# 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}{l l l l} \hline
**Byte Index** & **Swapped Byte** & **Entropy Byte** & **XOR Result** \\ \hline
0 & 01100100 (100) & 10101100 & 11001000 \\ \hline
1 & 11010101 (213) & 11110000 & 00100101 \\ \hline
2 & 10011011 (155) & 00001111 & 10010100 \\ \hline
3 & 0000000 (0) & 1111111 & 11111111 \\ \hline
4 & 0000000 (0) & 10101010 & 10101010 \\ \hline
5 & 00000000 (0) & 11001100 & 11001100 \\ \hline \end{tabular}
\end{table} 
Table 2: Byte-wise exclusive OR operation between the permuted key matrix and an entropy-derived key. Each row shows the index, the original byte after permutation, the corresponding entropy byte, and the resulting byte after XOR. This operation ensures additional obfuscation and entropy infusion, enhancing the resistance of the key material to reverse engineering and correlation attacks. Final hexadecimal output: C8 25 94 FF AA CC. This output can be used directly as a symmetric key, passed to a key derivation function for higher-level cryptographic protocols, or encapsulated in a post-quantum scheme such as Kyber for secure transmission. In terms of security implications, the fusion process introduces structural and stochastic transformations that reduce predictability, increase bit entropy, and frustrate reverse engineering attempts. By layering the reshaping and permutation operations with key-dependent XOR, the method achieves resistance to differential attacks and preserves entropy diffusion, even in the presence of limited entropy sources or partially compromised pseudo-randomness. As a result, we obtain three advantages: security driven by a multiscale prime number generation algorithm, security based on a quantum-inspired approach, and a third ingredient driven by a specific information fusion technique. Thanks to the fusion of the QPIF described above, it is possible to obtain the corresponding hybrid quantum key as a numerical vector similar to a complex string of numbers. The hybrid quantum key is obtained by multiplying the two prime numbers and the private key (1024 bits) using the RSA algorithm. From the fusion of this information, as mentioned above, we obtain a hybrid quantum key with information passed in a chain that appears very random to an intruder. The critical aspect is to understand how robust the key is in terms of cryptographic attacks; this analysis must be carried out in order to authorise the randomness of the constructed key and thus determine whether this solution is suitable for high-security environments. The NIST (National Institute of Standards and Technology) provides a collection of NIST statistical tests that validate the randomness of a fixed-length bit sequence. Following the procedures described above for merging, the NIST tests are performed on a sample of 100 hybrid keys. To perform these tests on the keys obtained, some modifications are necessary: A modulo operation is required to obtain the same size as the 100 keys; in addition, a binary conversion has been performed. The NIST tests used are:  
* Block frequency: The proportion of 0s and 1s present in the M-bit blocks of the sequence. * Cumulative sums: The maximum distance from 0 of a random mode defined by the cumulative sum in which 0s and 1s of the sequence are replaced by \(-1\) and +1, respectively. * Runs: The total sum of runs in the sequence, where a run is a continuous sequence of identical bits. * Longest run: The maximum length of a run of 1 within M-bit blocks of the sequence. The test results are summarised by the \(p\) value, a value between 0 and 1 that confirms the randomness of the sequence. In general, \(p\) values greater than 0.01 confirm that the sequence is random. In these tests, 1024-bit RSA keys are used and all the code generated by 100 irises is 2048 bits in size. The results obtained are shown in Table 3.