# Security Analysis of the Symmetric Cryptosystem Tiny Jambu
## 6 Conclusions  
In this work, the security of the symmetric cryptosystem TinyJambu was analyzed from two distinct and non-symmetric points of view.  
(1) We improved the best cryptanalytical attack against this cryptosystem found in the literature. It deals with a differential forgery attack against the nonce introduction. In fact, by making use of a refined model developed by [PERSON] et al. in [8], we obtained a maximum number of different trails with a minimum number of uncorrelated _AND_ gates. This search, which is much more exhaustive than previous ones, allows us to compute a differential probability of value \(p=2^{-65,9487}\), which is improved considerably compared to previous numerical results, e.g., the \(p=2^{-70,68}\) given by [PERSON] et al. and \(p=2^{-80}\) given by the TinyJambu designers. The new probability increments, in several orders of magnitude, the success probability of a forgery attack and approximates the ideal success probability of value \(p=2^{-64}\). As a future work, we intend to execute the Python programs used in this study in a more powerful computational environment to obtain a differential probability nearer to the bound specified for a successful attack. Moreover, the strategy sketch used to obtain the differential trails when the number of rounds increases was also presented.  
(2) In addition, we analyzed the degree of pseudorandomness of the sequences generated using TinyJambu. Traditionally, the cryptanalytic techniques employed against this cryptosystem were conducted under block cipher cryptanalysis. Nevertheless, in this work, TinyJambu was considered a stream cipher with keystream sequences obtained through the  
Figure 12: Example of Runs Test results for a TinyJambu keystream sequence. Notice that the test is passed by runs of zeros (red line) as well as by runs of ones (blue line) as both fall into the zone delimited by the green lines that bound the permission zone.  
concatenation of the bits used in the encryption/decryption process. Once the sequences were constructed symmetrically in emission and reception, we could study their degree of pseudorandomness. This is an original vision realized to evaluate the strength of the TinyJambu algorithm, which enlarges the possibilities of a security assessment. In this way, a complete and powerful battery of statistical tests was applied to these keystream sequences, which satisfactorily passed the empirical tests.  
This double study enhances the weaknesses of TinyJambu against differential attacks as well as the strength of TinyJambu against statistical analyses. Two different aspects were analyzed, and two non-symmetric conclusions may be drawn from the outcomes of this work.  
The results obtained here can be extrapolated to the updated version proposed by the designers that, in the nonce introduction, increases the keyed permutation to 640 rounds. In fact, the relationship between the number of rounds and the minimum number of uncorrelated _AND_ gates and the optimization of the updated version are our priorities for future works.  
All the authors have equally contributed to the reported research in terms of conceptualization, methodology, software and manuscript revision. All authors have read and agreed to the published version of the manuscript.  
This work is part of the R+D+i grant P2 QProMeTe (PID2020-112586 RB-I00), funded by MCIU/AEI/10.13039/501100011033. The authors are also supported by the University of Malaga (Spain) through \"Red tematica BIOMED-SEC\", reference D5-2022-04.  
Our results are already depicted in the article. The links are given in the references.  
The authors declare no conflicts of interest.