The Implementation of f(x) = 3(x 3 − x 2 − x) + 2 as CSPRNG Chaos-Based Random Number Generator

  • Maria Rosalina Yopeng Publkasi Jurnal
  • Alz Danny Wowor
Abstract views: 59 , 64 downloads: 37
Keywords: f(x) = 3(x^3 - x^2 -x) 2, Fixed Point Iteration, CSPRNG Chaos

Abstract

This research implemented the cubic function f(x) = 3(x^3 − x^2 − x) + 2 using a FixedPoint Iteration to produce several iteration functions that can be used as random number generator. The test results obtain six iteration functions, and based on graphic visualization
with Scatter plot and randomness test with mono bit test, bit block, and run test, the results only obtain two iteration functions namely x2 − 1 + 2/(3x) and f(x) = 1 + 1/x − 2/(3x^2)which can produce CSPRNG Chaos-based random number. Encryption testing shows that both functions can generate keys that make plaintext and ciphertext statistically unrelated, so the f(x) = 1 + 1/x − 2/(3x^2) function can be used as a CSPNRG chaos-based random number generator function.

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References

[1] Holt, Nathan, Chaotic Cryptography: Applications of Chaos Theory to Cryptography, Rochester Institute of Technology, 2017.
[2] Wang, L., & Cheng, H., Pseudo-Random Number Generator Based on Logistic Chaotic System, Entropy Journal, 2019.
[3] Wowor, Alz Danny, Regenerasi Fungsi Polinomial Dalam Rancangan Algoritma Berbasis CSPRNG Chaos Sebagai PembangkitKunci pada Kriptografi Block Cipher. Limits Journal, 14 : 4, 2017.
[4] Suling, P.M.C., & Wowor, A.D., Regenerasi Fungsi Kuadrat sebagai Pembangkit Kunci Berbasis Metode Iterasi Titik Tetap(Fixed Point) pada Kriptografi. UKSW: Skripsi S1 Teknik Informatika, 2017.
[5] Lihananto, D., & Wowor, A.D., Regenerasi Fungsi x
2 − 9x − 99 dalam Pembangkit Bilangan Acak Berbasis CSPRNG Chaos.
UKSW: Skripsi S1 Teknik Informatika, 2020.
[6] Balamu, M., & Wowor, A.D., Pencarian Interval Solusi Untuk Koefisien dan Konstanta f(x) = x − (x
2 − 3)/176 Sebagai
Fungsi Pembangkit Bilangan Acak. UKSW: Skripsi S1 Teknik Informatika, 2019.
[7] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray,
J., & Vo, S., A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,
Gaithersburg: National Institute of Standards and Technology, 2010.
[8] Steward, J., Calculus; Early Transcendentals, Belmont: Brooks/Cole, 2015.
[9] Chapra, S. & Canale, R., Numerical Methoods for Engineers, Sixth Edition, New York: Mc Graw Hill, 2010.
[10] Munir, R., Kriptografi, Bandung: Informatika, 2019.
[11] Montgomery, D.C. & Runger, G.C., Applied Statistics and Probability for Engineers, Third Edition, New York: John Wiley
& Sons, 2003.
Published
2021-05-03
How to Cite
Yopeng, M. R., & Wowor, A. D. (2021). The Implementation of f(x) = 3(x 3 − x 2 − x) + 2 as CSPRNG Chaos-Based Random Number Generator. Indonesia Journal on Computing (Indo-JC), 6(1), 41-52. https://doi.org/10.34818/INDOJC.2021.6.1.546
Section
Information Technology