# American Institute of Mathematical Sciences

doi: 10.3934/amc.2021053
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Security analysis of public key encryption with filtered equality test

 Department of Computer Science and Engineering, Yuan Ze University, Taoyuan 320, Taiwan

Received  June 2021 Revised  August 2021 Early access November 2021

Fund Project: Y. Chen is supported by Ministry of Science and Technology of Taiwan, under grants Nos. 109-2628-E-155-001-MY3 and 110-2218-E-004-001-MBK

Public key encryption with equality test can provide a very simple add-on in which any one can directly perform testing over a pair of ciphertexts to check whether the underlying messages are identical or not without decryption. To restrict the such test power for different scenarios, that of delegated equality test is introduced to allow only the authenticated party to perform the test. In this paper, we focus on the security of public key encryption with filtered equality test (PKE-FET). The delegation to the party is only of a message set for designated testers in PKE-FET, which implies it cannot test any underlying message out of the set. We aim for investigating distinct security notions (static and adaptive security) with specific properties of the potential adversaries. Finally, we show the relationship between the security and complexity, and show the scheme of Huang et al. can reach adaptive security.

Citation: Yu-Chi Chen. Security analysis of public key encryption with filtered equality test. Advances in Mathematics of Communications, doi: 10.3934/amc.2021053
##### References:
 [1] K. Huang, R. Tso and Y.-C. Chen, Somewhat semantic secure public key encryption with filtered-equality-test in the standard model and its extension to searchable encryption, Journal of Computer and System Sciences, 89 (2017), 400-409.  doi: 10.1016/j.jcss.2017.06.001. [2] K. Huang, R. Tso, Y.-C. Chen, W. Li and H.-M. Sun, A new public key encryption with equality test, In International Conference on Network and System Security, Springer, 2015,550–557. doi: 10.1007/978-3-319-11698-3_45. [3] S. Ma, Identity-based encryption with outsourced equality test in cloud computing, Information Sciences, 328 (2016), 389-402. [4] S. Ma, Q. Huang, M. Zhang and B. Yang, Efficient public key encryption with equality test supporting flexible authorization, IEEE Transactions on Information Forensics and Security, 10 (2015), 458-470.  doi: 10.1109/TIFS.2014.2378592. [5] S. Ma, M. Zhang, Q. Huang and B. Yang, Public key encryption with delegated equality test in a multi-user setting, The Computer Journal, 58 (2015), 986-1002.  doi: 10.1093/comjnl/bxu026. [6] K. Peng, C. Boyd, E. Dawson and B. Lee, Ciphertext comparison, a new solution to the millionaire problem, In International Conference on Information and Communications Security, Springer, 3783 (2005), 84–96. doi: 10.1007/11602897_8. [7] Q. Tang, Public key encryption schemes supporting equality test with authorisation of different granularity, International Journal of Applied Cryptography, 2 (2012), 304-321.  doi: 10.1504/IJACT.2012.048079. [8] G. Yang, C. H. Tan, Q. Huang and D. S. Wong, Probabilistic public key encryption with equality test, In Cryptographers'Track at the RSA Conference, Springer, 5985 (2010), 119–131. doi: 10.1007/978-3-642-11925-5_9.

