To address the challenges of key exchange in symmetric communication, this study proposes a novel pseudorandom number generator (PRNG) paradigm named the ""High-Dimensional Polynomial Randomness Framework"" (HDPRF). The core innovation of this framework lies in its ""logic-configurability,"" where the chaotic behavior is driven by user-defined polynomials rather than a fixed, one-size-fits-all algorithm, offering a new approach to keystream generation. Through a unique ""high-dimensional mixing and projection"" mechanism, the HDPRF framework efficiently expands simple prime number inputs into complex sequences. We conducted rigorous validation using multiple authoritative statistical test suites, including NIST SP 800-22, TestU01, and Dieharder. The results demonstrate that HDPRF possesses an excellent avalanche effect and robust statistical randomness. More importantly, this research not only successfully implements a high-performance PRNG but also identifies a critical structural flaw arising from ""periodic input reuse"" in the current architecture through stringent testing. Furthermore, it proposes an ""optimal practice dimension interval"" that balances security and performance. This study lays a theoretical foundation for configurable PRNG design and presents a novel design pathway that combines theoretical depth with practical value.