A Provably Secure IBE Transformation Model for PKC Using Conformable Chebyshev Chaotic Maps under Human-Centered IoT Environments
Abstract
:1. Introduction
1.1. Contribution
- ■
- We provide a provably secure IBE transformation model under the human-centered IoT contexts comprising a KGS with extremely low processing computation complexity;
- ■
- We show that the presented transformation procedure is accomplished by interpreting a well-designed and secure conformable Chebyshev chaotic map-based scheme into an equally robust ID-based cryptosystem under human-centered IoT environments;
- ■
- We demonstrate that our new model provides the same level of suitability and client-friendliness compared to the original conformable Chebyshev chaotic map-based PKC;
- ■
- We show that there is no need for an extensive public key database under the new architecture;
- ■
- We test the proposed ID-based system against IND-sID-CCA in the ROM by employing the reductionist method.
1.2. Paper Organization
2. Related Works
3. Background and Materials
3.1. Chebyshev Chaotic Polynomials
- (1)
- Semi-group feature: A semi-possession group must meet the following criteria:
- (1)
- Given two and , the objective of the discrete log (DL) is to invent an integer with the ultimate aim .
- (2)
- The goal of the Diffie–Hellman problem (DHP) is to calculate the element using three elements: , , and .
3.2. Conformable Chebyshev Chaotic Maps (CCCM)
4. Proposed IBE Transformation Model for PKC under Human-Centered IoT Environments
4.1. Setup Phase
- Private Key Generator (PKG) selects any к users who refuse to work together. The minimum bit size of the user’s identity is then determined by the security limitation. Now, let be a huge prime, s. t. and let be a subgroup of the multiplicative group with prime order where is an order prime generator, and is a random rational number. Suppose that 𝑣 and and 𝑣 are the public key and secret key of PKG.
- PKG chooses private info at random, where and the consistent public info , where .
- Each user has a distinct -bit identity , where , .
- Express the hash function
4.2. Key Generation Phase
- A user gives PKG her/his hashed identification , where , .
- PKG examines whether an identity follows a given pattern. At that point, the identity is verified, PKG uses its secret information to compute .
- 3.
- PKG secretly transmits to as ’s private key.
- 4.
- checks whether the condition holds, where can be deduced from public data without any disagreement.
4.3. IBE Transformation Model for PKC
- a.
- Describe the formation of the identity
- b.
- Calculate the private key according to the instructions provided by the key generation (KG) process
4.4. Verification of the Transformation Mechanism
- Describe the identity prearrangement for as .
- For example, during the key generation step, will receive their secret value. Now is translated into an ID-based encryption model as , where is determined by Equation (3), and is determined by Equation (4). In these lines, the original signature structure based on conformable Chebyshev chaotic maps can be rewritten as , where and .
5. Security Examination and Performance Investigation
5.1. Security Examination
- Else, if is true, it generates an arbitrary and processes , otherwise sets and . mu is a special notation in this case.
- adds the tuple to and returns to .
- If is true. Then the -inquiry method is executed to make the connecting tuple on . Then it uses to respond to the decryption question.
- If is true, and the decryption inquiry is executed by with and the response of the challenger are transferred back to .
- The challenger receives and from . The challenger responds to the PKC’s s. t. is the encryption of for any coin
- executes the -query method to retrieve so that and responds with a to .
