An Efficient Electronic Cash System Based on Certificateless Group Signcryption Scheme Using Conformable Chaotic Maps
Abstract
:1. Introduction
1.1. Contributions
1.2. Paper Organization
2. Related Works
3. Background and Materials
3.1. Chebyshev Chaotic Polynomials
- (1)
- The chaotic property: The CSP map is defined as with degree , is a chaotic map accompanying with the (invariant density) functional for the positive Lyapunov exponent .
- (2)
- Semi-group property: The possessions of a semi-group meet the following criteria:
- (1)
- The discrete log’s (DL) task is to invent an integer with the end goal given two items and .
- (2)
- The Diffie–Hellman problem (DHP) task is to measure the element due to three elements , , and .
3.2. Conformable Chebyshev Chaotic Maps (CCCM)
4. The Proposed Certificateless Group Signcryption Scheme Based on Conformable Chaotic Maps
4.1. Setup
4.2. Partial Private Key Generation (PPKG)
4.3. Private Key Generation (PKG)
4.4. User Key Generation (UKG)
4.5. Signcryption
4.6. Verification
4.7. Opening
5. Security Investigation of the Proposed CGSS-CCM ECS Scheme
6. Proposed Electronic Cash System Based on CGSS Using Conformable Chaotic Maps
6.1. Initialization
6.2. Joining Phase
6.3. Withdrawal Phase
6.4. Payment Phase
6.5. Deposit Phase
6.6. Identity Revocation Phase
7. Security Analysis of the Proposed CGSS-CCM ECS Scheme
7.1. Unforgeability
7.2. Anonymity
8. Performance Comparison
9. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Zhang, J.; Wu, Q.; Wang, Y. A new efficient group signature with forward security. Informatica 2005, 29, 321–325. [Google Scholar]
- Chaum, D.; van Heyst, E. Advances in Cryptology—EUROCRYPT ’91. Trans. Comput. Sci. XI 1991, 547, 257–265. [Google Scholar] [CrossRef]
- Shamir, A. Identity-Based Cryptosystems and Signature Schemes. In Advances in Cryptology; Springer: Amsterdam, The Netherlands, 2000; pp. 47–53. [Google Scholar]
- Zhang, J.; Mao, J. A novel identity-based multi-signcryption scheme. Comput. Commun. 2009, 32, 14–18. [Google Scholar] [CrossRef]
- Wan, Z.; Weng, J.; Li, J. Security Mediated Certificateless Signatures Without Pairing. J. Comput. 2010, 5, 1862–1869. [Google Scholar] [CrossRef]
- Park, S.; Kim, S.; Won, D. ID-based group signature. Electron. Lett. 1997, 33, 1616–1617. [Google Scholar] [CrossRef]
- Tseng, Y.-M.; Jan, J.-K. A novel ID-based group signature. Inf. Sci. 1999, 120, 131–141. [Google Scholar] [CrossRef]
- Al-Riyami, S.S.; Paterson, K.G. Certificateless Public Key Cryptography. In Advances in Autonomous Robotics; Springer: Amsterdam, The Netherlands, 2003; Volume 2003, pp. 452–473. [Google Scholar]
- Ma, C.; Ao, F.; He, D. Certificateless group inside signature. In Proceedings of the Autonomous Decentralized Systems, 2005. ISADS 2005, Chengdu, China, 4–8 April 2005; IEEE: Manhattan, NY, USA, 2005; pp. 194–200. [Google Scholar]
- Li, F.; Shirase, M.; Takagi, T. Certificateless Hybrid Signcryption. Adv. Knowl. Discov. Data Min. 2009, 2009, 112–123. [Google Scholar] [CrossRef] [Green Version]
- Rastegari, P.; Susilo, W.; Dakhlalian, M. Efficient Certificateless Signcryption in the Standard Model: Revisiting Luo and Wan’s Scheme from Wireless Personal Communications (2018). Comput. J. 2019, 62, 1178–1193. [Google Scholar] [CrossRef]
- Lee, T.-F. Provably Secure Anonymous Single-Sign-On Authentication Mechanisms Using Extended Chebyshev Chaotic Maps for Distributed Computer Networks. IEEE Syst. J. 2018, 12, 1499–1505. [Google Scholar] [CrossRef]
