# American Institute of Mathematical Sciences

## An efficient RFID anonymous batch authentication protocol based on group signature

 1 School of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, Shaanxi, China 2 The State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China

* Corresponding author: Lanjun Dang

Received  June 2017 Revised  November 2017 Published  November 2018

In order to address the anonymous batch authentication problem of a legal reader to many tags in RFID (Radio Frequency Identification) system, an efficient RFID anonymous batch authentication protocol was proposed based on group signature. The anonymous batch authentications of reader to many tags are achieved by using a one-time group signature based on Hash function; the authentication of the tag to the reader is realized by employing MAC (Message Authentication Code). The tag's anonymity is achieved via the dynamic TID (Temporary Identity) instead of the tag's identity. The proposed protocol can resist replay attacks by using random number. Theoretical analyses show that, the proposed protocol reaches the expected security goals. Compared with the protocol proposed by Liu, the proposed protocol reduces the computation and storage of the server and tag while improving the security.

Citation: Jie Xu, Lanjun Dang. An efficient RFID anonymous batch authentication protocol based on group signature. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2019102
##### References:
 [1] M. Akram and M. Sarwar, Novel applications of m-polar fuzzy hypergraphs, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 32 (2017), 2747-2762. [2] W.-S. Bae, Formal verification of an RFID authentication protocol based on Hash function and secret code, Wireless Personal Communications, 79 (2014), 2595-2609. [3] A. Basar and M. Y. Abbasi, On ordered bi-ideals in ordered-semigroups, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 645-652. doi: 10.1080/09720529.2015.1130474. [4] L. Batina, Y. K. Lee and S. Seys, et al., Extending ECC-based RFID authentication protocols to privacy-preserving multi-party grouping proofs, Personal and Ubiquitous Computing, 16 (2012), 323-335. [5] X. Cao, W. Kou and H. Li, Secure mobile IP registration scheme with AAA from parings to reduce registration delay, CIS 2006, New York: IEEE Press, 2006, 1037-1042 [6] W. Gao and W. F. Wang, A tight neighborhood union condition on fractional (g, f, n', m)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298. doi: 10.4064/cm6959-8-2016. [7] J. B. Gurubani, H. Thakkar and D. R. Patel, Improvements over extended LMAP+: RFID authentication protocol, Proceedings of 6th International Conference on Trust Management IFIPTM, Surat: Springer Boston, 2012, 225-231. [8] D. He, N. Kumar and N. Chilamkurti, et al., Lightweight ECC based RFID authentication integrated with an ID verifier transfer protocol, Journal of Medical Systems, 38 (2014), 116. [9] A. Juels, Strengthening EPC Tag against Cloning, Proceedings of ACM Workshop on Wireless Security, Cologne, 2005, 67-76. [10] M. Kianersi, M. Gardeshi and M. Arjmand, SULMA: A secure ultra light-weight mutual authentication protocol for lowcost RFID tags, International Journal of UbiComp (IJU), 2 (2011), 17-24. [11] S. Li, Handwritten character recognition technology combined with artificial intelligence, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 167-178. [12] H. Liu, X. Li and J. Bai, A new one-time group signature based on Hash function, Journal of Beijing Electronic Science and Technology Institute, 21 (2013), 25-29. [13] J. Liu, R.-J. Chen and D.-S. Yan, et al., Efficient identity-based ring signature for RFID authentication scheme, Proceeding of the IEEE International Conference on RFID-Technology and Applications, Guangzhou: IEEE, 2010, 7-10. [14] Y. L. Liu, X. L. Qin and B. H. Li, et al., A Forward-Secure Grouping-proof protocol for Multiple RFID tags, International Journal of Computational Intelligence Systems, 5 (2012), 824-833. [15] M. Ohkubo, K. Suzuki and S. Kinoshita, Hash-chain based forward secure privacy protection scheme for low-cost RFID, Proceedings of the 2004 Symposium on Cryptography and Information Security (SCIS 2004), Sendai, 2004, 719-724. [16] S. E. Sarma, S. A. Weis and D. W. Engels, RFID systems and security and privacy implications, Proceedings of the 4th International Workshop on Cryptographic Hardware and Embedded Systems (CHES 2002), LNCS, 2523, Berlin: Springer-Verlag, 2003, 454-469. [17] Y. Tian, G. L. Chen and J. Li, A New Ultralightweight RFID Authentication Protocol with Permutation, IEEE Communications Letters, 16 (2012), 702-705. [18] S. A. Weis, S. E. Sarma, R. L. Rivest and D. W. Engels, Security and privacy aspects of lowcost radio frequency identification systems, Proceedings of the 1st International Conference on Security in Pervasive Computing, LNCS, 2802, Berlin: Springer-Verlag, 2004, 719-724. [19] J. P. de Wet and S. A. van Aardt, Traceability of locally Hamiltonian and locally traceable graphs, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 245-262.

