Publications

  1. The space of two-sided generalized Fibonacci sequences (with M. Bunder), Rocky Mountain Journal of Mathematics 55(1)(2025), 35-44. [pdf] https://doi.org/10.1216/rmj.2025.55.35

  2. Nested fifth root radical identities from elliptic curves, Journal of Computational Algebra 13(2025), #100032. https://doi.org/10.1016/j.jaca.2025.100032

  3. Enumerating irreducible polynomials over the binary field, Discrete Mathematics, Algorithms and Applications, 2025, #2550085. https://doi.org/10.1142/S1793830925500855

  4. Fibonacci and Pi squared, The Fibonacci Quarterly 62(1)(2024), 65-74. https://doi.org/10.1080/00150517.2024.12427379

  5. Fibonacci-related formulas for pi, The Mathematical Intelligencer 46(3)(2024), 214-221. [pdf] https://doi.org/10.1007/s00283-023-10284-4

  6. Enhanced S-boxes for the Advanced Encryption Standard with maximal periodicity and better avalanche property (with A. Nitaj, W. Susilo), Computer Standards & Interfaces 87 (2024), #103769. https://doi.org/10.1016/j.csi.2023.103769

  7. A new attack on some RSA variants (with A. Nitaj, W. Susilo), Theoretical Computer Science 960 (2023), #113898. https://doi.org/10.1016/j.tcs.2023.113898

  8. Message-locked searchable encryption: a new versatile tool for secure cloud storage (with X. Liu, G. Yang, W. Susilo, R. Chen, L. Xixiang), IEEE Transactions on Services Computing 15(3)(2022), 1664-1677. https://doi.org/10.1109/TSC.2020.3006532

  9. A generalized attack on the multi-prime power RSA (with A. Nitaj, W. Susilo), Proceedings of the 13th International Conference on Cryptology in Africa, Lecture Notes in Computer Science 13503, 2022, 537-549. https://doi.org/10.1007/978-3-031-17433-9_23

  10. An exact formula for the harmonic continued fraction (with M. Bunder, P. Nickolas), Bulletin of the Australian Mathematical Society 103(2021), 11-21. https://doi.org/10.1017/S0004972720000544

  11. A Wiener-type attack on an RSA-like cryptosystem constructed from cubic Pell equations (with W. Susilo), Theoretical Computer Science 885 (2021), 125-130. https://doi.org/10.1016/j.tcs.2021.06.033

  12. Divide and Capture: An improved cryptanalysis of the encryption standard algorithm RSA (with W. Susilo, G. Yang), Computer Standards & Interfaces 74 (2021), #103470. https://doi.org/10.1016/j.csi.2020.103470

  13. Privacy-preserving multi-keyword searchable encryption for distributed systems (with X. Liu, G. Yang, W. Susilo, X. Liu, J. Shen), IEEE Transactions on Parallel and Distributed Systems 32(3)(2021), 561-574. https://doi.org/10.1109/TPDS.2020.3027003

  14. Broadcast authenticated encryption with keyword search (with X. Liu, K. He, G. Yang, W. Susilo, Q. Huang), Proceedings of the 26th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 13083, 2021, 193-213. https://doi.org/10.1007/978-3-030-90567-5_10

  15. Cryptanalysis of RSA variants with primes sharing most significant bits (with M. Cherkaoui-Semmouni, A. Nitaj, W. Susilo), Proceedings of the 24th International Conference on Information Security, Lecture Notes in Computer Science 13118, 2021, 42-53. https://doi.org/10.1007/978-3-030-91356-4_3

  16. Generalized Fibonacci numbers and their 2-adic order (with M. Bunder), Integers: Electronic Journal of Combinatorial Number Theory, 2020, #A105. https://doi.org/10.5281/zenodo.10802328

  17. A generalised bound for the Wiener attack on RSA (with W. Susilo, G. Yang), Journal of Information Security and Applications 53(2020), #102531. https://doi.org/10.1016/j.jisa.2020.102531

  18. A new improved AES S-box with enhanced properties (with A. Nitaj, W. Susilo), Proceedings of the 25th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 12248, 2020, 125-141. https://doi.org/10.1007/978-3-030-55304-3_7

  19. On the harmonic continued fractions (with M. Bunder, P. Nickolas), The Ramanujan Journal 49(3)(2019), 669-697. [pdf] https://doi.org/10.1007/s11139-018-0098-4

  20. Towards enhanced security for certificateless public-key authenticated encryption with keyword search (with X. Liu, H. Li, G. Yang, W. Susilo, Q. Huang), Proceedings of the 13th International Conference on Provable Security, Lecture Notes in Computer Science 11821, 2019, 113-129. https://doi.org/10.1007/978-3-030-31919-9_7

