Kajian Matematika Skema Tanda Tangan Rainbow Berbasis Multivariat

Authors

  • Arbi Nur'aini Labibah Badan Siber dan Sandi Negara
  • Sa’aadah Sajjana Carita Politeknik Siber dan Sandi Negara

DOI:

https://doi.org/10.56706/ik.v18i2.101

Keywords:

EUF-CMA, Kriptografi Multivariat, Oil and Vinegar, Tanda Tangan Rainbow, Post Quantum

Abstract

Skema tanda tangan Rainbow merupakan skema tanda tangan berbasis multivariat yang pertama kali diperkenalkan oleh Jintai Ding dan Dieter Schmidt pada tahun 2005, serta berhasil mencapai ronde 3 pada proyek standardisasi kriptografi post quantum NIST. Skema ini menerapkan penggunaan multilayer untuk meningkatkan efisiensi dari skema tanda tangan Unbalanced Oil and Vinegar (UOV). Skema tanda tangan Rainbow yang diikutsertakan merupakan hasil modifikasi dengan penambahan vektor biner salt r yang bertujuan untuk memenuhi klaim keamanan EUF-CMA. Pada penelitian  ini, penulis melakukan pengkajian terhadap dasar dan karakteristik, serta analisis dari klaim keamanan EUF-CMA yang dimiliki oleh skema modifikasi tanda tangan rainbow. Skema tanda tangan Rainbow terbukti memenuhi keamanan EUF-CMA dan karakteristik authentic, not reusable, unalterable, serta cannot be repudiated. Namun, skema ini tidak terjamin memenuhi karakteristik unforgeable dikarenakan key recovery attack yang dilakukan Ward Beullens pada tahun 2022.

References

V. Mavroeidis, K. Vishi, M. D., and A. Jøsang, “The Impact of Quantum Computing on Present Cryptography,” Int. J. Adv. Comput. Sci. Appl., vol. 9, no. 3, pp. 405–414, 2018, doi: 10.14569/IJACSA.2018.090354.

S. Vaudenay, A Classical Introduction to Cryptography. New York: Springer-Verlag, 2006.

H. Xu, K. Thakur, A. S. Kamruzzaman, and M. L. Ali, “Applications of Cryptography in Database: A Review,” in 2021 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS), Apr. 2021, pp. 1–6, doi: 10.1109/IEMTRONICS52119.2021.9422663.

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography. CRC Press, 2018.

E. Grumbling and M. Horowitz, Quantum Computing, vol. 9781461418. Washington, D.C.: National Academies Press, 2019.

A. Ferozpuri and K. Gaj, “High-speed FPGA Implementation of the NIST Round 1 Rainbow Signature Scheme,” in 2018 International Conference on ReConFigurable Computing and FPGAs (ReConFig), Dec. 2018, no. 1, pp. 1–8, doi: 10.1109/RECONFIG.2018.8641734.

NIST, “Proposed Submission Requirements and Evaluation Criteria for the Post-Quantum Cryptography Standardization Process,” 2016. https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf.

M. Jurkiewicz, “Improving Security of Existentially Unforgeable Signature Schemes,” Int. J. Electron. Telecommun., vol. 66, no. 3, pp. 473–480, Jan. 2020, doi: 10.24425/ijet.2020.131901.

J. Ding et al., “Rainbow Public Key : System of multivariate quadratic polynomials,” 2021. https://csrc.nist.gov/CSRC/media/Presentations/rainbow-round-3-presentation/images-media/session-1-rainbow-petzoldt.pdf.

J. Ding and D. Schmidt, “Rainbow, a New Multivariable Polynomial Signature Scheme,” in Lecture Notes in Computer Science, vol. 3531, 2005, pp. 164–175.

W. Beullens, “Breaking Rainbow Takes a Weekend on a Laptop,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13508 LNCS, Springer Nature Switzerland, 2022, pp. 464–479.

J. Vince, Mathematics for Computer Graphics. London: Springer London, 2010.

M. E. Mortenson, Mathematics for Computer Graphics Applications, 2nd ed. New York, NY: Industrial Press, Inc.

H. Anton and C. Rorres, Elementary Linear Algebra, 11th ed. Wiley.

J. Ding and B.-Y. Yang, “Multivariate Public Key Cryptography,” Post-Quantum Cryptogr., no. 1, pp. 193–241, 2009, doi: 10.1007/978-3-540-88702-7_6.

J. Ding and A. Petzoldt, “Current State of Multivariate Cryptography,” IEEE Secur. Priv., vol. 15, no. 4, pp. 28–36, 2017, doi: 10.1109/MSP.2017.3151328.

W. J. Buchanan, “The Oil and Vinegar Method,” no. September, 2020, doi: 10.6084/m9.figshare.13012016.v1.

K. Sakumoto, T. Shirai, and H. Hiwatari, “On provable security of UOV and HFE signature schemes against chosen-message attack,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 7071 LNCS, pp. 68–82, 2011, doi: 10.1007/978-3-642-25405-5_5.

B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, 2nd ed. 1996.

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Submitted

08-08-2024

Accepted

29-08-2024

Published

29-08-2024

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Articles