5.2. Performance Investigation
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ref. | Related Works | Limitations of Related Works | Our Proposed Scheme |
---|---|---|---|
Boneh and Franklin [15,16] | Identity-based encryption from the Weil pairing was projected. | The scheme has a high computation processing time. | Our proposed IBE transformation model provides an extremely low computational processing time. |
Sakai–Kasahara [17] | A bilinear pairing-based IBE scheme, which is faster than the Boneh and Franklin scheme, was reported. | The scheme possesses computationally intensive characteristics, which limits its usefulness in lightweight IoT-centered environments. | The projected IBE transformation model supports resource-constrained lightweight devices in IoT and human-centered environments. |
Liu et al. [21] | An efficient, provably secure IBS technique that uses multi-time usage of offline storage was proposed. | It is seen to take a long time for signing a few messages. This poses a significant limitation, especially when it is applied in complex wireless networks. | Our new model provides the desired offline storage and client-friendliness compared to the IBS technique that uses multi-time usage of offline storage. |
Liu and Zhou [39] | An efficient IBE scheme with short ciphertexts was presented. | The model can be executed ‘offline’ or inside some powerful devices only. This limits its usefulness in extremely lightweight devices and applications. | Our new procedure is accomplished by interpreting a well-designed and secure conformable Chebyshev chaotic maps-based scheme into an equally robust ID-based cryptosystem under human-centered IoT environments. |
Lai et al. [42] | An ordinary IBE scheme was converted to an online/offline IBE scheme. | The method adopted to separate the computation of the receiver’s identity into offline and online phases is cumbersome, and the security is limited. | Our new model is secure in the ROM under the IND-sID-CCA. |
Xu, Wu, and Xie [43] | An IBE scheme for lightweight devices was reported. | The model requires powerful devices to process heavy computations in the offline encryption phase. Additionally, the model is based on bilinear pairing on elliptic curves and requires point multiplication. | The proposed model is designed based on a conformable Chebyshev chaotic map without changing the original PKC configuration. |
Pourasad, Ranjbarzadeh, and Mardani [46] | The work presents a novel method for digital image encryption leveraging chaos theory. | The scheme requires an extensive database for the digital images. | Our projected architecture showed that there is no need for an extensive public key database. |
Parida et al. [47] | The work presents elliptic curve-based image encryption and authentication model that uses a secure elliptic curve Diffie–Hellman key exchange to compute a shared session key with the enhanced ElGamal encoding scheme. | The model uses the secure Elliptic Curve Diffie–Hellman(ECDH) key exchange to compute a shared session key along with the improved ElGamal encoding scheme, resulting in point multiplication operations, which are computationally expensive. | At a relatively low computing cost, our configuration may be easily transmitted to an existing system. |
Pourjabbar Kari [48] | A new image encryption scheme based on hybrid chaotic maps was proposed. | The work extends the original grayscale image matrix to the square matrix by adding the sequences generated with proper chaotic maps to implement the first step of the diffusion phase. This procedure takes time and requires massive computational resources. | Our new model, which combines the strengths of conformable Chebyshev chaotic maps and the IBE, is robust, secure, and poses broad application prospects. |
Talhaoui and Wang [49] | The work proposes a new fractional one-dimensional chaotic map with a sizeable chaotic space. | A new fractional one-dimensional chaotic map with a large chaotic space was employed, resulting in a longer processing time and huge communication costs. | The proposed work is based on conformable Chebyshev chaotic maps. The development of the IBE scheme depends on Chebyshev polynomial and conformable calculus, which facilitates low communication costs. |
Symbol | Meaning |
---|---|
Conformable Chebyshev chaotic maps | |
Large prime number of bit length | |
Large prime factors of | |
Identity of user | |
An arbitrary rational number | |
Public key | |
𝑣 | Private key |
Hash function | |
Random number | |
Message |
Model | |||
---|---|---|---|
Lee and Liao [62] | 𝓝 | 𝓝 | |
Meshram and Meshram [63] | Ƴ | Ƴ | |
Meshram et al. [64] | Ƴ | Ƴ | |
Tahat et al. [65] | 𝓝 | 𝓝 | |
Proposed IBE Model | Ƴ | Ƴ |
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Meshram, C.; Imoize, A.L.; Aljaedi, A.; Alharbi, A.R.; Jamal, S.S.; Barve, S.K. A Provably Secure IBE Transformation Model for PKC Using Conformable Chebyshev Chaotic Maps under Human-Centered IoT Environments. Sensors 2021, 21, 7227. https://doi.org/10.3390/s21217227
Meshram C, Imoize AL, Aljaedi A, Alharbi AR, Jamal SS, Barve SK. A Provably Secure IBE Transformation Model for PKC Using Conformable Chebyshev Chaotic Maps under Human-Centered IoT Environments. Sensors. 2021; 21(21):7227. https://doi.org/10.3390/s21217227
Chicago/Turabian StyleMeshram, Chandrashekhar, Agbotiname Lucky Imoize, Amer Aljaedi, Adel R. Alharbi, Sajjad Shaukat Jamal, and Sharad Kumar Barve. 2021. "A Provably Secure IBE Transformation Model for PKC Using Conformable Chebyshev Chaotic Maps under Human-Centered IoT Environments" Sensors 21, no. 21: 7227. https://doi.org/10.3390/s21217227
APA StyleMeshram, C., Imoize, A. L., Aljaedi, A., Alharbi, A. R., Jamal, S. S., & Barve, S. K. (2021). A Provably Secure IBE Transformation Model for PKC Using Conformable Chebyshev Chaotic Maps under Human-Centered IoT Environments. Sensors, 21(21), 7227. https://doi.org/10.3390/s21217227