# A Hybrid Key Generator Model Based on Multiscale Prime Sieve and Quantum-Inspired Approaches
## 10 Fusion Effects: An Example, Results, Discussion, and Perspectives
\begin{table}
\begin{tabular}{c c} \hline
**Test NIST** & \(p\)**-Value** \\ \hline Frequency & 0.643843 \\ \hline Block Frequency & 0.832141 \\ \hline Cumulative Sums1 & 0.672973 \\ \hline Cumulative Sums2 & 0.555273 \\ \hline Runs & 0.335148 \\ \hline Longest Run & 0.405573 \\ \hline \end{tabular}
\end{table} 
Table 3: \(p\)-value Test NIST. This work should be considered a conceptual framework for the development of hybrid algorithms inspired by quantum mechanics. Although current NIST randomness tests demonstrate its immediate applicability, the approach presented here will require further evolution with the advent of quantum computers to offer full quantum resistance guarantees. In this regard, the authors have already experimented with a quantum-resistant computational infrastructure (see, for example [35; 36]), which exploits four principles that could be quickly integrated into the current work:  
1. Fragmentation--already implemented here through the information fusion layer. 2. Obfuscation--achieved by composing a hybrid key that combines a numerical component derived from multiscale prime sieving with another component based on randomness inspired by quantum physics. 3. Computational puzzle--a mechanism yet to be implemented, in which key fragmentation introduces reconstruction difficulties for unauthorised parties, as it would require navigation in complex multidimensional spaces inaccessible without adequate authorisation (i.e., the legitimate owner). 4. Distributed key demons--two logical agents responsible for key recomposition and maintaining crypto-agility by (i) distributing sub-blocks of the key across different physical or logical units and (ii) allowing the temporary mixing of these sub-blocks, including exchanges of information similar to interactions between non-elementary quantum particles which, through interaction, emerge with altered physical properties (similar to entanglement and the subsequent diffusion of non-identical particles). Although this work is only a first step and several limitations remain, it provides a promising foundation. Future efforts will focus in particular on the further development of aspects 3 and 4 described above. Another relevant point considered here, but which will be examined more formally in the future, concerns cryptographic agility. The contribution to the security of the fusion path lies in the dynamic and non-linear transformation of the key material, which makes reverse engineering and statistical correlation significantly more difficult for potential attackers. This robustness emerges from multiple levels of transformation, culminating in the final exclusive OR (XOR) with a high-entropy key. However, it is not only the XOR operation that ensures greater security. Rather, the fusion process that precedes the XOR, in particular the internal reorganisation and quantum manipulation of the key structure, is crucial. More specifically, our algorithm employs a fragmentation and dispersion mechanism inspired by the principles of quantum dispersion theory. After the XOR operation has produced an intermediate key matrix, the system dynamically fragments the rows of the matrix and collides them using random transformations. At irregular intervals, two contiguous rows, referred to as row \"m\" and row \"m + 1\", are selected by a demon-like scheduler when the system is idle. These rows are then split asymmetrically into fragments (e.g., a 70%/30% split), producing four components: \(\mathrm{FrA_{1}}\), \(\mathrm{FrA_{2}}\) from row \"m\" and \(\mathrm{FrB_{1}}\), \(\mathrm{FrB_{2}}\) from row \"m + 1\". A cross-mixing operation is applied:  
* Fragment \(\mathrm{FrA_{1}}\) is combined with \(\mathrm{FrB_{2}}\) to form a new row. * Fragment \(\mathrm{FrB_{1}}\) is combined with \(\mathrm{FrA_{2}}\) to form another row. These recombined rows replace the original rows in the matrix, altering the spatial and informational distribution of the key material.