Algorithm 1: Embedding process

Input: Carrier image (CIm), Confidential image (SIm), and Initial key parameters ($\mathrm{V},\mathrm{B},\mathsf{\theta },{\mathsf{\alpha }}_0,{\mathsf{\alpha }}_2$)

Output: Stego image (Stgo)

P← CAQWs ($\mathrm{V},\mathrm{B},\mathsf{\theta },{\mathsf{\alpha }}_0,{\mathsf{\alpha }}_2$) // Operate CAQWs using initial key parameters

[h, w, c] ← size (CIm) // Obtain the size of the carrier image

D← resize (P, [h, w × c ]) // Resize the matrix P to the dimension of the cover image

E← order (D) // Order the elements of D in decreasing order

K= index (D, E) // Obtain the index of each element of D in E

ESIm ← expand (SIm) // Expand the 8-bit and $\frac{\mathrm{h}}{2}\times \frac{\mathrm{w}}{2}$ dimensional confidential image SIm to a 2-bit image of h × w dimension.

// Transform the expanded secret image ESIm and the carrier image CIm into vectors

SVec← reshape (ESIm, 1, h × w × c)

CVec← reshape (CIm, 1, h × w × c)

// Embedding process

for i←1 to h × w × c

StgoVec(k(i))←Replace 2LSBs of CVec(k(i)) with 2bits of SVec(i);

end

// Transform the vector StgoVec into an image

Stgo←reshape (StgoVec, h, w, c)