- Zheng, Y. Digital signcryption or how to achieve cost (signature & encryption). In Advances in Cryptology—CRYPTO ’97; Springer: Amsterdam, The Netherlands, 1997; pp. 165–179. [Google Scholar]
- Zheng, Y.; Imai, H. How to construct efficient signcryption schemes on elliptic curves. Inf. Process. Lett. 1998, 68, 227–233. [Google Scholar] [CrossRef]
- Bao, F.; Deng, R.H. A signcryption scheme with signature directly verifiable by public key. Comput. Vis. 1998, 55–59. [Google Scholar] [CrossRef]
- Daniel, R.; Rajsingh, E.B.; Silas, S. A forward secure signcryption scheme with ciphertext authentication for e-payment systems using conic curve cryptography. J. King Saud Univ. Comput. Inf. Sci. 2021, 33, 86–98. [Google Scholar] [CrossRef]
- Gamage, C.; Leiwo, J.; Zheng, Y. Encrypted Message Authentication by Firewalls. In Public Key Cryptography; Springer: Berlin/Heidelberg, Germany, 1999; pp. 69–81. [Google Scholar]
- Diffie, W.; Hellman, M.E. New directions in cryptography. IEEE Trans. Inf. Theory 1976, 22, 644–654. [Google Scholar] [CrossRef] [Green Version]
- Chow, S.S.M.; Yiu, S.M.; Hui, L.C.K.; Chow, K.P. Efficient Forward and Provably Secure ID-Based Signcryption Scheme with Public Verifiability and Public Ciphertext Authenticity. In Information Security and Cryptology—ICISC 2003; Springer: Amsterdam, The Netherlands, 2004; pp. 352–369. [Google Scholar]
- Ullah, I.; Alkhalifah, A.; Rehman, S.U.; Kumar, N.; Khan, M.A. An Anonymous Certificateless Signcryption Scheme for Internet of Health Things. IEEE Access 2021, 9, 101207–101216. [Google Scholar] [CrossRef]
- Han, Y.; Yang, X.; Hu, Y. Signcryption based on elliptic curve and its multi-party schemes. In Proceedings of the 3rd International Conference on Information Security, Shanghai, China, 14–16 November 2004; ACM: New York, NY, USA, 2004; pp. 216–217. [Google Scholar]
- Elkamchouchi, H.; Nasr, M.; Ismail, R. A new efficient strong proxy signcryption scheme based on a combination of hard problems. In Proceedings of the 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, USA, 11–14 October 2009; IEEE: Manhattan, NY, USA, 2009; pp. 5123–5127. [Google Scholar]
- Iqbal, W.; Afzal, M.; Ahmad, F. An efficient elliptic curve based signcryption scheme for firewalls. In Proceedings of the 2013 2nd National Conference on Information Assurance (NCIA), Rawalpindi, Pakistan, 11–12 December 2013; IEEE: Manhattan, NY, USA, 2013; pp. 67–72. [Google Scholar]
- Chaudhry, S.A.; Farash, M.S.; Naqvi, H.; Sher, M. A secure and efficient authenticated encryption for electronic payment systems using elliptic curve cryptography. Electron. Commer. Res. 2016, 16, 113–139. [Google Scholar] [CrossRef]
- Ahmed, F.; Bashir, F.; Masood, A. A Publicly Verifiable Low Cost Signcryption Scheme Ensuring Confidentiality. In Proceedings of the 2010 Second International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China, 24–25 April 2010; IEEE: Manhattan, NY, USA, 2010; Volume 1, pp. 232–235. [Google Scholar]
- Gutub, A.; Aljuaid, N.; Khan, E. Counting-based secret sharing technique for multimedia applications. Multimed. Tools Appl. 2019, 78, 5591–5619. [Google Scholar] [CrossRef]
- Wang, H.; Cao, J.; Zhang, Y. Untraceable Electronic Cash System in the Internet of Things. In Access Control Management in Cloud Environments; Springer: Berlin/Heidelberg, Germany, 2020; pp. 43–63. [Google Scholar] [CrossRef]
