# A Hybrid Key Generator Model Based on Multiscale Prime Sieve and Quantum-Inspired Approaches
## 6 Analysis of Results for the First Implementation  
A comparative analysis of the five methods of quantum key generation (Schrodinger eigenvalues, quantum random number generator (QRNG), quantum key distribution (QKD), quantum simulation, and quantum hashing) highlights different performance characteristics based on different criteria:  
1. Execution time: the time required to generate a 2048-bit key varies depending on the methods, reflecting differences in computational complexity and resource requirements. 2. Entropy: this metric evaluates the randomness of the generated keys. Higher entropy values indicate results closer to ideal randomness, which is essential for cryptographic security. 3. Mean and standard deviation: these statistical measures provide information about the distribution of key values, with ideal random sequences exhibiting specific expected behaviours. We compare this result with those reported in the previous literature. Over the last decade, enormous progress has been made in quantum key generation techniques. Among the most interesting developments are:  
Quantum key distribution with decoy states: To address vulnerabilities in real-world QKD systems, such as photon number splitting attacks, the decoy state method was created. This method uses more than one intensity level at the transmitter source so that interception attempts can be detected and the secure transmission rate increased. Dual-field QKD: Developed in 2018, this avoids the speed-distance limitations of traditional QKD by enabling secure key exchange over longer distances without the need for quantum repeaters. Experimental demonstrations have revealed that it can violate the secret key capacity limit without repeaters. Quantum random number generators (QRNGs): Technological advances in the field of QRNGs have enabled hardware solutions based on emulated quantum effects that produce random (true pseudo-random) numbers. Generators are essential for cryptographic applications that require high-quality randomness. References [30; 31; 32; 33] provide a clear summary of the progress made over the last decade in quantum key generation methods, with the continued pursuit of improved security and efficiency in cryptographic applications. We have developed two comparative graphs:  
1. Comparison of execution times: this graph illustrates the computational efficiency of our five quantum key generation methods compared to those reported in the scientific literature. 2. Comparison of entropy: this graph shows the random quality of the generated keys, comparing our methods with established quantum cryptography techniques from published research. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **Execution Time (ms)** & **Entropy** & **Mean** & **Std Dev** \\ \hline Schrodinger & 1.031 & 2290 & 4117 & 2837 \\ \hline QRNG & 0.097 & 2308 & 4500 & 2756 \\ \hline QKD & 0.150 & 2299 & 4691 & 2987 \\ \hline Quantum & 0.261 & 2298 & 4336 & 2825 \\ Simulation & 2.388 & 2281 & 4309 & 2978 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative analysis of key generation methods (the comparative analysis is based on a combination of data extracted from the literature and benchmarking results conducted under controlled conditions in present work). quantum mechanics. Our ranking of the five methods is as follows: (i) QRNG: 2 nd place, (ii) QKD: 3 rd place, (iii) quantum simulation: 5 th place, (iv) Schrodinger eigenvalues: 6 th place, and (v) quantum hashing: 7 th place. This analysis shows that QRNG and QKD (where we refer to computational QKD as in [21]) achieve the best results among our approaches, closely competing with the state-of-the-art methods in the literature. However, Schrodinger eigenvalues and quantum hashing ranked lower due to their longer execution times and lower entropy values. Furthermore, we would like to highlight that the work introduces a quantum mechanics-inspired key generation strategy that has proved strong statistical randomness based on NIST STS.