Page 95 - 2024-Vol20-Issue2
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91 | Shumran & Al-Hussein
Fig. 6. Block diagram of the two chaotic levels secure Fig. 7. Map of Arnold Cats, adopted from [23].
proposed system, adopted from [21].
Cat Map, which was first proposed by Vladimir
Arnold in 1960. Arnold Cat Map system given by
(4) [22]:
Xi + 1 = 1 + aXi2 +Yi (5)
Yn + 1 = bXi
Xn + 1 = Xn + AYn mod (N) (4)
Yn + 1 = BXn + ABYn mod (N)
where, samples’ positions in the matrix (N *N)are represented The map displays a basic 2-D chaotic map with quadratic
by Xn,Yn and the transformed positions following the cat map nonlinearity, contingent on parameters a, b initial values(X0, X1).
are represented by (n = 1, 2, 3, ..., N1) and (Xn + 1,Yn + 1) and The value of a is between 1.07 and 1.4. Fig. 8. displays the
A are two positive integer control parameters. The cat map is bifurcation of X in relation to parameter a, while Fig. 9. illus-
used to iterate through the encryption process. After a total trates the iteration property at a = 1.4.
of M iterations, T positive integers exist such that (Xn + 1
, Yn + 1) = (Xn, Yn) . The parameters A, B and the sample In 2019, Krasimir Kordov [24], studied a cryptographic
matrix’s size (N * Nmatrix) determine the period, T . algorithm that relies on permutation-substitution architecture
realized by using a chaotic circle map and modified rotation
2) The Henon Map is a dynamical system with equations. The encryption technique is based on traditional
discrete time. It is among the most researched illus- symmetric models and makes use of a pseudo-random number
trations of chaotic behavior in dynamical systems. generator made of altered rotation equations and a chaotic
A point (Xi,Yi) in the plane is taken and mapped to circle map. A novel pseudo-random generator scheme is intro-
a new point using the Henon map. An equation de- duced and utilized as the foundation for erratic bit-level per-
scribes a Henon Chaotic system given by (5) [22],: mutations and substitutions applied to the structure of audio
files in order to achieve successful encryption. The encryption
process diagram can be illustrated as in Fig. 10. and Fig. 11.
illustrates the decryption process.
