# A Novel Hybrid Elementary Cellular Automata and Its Application in a Stream Cipher
## 4 Stream Cipher Based on HECA-M
### Description of Proposed Stream Cipher
The HECA-Ms exhibit different properties under different rule groups (\(r0\), \(r1\), \(rm\)). Thus, the information entropy (IE) is introduced to test the randomness of the sequences generated by the different HECA-Ms. The HECA-Ms with 27 chaotic rule groups stand out in this test, which are selected to build the stream cipher. The proposed stream cipher comprises the HASH function, HECA-M, and a buffer. The HASH function provides good diffusion and initial sensitivity. Meanwhile, the weak initial value of the HECA-M can be avoided effectively through the HASH function and a constant vector. The HECA-M can generate the original keystream with good randomness that has passed the NIST test. The buffer can control the output of the keystream, including intercepting initial iterations and selecting sequences from the original keystream to form the final keystream. The security analyses prove that the proposed stream cipher can resist traditional attacks, such as B-M synthesis, linear analysis, and correlation analysis. In addition, it also possesses good resistance to the novel attack, including the time-memory-data tradeoff attack and the guess-and-determine attack. The proposed stream cipher is highly efficient and feasible in terms of its time and space consumption, making it suitable for multimedia encryption applications that involve large amounts of data. In the future, a valuable research direction would be to optimize the stream cipher further and integrate it into hardware in a lightweight form. Conceptualization, P.D. and Y.D. ; methodology, Y.D. and Q.C. ; formal analysis, Q.C. ; investigation, Y.D. ; resources, H.L. ; writing--original draft preparation, P.D. and Y.D. ; writing--review and editing, Q.C. ; supervision, H.L. ; funding acquisition, H.L. and Y.D. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China, grant number 2022 YFC3302401, and the Fundamental Research Funds for the Central Universities, grant number 3282024020. Not applicable. Data Availability StatementThe original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest. ## References

* (1) [PERSON]; [PERSON]; [PERSON] The Odyssey of Entropy: Cryptography. _Entropy_**2022**, _24_, 266. [CrossRef]
* (2) [PERSON]; [PERSON]; [PERSON] Design and Analysis of Stream Ciphers: Past, Present and Future Directions. _J. Cryptologic Res._**2016**, \(3\), 527-545. * (3) [PERSON]; [PERSON]; [PERSON] _Handbook of Applied Cryptography_; CRC Press: Boca Raton, FL, USA, 1997. * (4) [PERSON]; [PERSON] Image encryption using modified perfect shuffle-based bit level permutation and learning with errors based diffusion for IoT. _Comput. Electr. Eng._**2022**, _100_, 107954. * (5) [PERSON]; [PERSON]; [PERSON]; [PERSON] Security and Efficiency of Linear Feedback Shift Registers in GF(2(n)) Using n-Bit Grouped Operations. _Mathematics_**2022**, _10_, 996. [CrossRef]
* (6) [PERSON] _Analysis and Design of Stream Ciphers_; Springer: New York, NY, USA, 1986. * (7) [PERSON]; [PERSON]; [PERSON] Multiples of primitive polynomials and their products over GF(2). In Proceedings of the 9 th Annual International Workshop on Selected Areas in Cryptography, St. John's, NF, Canada, 15-16 August 2003; pp. 214-231. * (8) [PERSON]; [PERSON]; [PERSON] Practical Cryptanalysis of Bluetooth Encryption with Condition Masking. _J. Cryptol._**2018**, _31_, 394-433. [CrossRef]
* (9) [PERSON]; [PERSON] Chaos-based medical image encryption scheme using special nonlinear filtering function based LFSR. _Multimed. Tools Appl._**2021**, _80_, 19803-19826. [CrossRef]
* (10) [PERSON]; [PERSON]; [PERSON]; [PERSON] Key-Dependent Feedback Configuration Matrix of Primitive sigma-LFSR and Resistance to Some Known Plaintext Attacks. _IEEE Access_**2022**, _10_, 44840-44854. [CrossRef]
* (11) [PERSON]; [PERSON]; [PERSON] When Lagged Fibonacci Generators jump. _Discrete Appl.