- Maitland, G.; Boyd, C. Fair Electronic Cash Based on a Group Signature Scheme. Comput. Vis. 2001, 461–465. [Google Scholar] [CrossRef]
- Lee, H.J.; Choi, M.S.; Rhee, C.S. Traceability of double spending in secure electronic cash system. In Proceedings of the 2003 International Conference on Computer Networks and Mobile Computing, 2003. ICCNMC 2003, Shanghai, China, 20–23 October 2003; IEEE: Manhattan, NY, USA, 2004; pp. 330–333. [Google Scholar]
- Nishide, T.; Sakurai, K. Security of Offline Anonymous Electronic Cash Systems against Insider Attacks by Untrusted Authorities Revisited. In Proceedings of the 2011 Third International Conference on Intelligent Networking and Collaborative Systems, Fukuoka, Japan, 30 November–2 December 2011; IEEE: Manhattan, NY, USA, 2011; pp. 656–661. [Google Scholar]
- Kutubi, M.A.A.R.; Alam, K.M.R.; Morimoto, Y. A Simplified Scheme for Secure Offline Electronic Payment Systems. High-Confid. Comput. 2021, 1, 100031. [Google Scholar] [CrossRef]
- Islam, S.H.; Amin, R.; Biswas, G.P.; Obaidat, M.S.; Khan, M.K. Provably Secure Pairing-Free Identity-Based Partially Blind Signature Scheme and Its Application in Online E-cash System. Arab. J. Sci. Eng. 2016, 41, 3163–3176. [Google Scholar] [CrossRef]
- Xu, Y.; Li, J. An Exchange Center Based Digital Cash Payment Solution. In Advances in Intelligent Systems and Computing; Springer: Amsterdam, The Netherlands, 2021; pp. 265–274. [Google Scholar]
- Shamsabadi, F.A.; Chehelcheshmeh, S.B. A cloud-based mobile payment system using identity-based signature providing key revocation. J. Supercomput. 2021, 1–25. [Google Scholar] [CrossRef]
- Mason, J.C.; Handscomb, D.C. Chebyshev Polynomials; Chapman & Hall/CRC: Boca Raton, FL, USA, 2003. [Google Scholar]
- Meshram, C.; Li, C.-T.; Meshram, S.G. An efficient online/offline ID-based short signature procedure using extended chaotic maps. Soft Comput. 2019, 23, 747–753. [Google Scholar] [CrossRef]
- Meshram, C.; Lee, C.-C.; Ranadive, A.S.; Li, C.-T.; Meshram, S.G.; Tembhurne, J.V. A subtree-based transformation model for cryptosystem using chaotic maps under cloud computing environment for fuzzy user data sharing. Int. J. Commun. Syst. 2020, 33, e4307. [Google Scholar] [CrossRef]
- Meshram, C.; Ibrahim, R.W.; Obaid, A.J.; Meshram, S.G.; Meshram, A.; El-Latif, A.M.A. Fractional chaotic maps based short signature scheme under human-centered IoT environments. J. Adv. Res. 2020, 32, 139–148. [Google Scholar] [CrossRef]
- Meshram, C.; Lee, C.-C.; Meshram, S.G.; Meshram, A. OOS-SSS: An Efficient Online/Offline Subtree-Based Short Signature Scheme Using Chebyshev Chaotic Maps for Wireless Sensor Network. IEEE Access 2020, 8, 80063–80073. [Google Scholar] [CrossRef]
- Zhang, L. Cryptanalysis of the public key encryption based on multiple chaotic systems. Chaos Solitons Fractals 2008, 37, 669–674. [Google Scholar] [CrossRef]
- Anderson, D.; Camrud, E.; Ulness, D.J. On the nature of the conformable derivative and its applications to physics. arXiv 2018, arXiv:1810.02005. [Google Scholar]
- Meshram, C.; Ibrahim, R.W.; Obaidat, M.S.; Sadoun, B.; Meshram, S.G.; Tembhurne, J.V. An effective mobile-healthcare emerging emergency medical system using conformable chaotic maps. Soft Comput. 2021, 25, 8905–8920. [Google Scholar] [CrossRef]
- Meshram, C.; Powar, P.L.; Obaidat, M.S.; Lee, C.; Meshram, S.G. Efficient online/offline IBSS protocol using partial discrete logarithm for WSNs. IET Networks 2018, 7, 363–367. [Google Scholar] [CrossRef]
