A chaotic flux cipher based on the random cubic family $f_{c_n}(z)=z^3+c_n z$

Computer Science > Cryptography and Security [Submitted on 21 Mar 2026] A chaotic flux cipher based on the random cubic family f_{c_n}(z)=z^3+c_n z Pouya Mehdipour, Alexandre Miranda Alves, Gerardo Honorato, Mostafa Salarinoghabi This paper presents a symmetric stream cipher that utilizes the dynamic properties of random cubic mappings in the complex plane to generate pseudo-random key streams. The system is based on the iterations of the random cubic polynomial f_n(z)=z^3+c_n z, where the parameters c_n are chosen randomly from a disc of radius \delta and with center at the origin, aiming to improve the chaotic behaviour and, consequently, the randomness of the generated sequence. The stability of the Julia set under small parameter perturbations, when \delta < \delta_0\simeq 0.89, is considered to ensure key consistency in noisy environments, such as 5G networks. On the other hand, for \delta > 3, the system exhibits instability and chaos, ideal for generating ultra-secure keys. The Python implementation integrates secure key derivation, robust key stream generation via warmed-up iteration, and an authenticated encryption scheme using the modern cryptographic primitives (\texttt{HKDF} and\texttt{HMAC-SHA-256}), to ensure message integrity and authenticity. Statistical analyses, including chi-square test and entropy calculation, are performed on the output of the key stream generator to evaluate its randomness and distribution. In addition, a complete statistical validation, compliant with \texttt{NIST SP 800-22} standards in modern cryptography, was performed to enhance the proposed system's credibility. Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2603.20937 [cs.CR]   (or arXiv:2603.20937v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2603.20937 Focus to learn more Submission history From: Pouya Mehdipour [view email] [v1] Sat, 21 Mar 2026 20:35:40 UTC (1,089 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-03 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)