_{p}$ |

Jia et al. [52] | $4n{T}_{m}+n{T}_{e}+5n{T}_{h}$ | $n{T}_{p}+5n{T}_{m}+\left(2n+1\right){T}_{a}+5n{T}_{h}$ |

Proposed work (authentication scheme) | $2n{T}_{m}+n{T}_{h}+4n{T}_{xor}$ | $n{T}_{m}+3n{T}_{xor}+n{T}_{h}+n{T}_{p}+n{T}_{a}$ |

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## Share and Cite

**MDPI and ACS Style**

Rajasekaran, A.S.; Maria, A.; Rajagopal, M.; Lorincz, J.
Blockchain Enabled Anonymous Privacy-Preserving Authentication Scheme for Internet of Health Things. *Sensors* **2023**, *23*, 240.
https://doi.org/10.3390/s23010240

**AMA Style**

Rajasekaran AS, Maria A, Rajagopal M, Lorincz J.
Blockchain Enabled Anonymous Privacy-Preserving Authentication Scheme for Internet of Health Things. *Sensors*. 2023; 23(1):240.
https://doi.org/10.3390/s23010240

**Chicago/Turabian Style**

Rajasekaran, Arun Sekar, Azees Maria, Maheswar Rajagopal, and Josip Lorincz.
2023. "Blockchain Enabled Anonymous Privacy-Preserving Authentication Scheme for Internet of Health Things" *Sensors* 23, no. 1: 240.
https://doi.org/10.3390/s23010240