- Meshram, C.; Lee, C.-C.; Li, C.-T.; Chen, C.-L. A secure key authentication scheme for cryptosystems based on GDLP and IFP. Soft Comput. 2017, 21, 7285–7291. [Google Scholar] [CrossRef]
- Chen, Y.; Chou, J.-S.; Sun, H.-M.; Cho, M.-H. A novel electronic cash system with trustee-based anonymity revocation from pairing. Electron. Commer. Res. Appl. 2011, 10, 673–682. [Google Scholar] [CrossRef]
- Eslami, Z.; Talebi, M. A new untraceable off-line electronic cash system. Electron. Commer. Res. Appl. 2011, 10, 59–66. [Google Scholar] [CrossRef]
- Zhang, L.; Zhang, F.; Qin, B.; Liu, S. Provably-secure electronic cash based on certificateless partially-blind signatures. Electron. Commer. Res. Appl. 2011, 10, 545–552. [Google Scholar] [CrossRef]
- Chang, C.-C.; Chen, W.-Y.; Chang, S.-C. A highly efficient and secure electronic cash system based on secure sharing in cloud environment. Secur. Commun. Netw. 2016, 9, 2476–2483. [Google Scholar] [CrossRef] [Green Version]
- Kang, B.; Xu, D. Secure Electronic Cash Scheme with Anonymity Revocation. Mob. Inf. Syst. 2016, 2016, 1–10. [Google Scholar] [CrossRef] [Green Version]
- Meshram, C.; AlSanad, A.; Tembhurne, J.V.; Shende, S.W.; Kalare, K.W.; Meshram, S.G.; Akbar, M.A.; Gumaei, A. A Provably Secure Lightweight Subtree-Based Short Signature Scheme with Fuzzy User Data Sharing for Human-Centered IoT. IEEE Access 2021, 9, 3649–3659. [Google Scholar] [CrossRef]
- Lee, C.-C.; Hsu, C.-W. A secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps. Nonlinear Dyn. 2012, 71, 201–211. [Google Scholar] [CrossRef]
- Lee, C.-C.; Li, C.-T.; Hsu, C.-W. A three-party password-based authenticated key exchange protocol with user anonymity using extended chaotic maps. Nonlinear Dyn. 2013, 73, 125–132. [Google Scholar] [CrossRef]
- Mohanty, S.; Majhi, B.; Das, S. A secure electronic cash based on a certificateless group signcryption scheme. Math. Comput. Model. 2013, 58, 186–195. [Google Scholar] [CrossRef]
- Imoize, A.; Adedeji, O.; Tandiya, N.; Shetty, S. 6G Enabled Smart Infrastructure for Sustainable Society: Opportunities, Challenges, and Research Roadmap. Sensors 2021, 21, 1709. [Google Scholar] [CrossRef]
Symbol | Meaning |
---|---|
Conformable Chebyshev chaotic maps | |
Large integer | |
Large prime numbers | |
Identity of | |
Identity of | |
Identity of client | |
An arbitrary rational number | |
Master secret key | |
Group’s public key | |
Group’s private key | |
Cipher | |
Hash function | |
Public constraint | |
Message | |
Key |
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Meshram, C.; Imoize, A.L.; Aljaedi, A.; Alharbi, A.R.; Jamal, S.S.; Barve, S.K. An Efficient Electronic Cash System Based on Certificateless Group Signcryption Scheme Using Conformable Chaotic Maps. Sensors 2021, 21, 7039. https://doi.org/10.3390/s21217039
Meshram C, Imoize AL, Aljaedi A, Alharbi AR, Jamal SS, Barve SK. An Efficient Electronic Cash System Based on Certificateless Group Signcryption Scheme Using Conformable Chaotic Maps. Sensors. 2021; 21(21):7039. https://doi.org/10.3390/s21217039
Chicago/Turabian StyleMeshram, Chandrashekhar, Agbotiname Lucky Imoize, Amer Aljaedi, Adel R. Alharbi, Sajjad Shaukat Jamal, and Sharad Kumar Barve. 2021. "An Efficient Electronic Cash System Based on Certificateless Group Signcryption Scheme Using Conformable Chaotic Maps" Sensors 21, no. 21: 7039. https://doi.org/10.3390/s21217039