Comparison Between Algebraic Cryptanalysis on DES and NTRU
Abstract
Algebraic cryptanalysis is a cryptanalysis method that aims to exploit the algebraic structure of an encryption algorithm to obtain the secret key. Algebraic cryptanalysis becomes interesting because it uses a small amount of known plaintext, which in real life very few known plaintexts are available. Algebraic cryptanalysis has previously been performed on several block cipher algorithms and public key lattice-based algorithms. In this study, DES and NTRU were chosen as the objects of algebraic cryptanalysis. This research aims to compare algebraic cryptanalysis on DES and NTRU in terms of their applicability, and to what extent algebraic cryptanalysis can be successful in obtaining keys.
Keywords: Algebraic Cryptanalysis; DES; NTRU; polynomial equation.
Abstrak
Algebraic cryptanalysis adalah metode kriptanalisis yang bertujuan untuk memanfaatkan struktur aljabar pada algoritma enkripsi untuk mendapatkan kunci. Algebraic cryptanalysis menarik karena hanya membutuhkan sedikit plaintext, di mana pada kehidupan nyata hanya sedikit plaintext yang bisa didapatkan. Algebraic cryptanalysis sebelumnya dilakukan pada algorima block cipher dan algoritma kunci publik berbasis latis. Pada penelitian ini, DES dan NTRU dipilih sebagai objek algebraic cryptanalysis. Penelitian ini bertujuan untuk membandingkan algebraic cryptanalysis pada DES dan NTRU, serta sejauh mana algebraic cryptanalysis bisa mendapatkan nilai kunci.
Kata Kunci: Kriptanalisis aljabar; DES; NTRU; persamaan polinomial.
2020MSC: 94A60.
Keywords
References
G. Simmons, "Cryptology," Encyclopaedia Britannica, Inc., 2 August 2022. [Online]. Available: https://www.britannica.com/topic/cryptology. [Accessed 2 April 2023].
A. Al-Sabaawi, "Cryptanalysis of Classic Ciphers: Methods Implementation Survey," 2021 International Conference on Intelligent Technologies (CONIT), pp. 1-6, Hubli, India, 2021, doi: 10.1109/CONIT51480.2021.9498530.
T.W. Edgar, D.O. Manz, “Chapter 2 - Science and Cyber Security,” Research Methods for Cyber Security, pp. 33-62, Syngress, 2017, doi: 10.1016/B978-0-12-805349-2.00002-9.
N. Curtois and G. Bard, "Algebraic Attack of the Data Encryption Standard," Proceedings of the 11th IMACC'07, Lecture Notes in Computer Science, vol. 4887, pp. 152-169, Springer, Berlin, Heidelberg, 2008, doi: 10.1007/978-3-540-77272-9_10.
J. Ding, D. Schmidt, “Algebraic Attack on Lattice-Based Cryptosystems Via Solving Equations Over Real Numbers,” IACR Cryptology ePrint Archive 94, 2012.
National Institute of Standards and Technology (NIST), "Data Encryption Standard (DES)," Federal Information Processing Standards (FIPS) Publication 46-3, 1999. Available: https://csrc.nist.gov/CSRC/media/Publications/fips/46/3/archive/1999-10-25/documents/
fips46-3.pdf.
IEEE, "IEEE Standard Specification for Public Key Cryptographic Techniques Based on Hard Problems over Lattices," IEEE Std 1363.1-2008, pp. 1-81, 10 March 2009, doi: 10.1109/IEEESTD.2009.4800404.
D. Micciancio and O. Regev, “Lattice-based Cryptography,” In: D. J. Bernstein, J. Buchmann, E. Dahmen, (eds) Post-Quantum Cryptography, Springer, Berlin, Heidelberg, pp. 147-191, 2009, doi: 10.1007/978-3-540-88702-7_5.
C. Chen, O. Danba, J. Hoffstein, A. Hulsing, J. Rijnveld, J. M. Scanck and T. Saito, P. Schwabe, W. Whyte, K. Xagawa, T. Yamakawa, Z. Zhang, "NTRU: Algorithm Specifications and Supporting Documentation," NTRU Inc., 2020. [Online]. Available: https:// https://ntru.org/release/NIST-PQ-Submisssion-NTRU-20190330.tar.gz.
NIST.IR.8309, "Status Report on The Second Round of NIST Post-Quantum Cryptography Standardization Process," NIST, Gaithersburg, 2020.
D. Liestyowati, “Public Key Cryptography,” Journal of Physics: Conference Series, vol. 1477, 2019, doi: 10.1088/1742-6596/1477/5/052062.
J. Hoffstein, J. Pipher and J. H. Silverman, "NTRU: A ring-based public key cryptosystem," Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol. 1423, Springer, Berlin, Heidelberg, 1998, doi: 10.1007/BFb0054868.
W.I. Alsobky, H. Saeed, “Different Types of Attacks on Blocks Ciphers,” International Journal of Recent Technology and Engineering (IJRTE), vol. 9, 2020, doi: 10.35940/ ijrte.C4214.099320.
A. Hossein, B. Sadeghiyan, J. Pieprzyk, “S-boxes Representation and Efficiency of Algebraic Attack,” IET Information Security 13, pp. 448-458, 2019, doi: 10.1049/iet-ifs.2018.5201.
G.V. Bard, “Algebraic Cryptanalysis,” Springer Dordrecht Heidelberg, New York, 2009, doi: 10.1007/978-0-387-88757-9.
M. Bardet, M. Bertin, A. Couvreur, A. Otmani, “Practical Algebraic Attack on DAGS,” In: Baldi, M., Persichetti, E., Santini, P. (eds) Code-Based Cryptography, Lecture Notes in Computer Science, vol 11666. Springer, Cham. 2019, doi: 10.1007/978-3-030-25922-8_5.
H. Wang, L. Zhang, Q. Wang, S. Yan, “The Gröbner Bases Algorithm and its Application in Polynomial Ideal Theory,”. 2019 Chinese Control and Decision Conference (CCDC), pp. 494-499, Nanchang, China, 2019, doi: 10.1109/CCDC.2019.8833013.
C. Mascia, E. Piccione, M. Sala, “An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG”, 2021, doi: 10.48550/arXiv.2112.12268.
A. Abdel-Hafez, R.A. Elbarkouky, W. Hafez, “Comparative Study of Algebraic Attacks,” International Advanced Research Journal in Science, Engineering and Technology, vol. 3, pp. 85-90, 2016, doi: 10.17148/IARJSET.2016.3519.
S.L. Yeo, D.P. Le, K. Khoo, “Improved algebraic attacks on lightweight block ciphers,”
J Cryptogr Eng 11, pp. 1–19, 2021. doi: 10.1007/s13389-020-00237-4.
R. Biyashev, D. Dyusenbayev, K. Algazy, N. Kapalova, “Algebraic Cryptanalysis of Block Ciphers,” Proceedings of the 2019 International Conference on Wireless Communication, Network and Multimedia Engineering (WCNME 2019), pp. 129-132, Atlantis Press, doi: 10.2991/wcnme-19.2019.30.
DOI: 10.15408/inprime.v5i2.32011
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