  21. Improved cryptanalysis of the KMOV elliptic curve cryptosystem (with A. Nitaj, W. Susilo), Proceedings of the 13th International Conference on Provable Security, Lecture Notes in Computer Science 11821, 2019, 206-221. https://doi.org/10.1007/978-3-030-31919-9_12

  22. The Wiener attack on RSA revisited: a quest for the exact bound (with W. Susilo, G. Yang), Proceedings of the 24th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 11547, 2019, 381-398. https://doi.org/10.1007/978-3-030-21548-4_21

  23. A generalized attack on some variants of the RSA cryptosystem (with A. Nitaj, Y. Pan), Proceedings of the 25th International Conference on Selected Areas in Cryptography, Lecture Notes in Computer Science 11349, 2019, 421-433. https://doi.org/10.1007/978-3-030-10970-7_19

  24. A new elementary proof of Euler's continued fractions, The Mathematical Gazette 102(2018), 105-111. https://doi.org/10.1017/mag.2018.15

  25. Cryptanalysis of RSA-type cryptosystems based on Lucas sequences, Gaussian integers and elliptic curves (with M. Bunder, A. Nitaj, W. Susilo), Journal of Information Security and Applications, 40(2018), 193-198. https://doi.org/10.1016/j.jisa.2018.04.006

  26. Closed form expressions for two harmonic continued fractions (with M. Bunder), The Mathematical Gazette 101(552)(2017), 439-448. https://doi.org/10.1017/mag.2017.125

  27. A continued fraction inspired by an identity of Euler, The Mathematical Gazette 101(550)(2017), 115-121. https://doi.org/10.1017/mag.2017.16

  28. A new attack on the RSA cryptosystem based on continued fractions (with M. Bunder), Malaysian Journal of Mathematical Sciences 11(S3)(August 2017), 45-57.

  29. A QR code watermarking approach based on the DWT-DCT technique (with Y.-W. Chow, W. Susilo, W. Zong), Proceedings of the 22nd Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 10343, 2017, 314-331. https://doi.org/10.1007/978-3-319-59870-3_18

  30. A generalized attack on RSA type cryptosystems (with M. Bunder, A. Nitaj, W. Susilo), Theoretical Computer Science 704(2017), 74-81. https://doi.org/10.1016/j.tcs.2017.09.009

  31. Dirichlet product for Boolean functions (with A. Nitaj, W. Susilo), Journal of Applied Mathematics and Computing 55(2017), 293-312. https://doi.org/10.1007/s12190-016-1037-4

  32. Trisecting an angle correctly up to arcminute, Forum Geometricorum 16 (2016), 37-41. [pdf]

  33. A simple proof of Euler's continued fraction of e1/M, The Mathematical Gazette 100(548)(2016), 279-287. https://doi.org/10.1017/mag.2016.65

  34. A new improved attack on RSA (with M. Bunder), Proceedings of the 5th International Cryptology and Information Security Conference, 2016, 101-110.

  35. A new attack on three variants of the RSA cryptosystem (with M. Bunder, A. Nitaj, W. Susilo), Proceedings of the 21st Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 9723, 2016, 258-268. https://doi.org/10.1007/978-3-319-40367-0_16

  36. Some constructions of mutually orthogonal Latin squares and superimposed codes (with J. Seberry), Discrete Mathematics, Algorithms and Applications 4(3)(2012), 1250022-(1-8). https://doi.org/10.1142/S179383091250022X

  37. A new generic digital signature algorithm (with J. Seberry, V. To), Groups - Complexity - Cryptology 3(2)(2011), 221-237. https://doi.org/10.1515/gcc.2011.008

  38. Fuzzy universal hashing and approximate authentication (with R. Safavi-Naini), Discrete Mathematics, Algorithms and Applications 3(4)(2011), 587-607. https://doi.org/10.1142/S1793830911001425

  39. On "the power of verification queries" in unconditionally secure message authentication (with R. Safavi-Naini, P. Wild), Discrete Mathematics, Algorithms and Applications 3(3)(2011), 287-303. https://doi.org/10.1142/S1793830911001218

  40. Breaking and repairing an approximate message authentication scheme (with R. Safavi-Naini, P. Nickolas), Discrete Mathematics, Algorithms and Applications 3(3)(2011), 393-412. https://doi.org/10.1142/S1793830911001292

  41. Unconditionally secure approximate message authentication (with R. Safavi-Naini, P. Nickolas, Y. Desmedt), Proceedings of the 2009 International Workshop on Coding and Cryptology, Lecture Notes in Computer Science 5557, 2009, 233-247. https://doi.org/10.1007/978-3-642-01877-0_19

  42. Birthday paradox for multi-collisions (with K. Suzuki, K. Kurosawa, K. Toyota), The Institute of Electronics, Information and Communication Engineers Transactions, Special Section on Cryptography and Information Security 91A(1)(2008), 39-45. https://doi.org/10.1093/ietfec/e91-a.1.39

