Real-Time Analysis and Security Integration of Prime Generation Algorithms in Encryption Systems

In modern cryptography, the generation of prime numbers for encryption keys faces significant challenges, particularly in balancing computational efficiency with security robustness. Existing algorithms like the Sieve of Eratosthenes and Atkin's Sieve struggle to meet the demands of real-time encryption systems, especially in resource-constrained environments. The Sieve of Eratosthenes, while simple, becomes increasingly inefficient for large prime generation, leading to slower key creation times. Atkin's Sieve, though theoretically faster, presents implementation complexities that can hinder practical application. Additionally, both methods face security vulnerabilities when used in predictable patterns for key generation. This study addresses these issues by proposing a Next Nearest Prime Key Generation Algorithm, designed to optimize speed without compromising security. We conduct a comprehensive comparison of our algorithm against traditional methods, evaluating key generation times, encryption/decryption speeds, and security implications across various data sizes and computational scenarios. Our research integrates advanced security measures like Key Encapsulation Mechanisms (KEM) and Key Derivation Functions (KDF) to enhance overall system security. Through real-time analysis in a Java-based encryption system, we demonstrate how our approach mitigates the efficiency-security trade-offs inherent in existing algorithms. This study offers crucial insights for developers and security professionals, providing a framework for selecting and implementing prime generation algorithms that balance performance and security in diverse computational environments, from IoT devices to high-performance systems.