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##### References:
 [1] M. Akram and M. Sarwar, Novel applications of m-polar fuzzy hypergraphs, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 32 (2017), 2747-2762. [2] W.-S. Bae, Formal verification of an RFID authentication protocol based on Hash function and secret code, Wireless Personal Communications, 79 (2014), 2595-2609. [3] A. Basar and M. Y. Abbasi, On ordered bi-ideals in ordered-semigroups, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 645-652. doi: 10.1080/09720529.2015.1130474. [4] L. Batina, Y. K. Lee and S. Seys, et al., Extending ECC-based RFID authentication protocols to privacy-preserving multi-party grouping proofs, Personal and Ubiquitous Computing, 16 (2012), 323-335. [5] X. Cao, W. Kou and H. Li, Secure mobile IP registration scheme with AAA from parings to reduce registration delay, CIS 2006, New York: IEEE Press, 2006, 1037-1042 [6] W. Gao and W. F. Wang, A tight neighborhood union condition on fractional (g, f, n', m)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298. doi: 10.4064/cm6959-8-2016. [7] J. B. Gurubani, H. Thakkar and D. R. Patel, Improvements over extended LMAP+: RFID authentication protocol, Proceedings of 6th International Conference on Trust Management IFIPTM, Surat: Springer Boston, 2012, 225-231. [8] D. He, N. Kumar and N. Chilamkurti, et al., Lightweight ECC based RFID authentication integrated with an ID verifier transfer protocol, Journal of Medical Systems, 38 (2014), 116. [9] A. Juels, Strengthening EPC Tag against Cloning, Proceedings of ACM Workshop on Wireless Security, Cologne, 2005, 67-76. [10] M. Kianersi, M. Gardeshi and M. Arjmand, SULMA: A secure ultra light-weight mutual authentication protocol for lowcost RFID tags, International Journal of UbiComp (IJU), 2 (2011), 17-24. [11] S. Li, Handwritten character recognition technology combined with artificial intelligence, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 167-178. [12] H. Liu, X. Li and J. Bai, A new one-time group signature based on Hash function, Journal of Beijing Electronic Science and Technology Institute, 21 (2013), 25-29. [13] J. Liu, R.-J. Chen and D.-S. Yan, et al., Efficient identity-based ring signature for RFID authentication scheme, Proceeding of the IEEE International Conference on RFID-Technology and Applications, Guangzhou: IEEE, 2010, 7-10. [14] Y. L. Liu, X. L. Qin and B. H. Li, et al., A Forward-Secure Grouping-proof protocol for Multiple RFID tags, International Journal of Computational Intelligence Systems, 5 (2012), 824-833. [15] M. Ohkubo, K. Suzuki and S. Kinoshita, Hash-chain based forward secure privacy protection scheme for low-cost RFID, Proceedings of the 2004 Symposium on Cryptography and Information Security (SCIS 2004), Sendai, 2004, 719-724. [16] S. E. Sarma, S. A. Weis and D. W. Engels, RFID systems and security and privacy implications, Proceedings of the 4th International Workshop on Cryptographic Hardware and Embedded Systems (CHES 2002), LNCS, 2523, Berlin: Springer-Verlag, 2003, 454-469. [17] Y. Tian, G. L. Chen