show all references

##### References:
 [1] K. Huang, R. Tso and Y.-C. Chen, Somewhat semantic secure public key encryption with filtered-equality-test in the standard model and its extension to searchable encryption, Journal of Computer and System Sciences, 89 (2017), 400-409.  doi: 10.1016/j.jcss.2017.06.001. [2] K. Huang, R. Tso, Y.-C. Chen, W. Li and H.-M. Sun, A new public key encryption with equality test, In International Conference on Network and System Security, Springer, 2015,550–557. doi: 10.1007/978-3-319-11698-3_45. [3] S. Ma, Identity-based encryption with outsourced equality test in cloud computing, Information Sciences, 328 (2016), 389-402. [4] S. Ma, Q. Huang, M. Zhang and B. Yang, Efficient public key encryption with equality test supporting flexible authorization, IEEE Transactions on Information Forensics and Security, 10 (2015), 458-470.  doi: 10.1109/TIFS.2014.2378592. [5] S. Ma, M. Zhang, Q. Huang and B. Yang, Public key encryption with delegated equality test in a multi-user setting, The Computer Journal, 58 (2015), 986-1002.  doi: 10.1093/comjnl/bxu026. [6] K. Peng, C. Boyd, E. Dawson and B. Lee, Ciphertext comparison, a new solution to the millionaire problem, In International Conference on Information and Communications Security, Springer, 3783 (2005), 84–96. doi: 10.1007/11602897_8. [7] Q. Tang, Public key encryption schemes supporting equality test with authorisation of different granularity, International Journal of Applied Cryptography, 2 (2012), 304-321.  doi: 10.1504/IJACT.2012.048079. [8] G. Yang, C. H. Tan, Q. Huang and D. S. Wong, Probabilistic public key encryption with equality test, In Cryptographers'Track at the RSA Conference, Springer, 5985 (2010), 119–131. doi: 10.1007/978-3-642-11925-5_9.
 [1] Felipe Cabarcas, Daniel Cabarcas, John Baena. Efficient public-key operation in multivariate schemes. Advances in Mathematics of Communications, 2019, 13 (2) : 343-371. doi: 10.3934/amc.2019023 [2] Gerhard Frey. Relations between arithmetic geometry and public key cryptography. Advances in Mathematics of Communications, 2010, 4 (2) : 281-305. doi: 10.3934/amc.2010.4.281 [3] Gérard Maze, Chris Monico, Joachim Rosenthal. Public key cryptography based on semigroup actions. Advances in Mathematics of Communications, 2007, 1 (4) : 489-507. doi: 10.3934/amc.2007.1.489 [4] Joan-Josep Climent, Juan Antonio López-Ramos. Public key protocols over the ring $E_{p}^{(m)}$. Advances in Mathematics of Communications, 2016, 10 (4) : 861-870. doi: 10.3934/amc.2016046 [5] Javier de la Cruz, Ricardo Villanueva-Polanco. Public key cryptography based on twisted dihedral group algebras. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022031 [6] Yang Lu, Jiguo Li. Forward-secure identity-based encryption with direct chosen-ciphertext security in the standard model. Advances in Mathematics of Communications, 2017, 11 (1) : 161-177. doi: 10.3934/amc.2017010 [7] Ramprasad Sarkar, Mriganka Mandal, Sourav Mukhopadhyay. Quantum-safe identity-based broadcast encryption with provable security from multivariate cryptography. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022026 [8] Anton Stolbunov. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 2010, 4 (2) : 215-235. doi: 10.3934/amc.2010.4.215 [9] Alvaro Sandroni, Eran Shmaya. A prequential test for exchangeable theories. Journal of Dynamics and Games, 2014, 1 (3) : 497-505. doi: 10.3934/jdg.2014.1.497 [10] Li Li, Xinzhen Zhang, Zheng-Hai Huang, Liqun Qi. Test of copositive tensors. Journal of Industrial and Management Optimization, 2019, 15 (2) : 881-891. doi: 10.3934/jimo.2018075 [11] Carla Mascia, Massimiliano Sala, Irene Villa. A survey on functional encryption. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021049 [12] Onur Teymur, Sarah Filippi. A Bayesian nonparametric test for conditional independence. Foundations of Data Science, 2020, 2 (2) : 155-172. doi: 10.3934/fods.2020009 [13] Pierre-Emmanuel Mazaré, Olli-Pekka Tossavainen, Daniel B. Work. Computing travel times from filtered traffic states. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 557-578. doi: 10.3934/dcdss.2014.7.557 [14] Angsuman Das, Avishek Adhikari, Kouichi Sakurai. Plaintext checkable encryption with designated checker. Advances in Mathematics of Communications, 2015, 9 (1) : 37-53. doi: 10.3934/amc.2015.9.37 [15] Debrup Chakraborty, Sebati Ghosh, Cuauhtemoc Mancillas López, Palash Sarkar. ${\sf {FAST}}$: Disk encryption and beyond. Advances in Mathematics of Communications, 2022, 16 (1) : 185-230. doi: 10.3934/amc.2020108 [16] Neal Koblitz, Alfred Menezes. Another look at security definitions. Advances in Mathematics of Communications, 2013, 7 (1) : 1-38. doi: 10.3934/amc.2013.7.1 [17] Isabelle Déchène. On the security of generalized Jacobian cryptosystems. Advances in Mathematics of Communications, 2007, 1 (4) : 413-426. doi: 10.3934/amc.2007.1.413 [18] Christoph Hauert, Nina Haiden, Karl Sigmund. The dynamics of public goods. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 575-587. doi: 10.3934/dcdsb.2004.4.575 [19] Kewei Zhang. On equality of relaxations for linear elastic strains. Communications on Pure and Applied Analysis, 2002, 1 (4) : 565-573. doi: 10.3934/cpaa.2002.1.565 [20] Yvo Desmedt, Niels Duif, Henk van Tilborg, Huaxiong Wang. Bounds and constructions for key distribution schemes. Advances in Mathematics of Communications, 2009, 3 (3) : 273-293. doi: 10.3934/amc.2009.3.273

2020 Impact Factor: 0.935