# A Hybrid Key Generator Model Based on Multiscale Prime Sieve and Quantum-Inspired Approaches
## 10 Fusion Effects: An Example, Results, Discussion, and Perspectives  
The JDL model acts here not only as a conceptual abstraction, but also as a structural constraint: it ensures that the hybridisation of entropy sources (an approach inspired by quantum mechanics and multiscale sieving) occurs in a logically correct and semantically layered manner. Level 1 fusion maps the combination of vector elements in the U matrix, while level 2 maps the context-sensitive permutation via private keys. These mappings reinforce consistency and interpretability between cryptographic layers. To illustrate the fusion mechanism described in Section 9, we present a complete numerical example that includes the phases of binary filling, reshaping into a structured matrix, private key-based permutation, and final obfuscation via an exclusive OR operation with an entropy-derived key. This example has been intentionally simplified in terms of size for clarity, but it retains the architectural principles of the large-scale implementation. Step 1: Filling the binary key sequence. Consider an initial binary sequence generated by the quantum-inspired pseudo-random number generator:  
Initial sequence (binary): 11010101 10011011 011001. This sequence contains twenty-two bits, which are not aligned to the nearest multiple of eight. To facilitate matrix-based transformation, the sequence is padded with two additional bits to reach a length of twenty-four bits (three full bytes):  
Filled sequence: 11010101 10011011 01100100. The filling method can use fixed patterns (e.g., zeros) or low-entropy suffixes, depending on the entropy profile and security requirements. Step 2: Reorganisation into a byte array. The three filled bytes are converted to their decimal equivalents:  
* 11010101 = 213. * 10011011 = 155. * 01100100 = 100. These values are then organised into a 2 \(\times\) 3 matrix in row order. Since only three bytes are available, the remaining elements of the matrix are filled with zeros or random entropy from the PRNG:  
Matrix before permutation: [213, 155, 100], [0, 0, 0]. This two-dimensional reorganisation facilitates the application of structured permutations using matrix transformation techniques. Step 3: Column permutation using a private key. Let us assume that the private key associated with the merge engine contains a permutation vector that indicates a reordering of the columns of the matrix. For example:  
Permutation vector: [2, 0, 1]. This indicates that column 2 must become column 0, column 0 becomes column 1, and column 1 becomes column 2. Applying this permutation results in the following transformed matrix:  
Matrix after column permutation: [100, 213, 155], [0, 0, 0]. The permutation introduces key-dependent diffusion, which improves resistance to statistical inference and provides entropy dispersion. Step 4: Matrix flattening. The permuted matrix is flattened again into a linear sequence of bytes:  
Flattened sequence: [100, 213, 155, 0, 0, 0]. Corresponding binary: 01100100 11010101 10011011 0000000 00000000 00000000. This relinialised form serves as the intermediate merged output before final obfuscation. Step 5: Exclusive OR with entropy-derived key. Let us assume that a six-byte entropy key has been independently derived or sampled:  
Entropy key (binary): 10101100 11110000 0000111 1111111 10101010 11001100. The fusion engine performs a byte-by-byte exclusive OR (XOR) between the flattened sequence and the entropy key (see Table 2). The result of this operation is a cryptographically fused key sequence:  
Final binary output: 11001000 00100101 10010100 11111111 10101010 1100100.