# A Lightweight and Provable Secured Certificateless Signcryption Approach for Crowdsourced IIoT Applications

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## Abstract

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## 1. Introduction

#### 1.1. Motivation and Contributions

- The scheme is using the concept of identity-based cryptosystem which suffers from the key escrow problem;
- Also, they used the mathematical concepts of bilinear pairing for the proposed scheme which needs huge computational power;
- Because of bilinear pairing, the scheme needs high bandwidth;
- The scheme does not fulfill the security property of resisting against a replay attack and forward secrecy;
- They did not validate the security requirement of their proposed scheme by utilizing the formal security validation tools like AVISPA, Scyther, etc.

- The scheme has just provided the authentication of IIoT crowdsourced data;
- Also, they used the mathematical concepts of bilinear pairing for the proposed scheme which needs high computational power;
- Because of bilinear pairing, the scheme needs high bandwidth.
- The scheme does not fulfill the security property of resisting against replay attack, confidentiality, and forward secrecy;
- The authentication of the scheme is not validated through the formal security validation tools like AVISPA, Scyther, etc.

- We design certificatelesssigncryption for crowdsourced IIoT based on the hyper elliptic curve;
- We remove the key escrow problem;
- We will showthe results for proving the efficiency in term of computational cost and communication overhead;
- Our scheme will provide security services such as confidentiality, anti-replay attack, integrity, authentication, sender authentication, message authentication, and unforgeability, respectively;
- We will validate our scheme security services through a well-known simulation tool AVISPA with the help of HLPSL language.

#### 1.2. Outlines of Paper

## 2. Related Work

## 3. Preliminary

^{*}is to be the algebraic closure of ultimate field f. Then the hyper elliptic curve H

_{ℇ}of genus $\mathcal{G}$ where $\mathcal{G}$ > 1 over the ultimate field f which can be defined as H

_{ℇ}: β

^{2}+ $\mathscr{H}$(α)β = F(α), where (α, β) ∈ f* × f. Further, $\mathscr{H}$(α) ∈ f(α) is a polynomial and the degree of this is at most $\mathcal{G}$ and F(α) ∈ f(α)is the monic polynomial and have degree is 2$\mathcal{G}$ + 1. The divisor of the hyper elliptic curve is the pair of polynomials and can be represented by using the Mumford [56]. The most important factor of every cryptographic system is the discrete logarithm problem in some Abelian group. Suppose there is a randomly selected number 𝓍 from the Abelian group and computing 𝓍.$\mathcal{D}$ = $\mathcal{D}$ + $\mathcal{D}$ + $\mathcal{D}$ +………+ $\mathcal{D}$ is scalar multiplication of divisors. And it is said to be a hyper elliptic curve discrete logarithm problem because finding the random number 𝓍 from 𝓍.$\mathcal{D}$ = $\mathcal{D}$ + $\mathcal{D}$ + $\mathcal{D}$ +………+ $\mathcal{D}$ is infeasible. Also, the Table 1 shows the symbols/notations used in the algorithm.

## 4. Proposed Model

## 5. Generic Model for Certificateless Signcryption

#### 5.1. Setup (STP)

#### 5.2. User Key Generation (UKG)

#### 5.3. Set Partial Private Key (SPPK)

#### 5.4. Set Private Key (SPK)

#### 5.5. CertificatelessSigncryption (CLSN)

#### 5.6. CL-Unsigncryption (CLUS)

## 6. Proposed CertificatelessSigncryption

#### 6.1. STP

#### 6.2. SPPK

#### 6.3. UKG

#### 6.4. SPK

#### 6.5. CLSN

#### 6.6. CLUS

## 7. Correctness

## 8. Security Analysis

#### 8.1. Confidentiality

#### 8.2. Replay Attack

#### 8.3. Integrity

#### 8.4. Authentication

#### 8.5. Unforgeability

## 9. Computational Cost

- The proposed scheme reduced at the computational time from AIK [27] is 4EX + 1BP − 7HDM/ 4EX + 1BP = 22.19 − 3.36/22.19 = 0.84*100 = 84.85%.
- The proposed scheme computational cost reduction From ASGMPM [8] is 6EX + 2BP − 7HDM/6EX + 2BP= 40.44 − 3.36/40.44 = 0.91*100 = 91.69%.
- The proposed scheme computational cost reduction from PM [47] is 8EX + 9BP − 7HDM/8EX + 9BP = 144.73 − 3.36/144.73 = 0.97*100 = 97%.
- The proposed scheme computational cost reduction from HB [48] is 10EX − 7HDM/10EX = 19.7 − 3.36/19.7 = 0.82*100 = 82.94%.
- The proposed scheme computational cost reduction from ZC [50] is 12EX + 5BP − 7HDM /12EX + 5BP = 95.19 − 3.36/95.19 = 0.96*100 = 96.47%.
- The proposed scheme computational cost reduction from LW [51] is 12EM − 7HDM /12EM = 11.64 − 3.36/11.64 = 0.71*100 = 71.13%.
- The proposed scheme computational cost reduction from LM [52] is 7EM − 7HDM /7EM = 6.79 − 3.36/6.79 = 0.50*100 = 50.51%.

