Table 3 Representation of state variables and control parameters, their value ranges, and initially perturbed bits.

From: Novel structures of chaos-based parallel multiple image encryption and FPGA implementation

Parameter

Format

Pattern in binary

Value range

Position of 16 perturbed bits

\(\gamma _n^{(2)}\)

\(\left\langle 52,49\right\rangle\)

xx1(.)xxx...xx

[1.0,2.0),

[3.0,4.0),

[5.0,6.0),

and [7.0,8.0)

\(b_{2}b_{1}b_{-1}...b_{-13}b_{-14}\)

\(\gamma _n^{(1)}\)

\(\left\langle 52,49\right\rangle\)

xx1(.)xxx...xx

[1.0,2.0),

[3.0,4.0),

[5.0,6.0),

and [7.0,8.0)

\(b_{2}b_{1}b_{-1}...b_{-13}b_{-14}\)

\(x_n^{(2)}\)

\(\left\langle 50,49\right\rangle\)

0(.)xxx...x1

[\(2^{-49}\),1.0)

\(b_{-1}b_{-2}...b_{-15}b_{-16}\)

\(x_n^{(1)}\)

\(\left\langle 50,49\right\rangle\)

0(.)xxx...x1

[\(2^{-49}\),1.0)

\(b_{-1}b_{-2}...b_{-15}b_{-16}\)