PEMILIHAN GRUP UNTUK KRIPTOSISTEM GTRU

Abdul Hadi, Musraini Musraini, Sri Gemawati

Abstract


Kriptosistem kunci publik seperti NTRU yang berdasarkan pada grup, dikenal dengan nama GTRU (Group Theory Research Unit) [1]. Dalam pengkonstruksian GTRU, tidak semua grup dapat digunakan. Hal ini disebabkan proses dekripsi pada GTRU  berhasil hanya pada grup dengan kondisi tertentu saja. Di [1], diberikan hanya dua contoh grup yang  dapat digunakan untuk mengkonstruksi GTRU, yaitu grup ${{\mathbb{Z}}^{\{{{\phi }_{i}}:1\le i\le n\}}}$ yang isomorfis dengan ${{\mathbb{Z}}^{n}}$ dan grup poly-$\mathbb{Z}$ ${{G}_{n}}={{\mathbb{Z}}^{n-3}}\times \mathcal{H}$ dimana $\mathcal{H}$ adalah grup Heisenberg Diskrit yang dapat diaplikasikan pada internet of thing (IoT). Pada tulisan ini disediakan beberapa pilihan grup lain yang dapat digunakan dan tidak dapat digunakan untuk mengkonstruksi kriptosistem GTRU.

 


Keywords


Grup; Subgrup Normal; Homomorfisma Grup; NTRU; GTRU

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DOI: https://doi.org/10.15548/map.v4i1.3394
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References


L. Shuai, H. Xu, L. Miao, and X. Zhou, “A Group-based NTRU-like Public-key Cryptosystem for IoT,” IEEE Access, vol. 7, pp. 75732–75740, 2019.

R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun ACM, vol. 26, no. 1, pp. 96–99, 1983.

N. Koblitz, “Elliptic curve cryptosystems,” Math Comput, vol. 48, no. 177, pp. 203–209, 1987.

R. J. McEliece, “A public-key cryptosystem based on algebraic,” Coding Thv, vol. 4244, pp. 114–116, 1978.

P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” in Proceedings 35th annual symposium on foundations of computer science, 1994, pp. 124–134.

J. Hoffstein, J. Pipher, and J. H. Silverman, “NTRU: A ring-based public key cryptosystem,” in International algorithmic number theory symposium, 1998, pp. 267–288.

W. D. Banks and I. E. Shparlinski, “A variant of NTRU with non-invertible polynomials,” in International Conference on Cryptology in India, 2002, pp. 62–70.

P. Gaborit, Julien Ohler, and Patrick Solé, a polynomial analogue of NTRU. Inria: Doctoral Dissertation, Inria, 2002.

M. Coglianese and B.-M. Goi, “MaTRU: A new NTRU-based cryptosystem,” in International conference on cryptology in India, 2005, pp. 232–243.

R. Kouzmenko, “Generalizations of the NTRU cryptosystem,” Diploma Project, École Polytechnique Fédérale de Lausanne,(2005–2006), 2006.

K. Jarvis and M. Nevins, “ETRU: NTRU over the Eisenstein integers,” Designs, Codes and Cryptography, vol. 74, no. 1, pp. 219–242, 2015.

N. Vats, “NNRU, a noncommutative analogue of NTRU,” arXiv preprint arXiv:0902.1891, 2009.

E. Malekian and A. Zakerolhosseini, “OTRU: A non-associative and high speed public key cryptosystem,” in 2010 15th CSI international symposium on computer architecture and digital systems, 2010, pp. 83–90.

E. Malekian, A. Zakerolhosseini, and A. Mashatan, “QTRU: quaternionic version of the NTRU public-key cryptosystems,” The ISC International Journal of Information Security, vol. 3, no. 1, pp. 29–42, 2011.

A. K. Nanda, R. Nayak, and L. K. Awasthi, “NTRU with Gaussian integer matrix,” Int J Adv Res Comput Sci Software Eng, vol. 5, pp. 359–365, 2015.

A. H. Karbasi and R. E. Atani, “ILTRU: An NTRU-like public key cryptosystem over ideal lattices,” Cryptology ePrint Archive, 2015.

H. R. Yassein and N. M. G. Al-Saidi, “HXDTRU Cryptosystem Based on Hexadecnion Algebra,” 2016.

N. M. G. Alsaidi and H. R. Yassein, “BITRU: binary version of the NTRU public key cryptosystem via binary algebra,” International Journal of Advanced Computer Science and Applications, vol. 7, no. 11, 2016.

D. J. Bernstein, C. Chuengsatiansup, T. Lange, and C. van Vredendaal, “NTRU prime: reducing attack surface at low cost,” in International Conference on Selected Areas in Cryptography, 2017, pp. 235–260.

H. R. Yassein and N. M. G. Al-Saidi, “BCTRU: A New Secure NTRU Crypt Public Key System Based on a Newly Multidimensional Algebra,” in proceeding of 6th international cryptology and information security conference, 2018, pp. 1–11.

W. Diffie and M. E. Hellman, “New Directions in Cryptography, 1976,” IEEE Transactions on Information Theory, vol. 22, no. 6, 2011.

D. S. M. J. N. Mordeson, M. K. Sen, and D. S. Malik, “Fundamentals Of Abstract Algebra,” The McCGraw-HILL Companies, Inc. New York st. Louis, san Francisco, printed in Singapore, 1997.

S. Wahyuni, I. E. Wijayanti, A. Munandar, and N. Hajriati, Teori Representasi Grup Hingga. Yogyakarta: Gadjah Mada University Press, 2018.


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