## 10. Communication Overhead

## 11. Conclusions

## 12. Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Implementation and Validation

role role_Clsn(Clsn:agent, Clus:agent,Ys:public_key, Yr:public_key, SND,RCV:channel(dy)) played_byClsn def= local State:nat,Nc:text,H:text,Y:text, M:text,En:hash_func,K:symmetric_key init State := 0 transition 1. State=0 /\ RCV(start) =|> State’:=1 /\ SND(Clsn.Clus) 2. State=1 /\ RCV(Clus.{Nc’}_Yr) =|> State’:=2 /\ Y’:=new() /\ H’:=new() /\ K’:=new() /\ M’:=new() /\ secret(M’,sec_2,{Clsn}) /\ witness(Clsn,Clus,auth_1,M’) /\ SND(Clsn.{En(M’)}_K’.{H’.Y’}_inv(Ys)) end role |

role role_Clus(Clsn:agent,Clus:agent, Ys:public_key,Yr:public_key, SND,RCV:channel(dy)) played_byClus def= local State:nat,Nc:text,H:text,Y:text,M:text, En:hash_func,K:symmetric_key init State := 0 transition 1. State=0 /\ RCV(Clsn.Clus) =|> State’:=1 /\ Nc’:=new() /\ SND(Clus.{Nc’}_Yr) 6. State=1 /\ RCV(Clsn.{En(M’)}_K’.{H’.Y’}_inv(Ys)) =|> State’:=2 /\ request(Clus,Clsn,auth_1,M’) /\ secret(M’,sec_2,{Clsn}) end role |

role session1(Clsn:agent,Clus:agent, Ys:public_key,Yr:public_key) def= local SND2,RCV2,SND1,RCV1:channel(dy) composition role_Clus(Clsn,Clus,Ys,Yr,SND2,RCV2) /\ role_Clsn(Clsn,Clus,Ys,Yr,SND1,RCV1) end role role session2(Clsn:agent,Clus:agent, Ys:public_key,Yr:public_key) def= local SND1,RCV1:channel(dy) composition role_Clsn(Clsn,Clus,Ys,Yr,SND1,RCV1) end role |

role environment() def= const hash_0:hash_func,ys:public_key,alice:agent,bob:agent,yr:public_key,const_1:agent,const_2:public_key,const_3:public_key,auth_1:protocol_id,sec_2:protocol_id intruder_knowledge = {alice,bob} composition session2(i,const_1,const_2,const_3) /\ session1(alice,bob,ys,yr) end role |

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No | Notation | Description |
---|---|---|

1 | H_{ℇ} | Hyper elliptic curve |

2 | $\mathcal{D}$ | Divisor of hyper elliptic curve |

3 | $\mathcal{G}$ | Means genus on a hyper elliptic curve |

4 | 𝒽 | Irreversible hash function |

5 | ID_{s} | Identity of the IIoT data owner/ CLSR |

6 | ID_{r} | Identity of the data consumer/ CLUR |

7 | $\mathcal{Y}$_{s},$\mathcal{Y}$_{r} | The public keys of data owner/ CLSR and data consumer/ CLUR |

8 | 𝘗_{s} = ($\mathcal{X}$_{s},δ_{s}) | The private key pair of IIoT data owner/ CLSR |

9 | 𝘗_{r} = ($\mathcal{X}$_{r},δ_{r}) | The private key pair of data consumer/ CLUR |

10 | $n$ | It is the largest prime number of H_{ℇ} and $n$ = 2^{80} |

11 | N_{c} | It is the nonce |

12 | 𝓂,$\mathcal{C}$ | Represents the plaintext and cipher text |

13 | K | Shared secret key |

14 | E_{K,} D_{K} | Means encryption and decryption |

15 | S | Means digital signature |

16 | Ω | Means signcryption tuple |

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## Share and Cite

**MDPI and ACS Style**

Ullah, I.; Ul Amin, N.; Zareei, M.; Zeb, A.; Khattak, H.; Khan, A.; Goudarzi, S.
A Lightweight and Provable Secured Certificateless Signcryption Approach for Crowdsourced IIoT Applications. *Symmetry* **2019**, *11*, 1386.
https://doi.org/10.3390/sym11111386

**AMA Style**

Ullah I, Ul Amin N, Zareei M, Zeb A, Khattak H, Khan A, Goudarzi S.
A Lightweight and Provable Secured Certificateless Signcryption Approach for Crowdsourced IIoT Applications. *Symmetry*. 2019; 11(11):1386.
https://doi.org/10.3390/sym11111386

**Chicago/Turabian Style**

Ullah, Insaf, Noor Ul Amin, Mahdi Zareei, Asim Zeb, Hizbullah Khattak, Ajab Khan, and Shidrokh Goudarzi.
2019. "A Lightweight and Provable Secured Certificateless Signcryption Approach for Crowdsourced IIoT Applications" *Symmetry* 11, no. 11: 1386.
https://doi.org/10.3390/sym11111386