and J. Li, A New Ultralightweight RFID Authentication Protocol with Permutation, IEEE Communications Letters, 16 (2012), 702-705. [18] S. A. Weis, S. E. Sarma, R. L. Rivest and D. W. Engels, Security and privacy aspects of lowcost radio frequency identification systems, Proceedings of the 1st International Conference on Security in Pervasive Computing, LNCS, 2802, Berlin: Springer-Verlag, 2004, 719-724. [19] J. P. de Wet and S. A. van Aardt, Traceability of locally Hamiltonian and locally traceable graphs, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 245-262.
A typical RFID system
The proposed RFID batch authentication protocol based on group signature
The comparison of the calculation time of server in the two protocols
The comparison of the storage amount of tag in the two protocols
The comparison of the storage amount of server in the two protocols
Notations
 $K_{ID_i}$ authentication key of each tag, used to authenticate a reader $K_{i}$ private key of each tag in the group signature scheme $X_{i}$ exclusive-OR of the Hash values of $n$ strings in one tag's private key $Y$ group public key $C_{i}$ exclusive-OR of the other $m$-1 tags' $X$ values except the tag that generated group signature $\sigma$ $\sigma =(\sigma_{1}, \sigma_{2}, \ldots, \sigma_{n}, C_{i})$, the group signature be generated by one tag ID$_{i}$ one tag's identity information $K$ MAC value of message $M$ under key $K$ $\vert\vert$ concatenation of two data
 $K_{ID_i}$ authentication key of each tag, used to authenticate a reader $K_{i}$ private key of each tag in the group signature scheme $X_{i}$ exclusive-OR of the Hash values of $n$ strings in one tag's private key $Y$ group public key $C_{i}$ exclusive-OR of the other $m$-1 tags' $X$ values except the tag that generated group signature $\sigma$ $\sigma =(\sigma_{1}, \sigma_{2}, \ldots, \sigma_{n}, C_{i})$, the group signature be generated by one tag ID$_{i}$ one tag's identity information $K$ MAC value of message $M$ under key $K$ $\vert\vert$ concatenation of two data
The security comparisons of the two protocols
 Mutualauthentication Taganonymity Messageconfidentiality Messageintegrity Messagefreshness The Protocol [13] $\backslash$ $\surd$ $\surd$ $\surd$ $\surd$ Our protocol $\surd$ $\surd$ $\surd$ $\surd$ $\surd$
 Mutualauthentication Taganonymity Messageconfidentiality Messageintegrity Messagefreshness The Protocol [13] $\backslash$ $\surd$ $\surd$ $\surd$ $\surd$ Our protocol $\surd$ $\surd$ $\surd$ $\surd$ $\surd$
The performance comparisons of the two protocols
 Tag'scalculation Server'scalculation Tag'sstorage Server'sstorage The protocol [13] 0 mSM+2$P$ 20$k(m$+2)bytes 20($k+m)$bytes Our protocol 82$h$ ($m$+81)$h$ 3260bytes (42$m$+20)bytes
 Tag'scalculation Server'scalculation Tag'sstorage Server'sstorage The protocol [13] 0 mSM+2$P$ 20$k(m$+2)bytes 20($k+m)$bytes Our protocol 82$h$ ($m$+81)$h$ 3260bytes (42$m$+20)bytes
The cryptography operation times of server (ms)
 Pairing Scalar multiplication Hash operation 3.16 0.79 0.0002
 Pairing Scalar multiplication Hash operation 3.16 0.79 0.0002