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Characteristics of FS-CES

The employed map is simple. Especially, rounding in $\tilde{F_A}$ is tractable for digital computers. However, it is to be noted that implementational easiness on hardware is a distinct matter.
The probability that the only X₁'s or only X₂'s are always chosen in n operations of $\tilde{F_A}^{-1}$ is $\{ a^2+(1-a)^2 \}^n \le 0.52^n$ . Then, those who intend differential or linear cryptanalysis must exhaustively solve nonlinear equations for each of 0.52^-n / 2 = 2^{0.94n + 1} pairs of plaintexts and ciphertexts (X₁,Y₁),(X₂,Y₂).
All the possible fixed points and cycles are repelling with no essential basin, and there are few short cycles [7,8]. Accordingly, our cryptosystem is strong against cryptanalysis utilizing them. This is in contrast with synchronization-based cryptosystems, which requires a substantial attractive region for robustness.
We required 0.4M<A<0.6M to get rid of pathological cases. Accordingly, $\left\vert K \right\vert = 0.2M$ . If the key space is smaller than the plaintext space, the cardinality of the key space provides an upper limit of security standard [9]; we must modify FS-CES to obtain the cardinality of the key space, at least equal to M.

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