## Journal of Applied Mathematics

### A Provably Secure Proxy Signcryption Scheme Using Bilinear Pairings

#### Abstract

As people in modern societies are busier than any human era and computer network has profound impact on how people work and live through fast and convenient information exchange, people need more help from each other to accomplish more work via network connections in limited period of time. Therefore, privilege delegation mechanism has become a necessary service in modern enterprises and organizations. Proxy signcryption scheme provides a secure privilege delegation mechanism for a person to delegate his privilege to his proxy agent to accomplish things. In 2010, Lin et al. had proposed an efficient signcryption scheme using bilinear pairings. However, we found that the proxy signcryption scheme of Lin et al. is vulnerable to the chosen warrant attack. A provably secure proxy signcryption scheme using bilinear pairings is introduced accordingly. In terms of performance efficiency, the proposed scheme is superior to other existing schemes. In addition, a new security model is proposed to describe proxy signcryption scheme; based on the security model we show that the proposed scheme is provably secure in terms of indistinguishability under adaptive chosen ciphertext attack (IND-CCA2), unforgeability under adaptive chosen message attack (EF-CMA), and unforgeability under adaptive chosen warrant attack (EF-CWA).

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 454393, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305774

Digital Object Identifier
doi:10.1155/2014/454393

#### Citation

Lo, Nai-Wei; Tsai, Jia-Lun. A Provably Secure Proxy Signcryption Scheme Using Bilinear Pairings. J. Appl. Math. 2014 (2014), Article ID 454393, 10 pages. doi:10.1155/2014/454393. https://projecteuclid.org/euclid.jam/1425305774

