## 2 Motivation
The GGHN cipher exhibits a better behavior in the BIC than the VMPC and RC4+ ciphers, the opposite of the SAC criterion. Using the SAC and BIC criteria extended to stream ciphers, one of the weaknesses in RC4 was the existence of statistical dependence between the outputs and inputs of RC4 (avalanche weaknesses). The RC4A and NGG variants were experimentally shown not to satisfy the SAC and BIC tests. Its behavior is even worse than that of the RC4; these variants do not eliminate the statistical dependence between the outputs and inputs of the RC4; on the contrary, they increase it. The VMPC, RC4+, and GGHN variants substantially reduce the statistical dependency between the RC4 inputs and outputs and meet the SAC and BIC tests. It is recommended not to use the RC4A and NGG variants as they do not eliminate the avalanche type weaknesses present in the RC4. ## 7 Conclusions

RC4 has been one of the most studied stream ciphers in the literature in recent decades, resulting in dozens of variant proposals through various modifications. In this work, five variants of RC4 were analyzed using the SAC and BIC criteria extended to stream ciphers. The VMPC, RC4+, and GGHN variants meet both criteria, while the RC4A and NGG variants do not meet both criteria. Even the NGG variant had worse results than RC4 itself. Future work should apply these criteria to other stream ciphers outside the RC4 scheme. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **RC4** & **RC4A** & **NGG** & **VMPC** & **RC4+** & **GGHN** \\ \hline \(Z_{T}\) & 2690.68 & 5497.67 & 4895.48 & 2.50 & 2.21 & 1.02 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of \(Z_{T}\) for each cipher. Figure 2: Distribution of the fails per bit changed in BIC for \(n=2048,m=32\), and \(l=\)16,384. **Author Contributions:** Conceptualization, E.J.M.-C. and C.M.L.-P.; methodology, E.J.M.-C., C.M.L.-P., O.R. and G.S.-G.; software, E.J.M.-C.; validation, E.J.M.-C., C.M.L.-P., O.R. and G.S.-G.; formal analysis, E.J.M.-C., C.M.L.-P., O.R. and G.S.-G.; investigation, E.J.M.-C., C.M.L.-P. and G.S.-G.; writing--original draft preparation, E.J.M.-C.; writing--review and editing, E.J.M.-C., C.M.L.-P., O.R. and G.S.-G.; visualization, E.J.M.-C.; supervision, E.J.M.-C., C.M.L.-P., O.R. and G.S.-G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. ## Conflicts of Interest

The authors declare no conflict of interest. ## References

* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON] Stream cipher designs: A review. _Sci. China Inf. Sci._**2020**, _63_, 1-25. [CrossRef]
* Specification (2003) Specification, B.C. Specifications List. 2003. Available online: [[https://www.bluetooth.com/specifications/specs/](https://www.bluetooth.com/specifications/specs/)]([https://www.bluetooth.com/specifications/specs/](https://www.bluetooth.com/specifications/specs/)) (accessed on 16 June 2021). * [PERSON] et al. (1999) [PERSON]; [PERSON]; [PERSON] A Pedagogical Implementation of the GSM A5/1 and A5/2 \"Voice Privacy\" Encryption Algorithms. 1999; Volume 26, p. 25. Available online: [[http://cryptome.org/gsm-a512.htm](http://cryptome.org/gsm-a512.htm)]([http://cryptome.org/gsm-a512.htm](http://cryptome.org/gsm-a512.htm)) (accessed on 5 June 2021). * [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] _RC4 Stream Cipher and Its Variants_; CRC Press: Boca Raton, FL, USA, 2011. * RC4 Cipher is No Longer Supported in Internet Explorer 11 or Microsoft Edge. Available online: [[https://support.microsoft.com/en-us/help/3151631/rc4-cipher-is-no-longer-supported-in-internet-explorer-11-or-microsoft](https://support.microsoft.com/en-us/help/3151631/rc4-cipher-is-no-longer-supported-in-internet-explorer-11-or-microsoft)]([https://support.microsoft.com/en-us/help/3151631/rc4-cipher-is-no-longer-supported-in-internet-explorer-11-or-microsoft](https://support.microsoft.com/en-us/help/3151631/rc4-cipher-is-no-longer-supported-in-internet-explorer-11-or-microsoft)) (accessed on 23 May 2021).