  43. Authentication codes in the query model (with R. Safavi-Naini, P. Wild), Proceedings of the First International Workshop on Coding and Cryptology, Series on Coding and Cryptology 4, 2008, 214-225. https://doi.org/10.1142/9789812832245_0016

  44. A simple visual proof of the Schroder-Bernstein theorem, Elemente der Mathematik 62(3)(2007), 118-120. https://doi.org/10.4171/EM/65

  45. Construction of deletion correcting codes using generalized Reed-Solomon codes and their subcodes (with R. Safavi-Naini), Designs, Codes and Cryptography 42(2007), 227-237. https://doi.org/10.1007/s10623-006-9032-7

  46. Combinatorial characterizations of authentication codes in verification oracle model (with R. Safavi-Naini, P. Wild), Proceedings of the 2007 ACM Symposium on Information, Computer and Communications Security , 183-193, 2007. https://doi.org/10.1145/1229285.1229311

  47. Cancellation law and unique factorization theorem for string operations, Journal of Algebra and Its Applications 5(2)(2006), 231-243. https://doi.org/10.1142/S0219498806001739

  48. On the Diophantine equation x! = pya, New Zealand Journal of Mathematics 35 (2006), 207-209.

  49. Recursive constructions of secure codes and hash families using difference function families (with R. Safavi-Naini), Journal of Combinatorial Theory Series A 113(4)(2006), 664-674. https://doi.org/10.1016/j.jcta.2005.07.001

  50. On a traitor tracing scheme from ACISP 2003, Information Processing Letters 100(1)(2006), 21-22. https://doi.org/10.1016/j.ipl.2006.04.016

  51. Multi-party concurrent signatures (with W. Susilo, R. Safavi-Naini), Proceedings of the 9th Information Security Conference, Lecture Notes in Computer Science 4176, 2006, 131-145. https://doi.org/10.1007/11836810_10

  52. Generic construction of hybrid public key traitor tracing with full-public-traceability (with D.H. Phan, R. Safavi-Naini), Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 4052, 2006, 264-275. https://doi.org/10.1007/11787006_23

  53. Birthday paradox for multi-collisions (with K. Suzuki, K. Kurosawa, K. Toyota), Proceedings of the 9th Annual International Conference on Information Security and Cryptology , Lecture Notes in Computer Science 4296, 2006, 29-40. https://doi.org/10.1007/11927587_5

  54. An efficient single-key pirates tracing scheme using cover-free families (with R. Safavi-Naini), Proceedings of the 4th International Conference on Applied Cryptography and Network Security, Lecture Notes in Computer Science 3989, 2006, 82-97. https://doi.org/10.1007/11767480_6

  55. 2-Secure codes from 2-SFP codes (with R. Safavi-Naini, Y. Wang), Journal of Discrete Mathematical Sciences & Cryptography 8(2) (2005), 287-304. https://doi.org/10.1080/09720529.2005.10698039

  56. Self-dual modular-graceful cyclic digraphs (with R. Safavi-Naini), Journal of Combinatorial Mathematics and Combinatorial Computing 52 (2005), 97-108.

  57. A note on Devaney's definition of chaos, Journal of Dynamical Systems and Geometric Theories 2 (2004), 23-26. https://doi.org/10.1080/1726037X.2004.10698476

  58. On the maximal codes of length 3 with the 2-identifiable parent property (with R. Safavi-Naini), SIAM Journal on Discrete Mathematics 17(4) (2004), 548-570. https://doi.org/10.1137/S0895480102400424

  59. Linear code implies public-key traitor tracing with revocation (with R. Safavi-Naini), Proceedings of the 9th Australasian Conference on Information Security and Privacy, Lecture Notes in Computer Science 3108, 2004, 24-35. https://doi.org/10.1007/978-3-540-27800-9_3

  60. New traitor tracing schemes using bilinear map (with R. Safavi-Naini, F. Zhang), Proceedings of the 2003 ACM Workshop on Digital Rights Management, 67-76, 2003. https://doi.org/10.1145/947380.947389

  61. Explicit construction of secure frameproof codes (with R. Safavi-Naini), International Journal of Pure and Applied Mathematics 6 (2003), 343-360.

  62. A 2-secure code with efficient tracing algorithm (with R. Safavi-Naini, Y. Wang), Proceedings of the 3rd International Conference on Cryptology in India , Lecture Notes in Computer Science 2551, 2002, 149-162. https://doi.org/10.1007/3-540-36231-2_13

  63. Dynamics of an elastic ball bouncing on an oscillating plane and the oscillon (with J.M. Hill, M.J. Jennings, K.A. Williams), Applied Mathematical Modelling 24(2000), 715-732. https://doi.org/10.1016/S0307-904X(00)00002-0

Ph.D. Thesis

Recreational math & miscellaneous



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