# A Hybrid Key Generator Model Based on Multiscale Prime Sieve and Quantum-Inspired Approaches
### Context and Related Works  
In ref. [2], a new algorithm was introduced to improve RSA prime number-based encryption with information fusion and fractal technology. Quantum features were introduced, namely the random evolution of key fragments and the recombination of key fragments to obtain a quantum-resistant key, as the key becomes cryptographically agile. Techniques that produce truly random numbers suitable for cryptographic systems have been available for decades [3]. The same is true for prime numbers [4]. However, the use of fractals as cryptographic tools is a recent idea and a rapidly growing field of research [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. It is clear that fractal geometry was born in a formal sense in 1982 with the publication of [PERSON]'s book [18] and, in recent times, so-called Mandelbrot sets are widely used in cryptographic practice. In this work, we would like to focus on number theory-based cryptography reinforced by an approach inspired by quantum mechanics to mimic real quantum behaviours [19; 20; 21; 22], also using fusion techniques as in [23]. What does a quantum mechanics-inspired approach mean and why use it? \"Quantum mechanics-inspired\" refers to the use of mathematical models and their numerical implementation used in quantum mechanics and computational physics. They are very useful for hybrid cryptography and during the transition from traditional to quantum computing. It is clear that quantum cryptography uses the properties of quantum mechanics to provide greater security than classical methods. The most important feature is quantum key distribution, which allows a cryptographic key to be generated and exchanged securely, detecting any interception. Just think of [PERSON]'s uncertainty principle. If we measure a quantum state, then we irreversibly alter the state itself. For this reason, if a hacker tries to intercept the key, the system recognises it immediately. Furthermore, in the quantum regime, the so-called entanglement applies. Two particles can be correlated in such a way that any change in one will have an immediate effect on the other, making the system extremely secure. Quantum theory is definitely the future of cryptography. It will be possible to send data in an inviolable way for banking, military, and government applications. There will be ultra-secure connections between quantum computers. Furthermore, classical cryptography is vulnerable to next-generation quantum computers, while quantum cryptography is able to resist them. In other words, quantum cryptography is a possible direction for ensuring secure communications in a post-quantum world. However, another important line of research, known as post-quantum cryptography, focuses on classical algorithms (such as lattice-based schemes, codes, or hashes) that are believed to be resistant to quantum attacks without relying on quantum communication channels. Without claiming to be exhaustive, a significant contribution to the state of the art, particularly with regard to hardware-based quantum algorithms, is provided in [24; 25; 26; 27]. In addition, post-quantum cryptography (PQC), such as lattice-based algorithms, including Kyber and Dilithium, also provides resistance to quantum attacks [19]. Note that this work is explicitly based on a quantum-inspired methodology, as indicated in the title. It does not rely on quantum hardware, but rather proposes post-quantum solutions suitable for immediate use on classical computing systems. Another relevant issue that we will discuss concerns quantum resistance [28; 29; 30; 31; 32; 33; 34; 35; 36]. Our approach does not rely on cryptographic assumptions that are known to be broken by quantum computers, such as factorisation or discrete logarithm problems. Although we do not formally prove quantum resistance, the multilayered design, which combines quantum-inspired entropy, prime-number-based structural complexity, and fusion-based composition, adds layers of obfuscation and entropy that can contribute to post-quantum resilience.