#### References

• W. Diffie and M. E. Hellman, “New directions in cryptography,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. IT-22, no. 6, pp. 644–654, 1976.
• R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the Association for Computing Machinery, vol. 21, no. 2, pp. 120–126, 1978.
• D. Boneh and M. Franklin, “Identity-based encryption from the Weil pairing,” in Advances in Cryptology–-CRYPTO 2001, vol. 2139 of Lecture Notes in Computer Science, pp. 213–229, Springer, Berlin, Germany, 2001.
• C. Gentry and A. Silverberg, “Hierarchical ID-based cryptography,” in Advances in Cryptology–-ASIACRYPT 2002, vol. 2501 of Lecture Notes in Computer Science, pp. 548–566, Springer, Berlin, Germany, 2002.
• D. Boneh, B. Lynn, and H. Shacham, “Short signatures from the Weil pairing,” in Advances in Cryptology–-ASIACRYPT 2001, vol. 2248 of Lecture Notes in Computer Science, pp. 514–532, Springer, Berlin, Germany, 2001.
• F. Zhang and K. Kim, “ID-based blind signature and ring signature from pairings,” in Advances in Cryptology–-ASIACRYPT 2002, vol. 2501 of Lecture Notes in Computer Science, pp. 533–547, Springer, Berlin, Germany, 2002.
• B. C. Neuman, “Proxy-based authorization and accounting for distributed systems,” in Proceedings of the IEEE 13th International Conference on Distributed Computing Systems, pp. 283–291, May 1993.
• V. Varadharajan, P. Allen, and S. Black, “An analysis of the proxy problem in distributed systems,” in Proceedings of the IEEE Computer Society Symposium on Research in Security and Privacy, pp. 255–275, May 1991.
• J. L. Tsai, N. W. Lo, and T. C. Wu, “Secure delegation-based authentication protocol for wireless roaming service,” IEEE Communications Letters, vol. 16, no. 7, pp. 1100–11102, 2012.
• M. Mambo, K. Usuda, and E. Okamoto, “Proxy signatures for delegating signing operation,” in Proceedings of the 3rd ACM Conference on Computer and Communications Security, pp. 48–57, March 1996.
• R. Lu, X. Dong, and Z. Cao, “Designing efficient proxy signature schemes for mobile communication,” Science in China, Series F: Information Sciences, vol. 51, no. 2, pp. 183–195, 2008.
• F. Li, M. Shirase, and T. Takagi, “Cryptanalysis of efficient proxy signature schemes for mobile communication,” Science China. Information Sciences, vol. 53, no. 10, pp. 2016–2021, 2010.
• A. Wang, J. Li, and Z. Wang, “A provably secure proxy signature scheme from bilinear pairings,” Journal of Electronics, vol. 27, no. 3, pp. 298–304, 2010.
• D. Hongzhen and W. Qiaoyan, “An efficient identity-based short signature scheme from bilinear pairings,” in Proceedings of the International Conference on Computational Intelligence and Security (CIS '07), pp. 725–729, Haerbin, China, December 2007.
• Y.-C. Lin, T.-C. Wu, and J.-L. Tsai, “ID-based aggregate proxy signature scheme realizing warrant-based delegation,” JISE. Journal of Information Science and Engineering, vol. 29, no. 3, pp. 441–457, 2013.
• J. L. Tsai, N. W. Lo, and T. C. Wu, “Numerical analysis of stress on pump blade by one-way coupled fluid-structure simulation,” Information Technology and Control, vol. 42, no. 4, pp. 315–324, 2014.
• Y. Zheng, “Digital signcryption or how to achieve cost(signature & encryption) $\ll$ cost(signature) + cost(encryption),” in Advances in Cryptology–-CRYPTO 1997, pp. 165–179, Springer, 1997.
• Y. Zheng, “Signcryption and its applications in efficient public key solutions,” in Proceedings of the Information Security Workshop, pp. 291–312, Springer, 1997.
• F. Bao and R. H. Deng, “A signcryption scheme with signature directly verifiable by public key,” in Proceedings of the Workshop on Public Key Cryptography, pp. 55–59, Springer, 1998.
• H. Petersen and M. Michels, “Cryptanalysis and improvement of signcryption schemes,” IEE Proceedings Computers and Digital Techniques, vol. 145, no. 2, pp. 149–151, 1998.
• W.-H. He and T.-C. Wu, “Cryptanalysis and improvement of Petersen-Michels signcryption scheme,” IEE Proceedings: Computers and Digital Techniques, vol. 146, no. 2, pp. 123–124, 1999.
• J.-L. Tsai, “Convertible multi-authenticated encryption scheme with one-way hash function,” Computer Communications, vol. 32, no. 5, pp. 783–786, 2009.
• C. Gamage, J. Leiwo, and Y. Zheng, “An efficient scheme for secure message transmission using proxy-signcryption,” in Proceedings of the 22nd Australasian Computer Science Conference, pp. 420–431, Springer, 1999.
• P. S. L. M. Barreto, H. Y. Kim, B. Lynn, and M. Scott, “Efficient algorithms for pairing-based cryptosystems,” in Advances in Cryptology–-CRYPTO 2002, vol. 2442 of Lecture Notes in Computer Science, pp. 354–368, Springer, Berlin, Germany, 2002.
• P. S. L. M. Barreto, B. Lynn, and M. Scott, “On the selection of pairing-friendly groups,” in Selected Areas in Cryptography, vol. 3006 of Lecture Notes in Computer Science, pp. 17–25, Springer, Berlin, Germany, 2004.
• X. Li and K. Chen, “Identity based proxy-signcryption scheme from pairings,” in Proceedings of the IEEE International Conference on Services Computing (SCC '04), pp. 494–497, September 2004.
• Q. Wang and Z. Cao, “Efficient ID-based proxy signature and proxy signcryption from bilinear pairings,” in Computational Intelligence and Security, pp. 167–172, Springer, 2005.
• S. Duan, Z. Cao, and Y. Zhou, “Secure delegation-by-warrant ID-based proxy signcryption scheme,” in Proceedings of Computational Intelligence and Security Conference (CIS '05), vol. 3802 of LNAI, pp. 445–450, Springer, 2005.
• S. Duan and Z. Cao, “Efficient and provably secure multi-receiver identity-based signcryption,” in Information Security and Privacy, pp. 195–206, Springer, 2006.
• H. Elkamchouchi and Y. Abouelseoud, A new proxy identity-based signcryption scheme for partial delegation of signing rights, Cryptology ePrint Archive, Report, 2008, http://eprint.iacr.org/.
• H.-Y. Lin, T.-S. Wu, S.-K. Huang, and Y.-S. Yeh, “Efficient proxy signcryption scheme with provable CCA and CMA security,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1850–1858, 2010.
• C.-L. Hsu and H.-Y. Lin, “Pairing-based strong designated verifier proxy signature scheme with low cost,” Security and Communication Networks, vol. 5, no. 5, pp. 517–522, 2012.
• H.-Y. Lin, T.-S. Wu, and S.-K. Huang, “Certificate-based secure three-party signcryption scheme with low costs,” JISE. Journal of Information Science and Engineering, vol. 28, no. 4, pp. 739–753, 2012.
• J. L. Tsai, N. W. Lo, and T. C. Wu, “ID-Based authenticated group key agreement protocol from bilinear pairings for wireless mobile devices,” Adhoc & Sensor Wireless Networks, vol. 17, no. 3-4, pp. 221–231, 2013.
• T. S. Wu and H. Y. Lin, “A novel probabilistic signature based on bilinear square Diffie-Hellman problem and its extension,” Security and Communication Networks, vol. 6, no. 6, pp. 757–764, 2013.
• J. L. Tsai, N. W. Lo, and T. C. Wu, “Secure handover authentication protocol based on bilinear pairings,” Wireless Personal Communications, vol. 73, no. 3, pp. 1037–1047, 2013.
• M. Scott, N. Costigan, and W. Abdulwahab, “Implementing cryptographic pairings on smartcards,” in Cryptographic Hardware and Embedded Systems–-CHES 2006, pp. 134–147, Springer, 2006. \endinput