*4.8. Encryption Efficiency Analysis*

In this paper, the simulation is performed on Inter(R) Core(TM) i7-6700K CPU @ 4.00 GHz with 16.0 GB in MATLAB R2019b. The average encryption time of a 256 × 256 image is 0.425 s, and the decrypted time is 0.452 s. To analyze the proposed encryption algorithm, the encryption throughput (ET) and number of cycles [33] are calculated by:

$$ET = \frac{Image\_{size}(byte)}{Energy\_{time}(second)},\tag{20}$$

$$Number\ of\ cycles\ per\ byte = \frac{\mathbb{C}Pul\_{speed}(Hertz)}{ET(byte)}.\tag{21}$$

The ET of the proposed algorithm is 0.1471 MBps (million byte per second) and the algorithm needs 25,932.68 cpu cycles to finish one-byte operation.

## **5. Conclusions**

In this paper, we constructed a new chaotic map, named TDSCL, which combines the delay tent map with the sine map, which is then cascaded with the logistic map. Compared with the DLCL and LSMCL methods, the simulation results indicated with the chaotic map that our proposed method has a larger Lyapunov exponent and permutation entropy, which demonstrates that it has a better initial value sensitivity and randomness. In addition, we proposed an image encryption algorithm with simultaneous confusion and diffusion in the vertical and horizontal directions. We analyzed the algorithm in terms of the key space, key sensitivity, ability against chosen-plain text attacks, and information entropy. The simulation results showed that this algorithm can resist statistical attacks and chosen-plain text attacks.

**Author Contributions:** Conceptualization, G.Z.; methodology, G.Z.; software, W.D.; validation, G.Z.; formal analysis, G.Z.; investigation, G.Z.; resources, G.Z.; writing—original draft preparation, G.Z.; writing—review and editing, W.D., L.L.; visualization, G.Z.; supervision, G.Z.; project administration, G.Z.; funding acquisition, G.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to thank the National Key R&D Program of China (Grant Nos. 2018YFB1003205 and 2017YFE0111900) and the 2019 Gansu Key Talent project for their support.

**Conflicts of Interest:** The authors declare no conflict of interest.
