Algorithm 1: The embedding algorithm

Input: Cover image C, Secret image S, embedding factor α.

Output: Steganographic image C*, Encrypted key matrix Uw1′, Vw1‘.

1: [LL2, HL2, LH2, HH2, HL, LH, HH] = DWT2level(C)

2: RS = [HH2, HL(1:128,129:256);LH(129:256,1:128), HH(1:128,1:128)] 3: RS’ = Arnold (RS) 4: P H PT = Hessenberg (RS’) 5: HUw ⋅ HSw $\cdot$ HVw = SVD (H) 6: S’ = Arnold (S) 7: Uw1 Sw1 Vw1T = SVD (S’) $8:{{HS}_w}_1*={HS}_w+\alpha$Sw1 9: H* = HUw HSw1* HVw 10: RSS’ = P H*PT 11: RSS = Rearnold(RSS’)//The hidden area after embedding secret information is shown in the Figure 5. In Figure 5, HL*, LH*, HH* and HH2* are HL, LH, HH, and HH2 embedded with secret information respectively. 12: HH2* = RSS (1:128,1:128) 13: HL* = HL, LH* = LH, HH* = HH 14: HL*(1:128,129:256) = RSS (129:256,1:128) 15: LH*(129:256,1:128) = RSS (1:128,129:256) 16: HH*(1:128,1:128) = RSS (129:256,129:256) 17: C* = IDWT2level [LL2, HL2, LH2, HH2*, HL*, LH*, HH*] 18: (Uw1′, Vw1‘) = ChaoticEncrypt ( Uw1, Vw)