New formula to calculate the number of designs in RADG cryptosystem

Document Type : Research Paper

Authors
Laith M Kadhum 1
Ahmad Firdaus 2
Mohamad Fadli Zolkiplib 3
Luay Saferalia 4
Mohd Faizal Ab Razaka 5
1 Faculty of Computing College of Computing and Applied Sciences, Universiti Malaysia Pahang 26600 Pekan, Pahang Darul Makmur, Malaysia; & University of Kufa, Najaf, Iraq
2 aFaculty of Computing College of Computing and Applied Sciences, Universiti Malaysia Pahang 26600 Pekan, Pahang Darul Makmur
3 School of Computing, UUM College Arts Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia
4 Faculty of Computing College of Computing and Applied Sciences, Universiti Malaysia Pahang 26600 Pekan, Pahang Darul Makmur, Malaysia
5 aFaculty of Computing College of Computing and Applied Sciences, Universiti Malaysia Pahang 26600 Pekan, Pahang Darul Makmur, Malaysia
10.22075/ijnaa.2021.4937
Abstract
Reaction automata direct graph (RADG) is a new technique that uses the automata direct graph method to represent a certain design for encryption and decryption. Jump states are available in the RADG design that enables the encipher to generate different ciphertexts each time from the same plaintext and wherein not a single ciphertext is related to a certain plaintext. This study created a matrix representation for RADG designs that allows the calculation of the number of cases ($F_{Q}$)mathematically possible for any design of the set $Q$. $F_{Q}$ is an important part of the function $\mathrm{F}(\mathrm{n}, \mathrm{m}, \lambda)$ that calculates the total number of cases of a certain design for the values $Q, R, \sum, \psi, J$ and $T$. This paper produces a mathematical equation to calculate $F_{Q}$.
Keywords
RADG
Cryptography
Block Cipher
Keyless
Graph Theory
[1] G. Baumslag, B. Fine, M. Kreuzer and G. Rosenberger, A Course in Mathematical Cryptography, De Gruyter, 2015.
[2] L. Mao, Mathematics after CC conjecture-combinatorial notions and achievements, Int. J. Math. Comb. 2 (2015) 1–31.
[3] S. Lovett, Additive combinatorics and its applications in theoretical computer science, Theory Comput. 2016 (2016) 1–53.
[4] S.A. Albermany and G.A. Safdar, Keyless Security in Wireless Networks, Wirel. Pers. Commun. 79(3) (2014) 1713–1731.
[5] J.L. Gross and J. Yellen, Handbook of Graph Theory, CRC Boca Raton, Florida, 2004.
[6] I. Anderson and R. Diestel, Graph theory, Math. Gazette 85(502) (2001) 176-177.
[7] S. Albermany, F. Radi Hamade and G.A. Safdar, New random block cipher algorithm, Int. Conf. Current Res. Comput. Sci. Inf. Technol. (ICCIT), 2017.
[8] S.A. Albermany and A.H. Alwan, RADG design on elliptic curve cryptography, ICCIIDT 2016 London - UK Proceedings, 2016.
[9] S. Albermany, M. Nathim and Z.M. Hussain, CRADG: A chaotic RADG security system, J. Eng. Appl. Sci. 12 (2017) 4118–4122.
[10] A. Salah, D. Amer and S. Kamal, S-RADG: A stream cipher RADG cryptography, J. Eng. Appl. Sci. 13 (2018) 2317–2321.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 821-829

  • Receive Date 07 October 2020
  • Revise Date 13 December 2021
  • Accept Date 24 February 2021

Article View 16,172
PDF Download 9,596