本研究提出一種基於 Tinkerbell 混沌系統與餘數數系（Residue Number System, RNS）的多偽隨機數產生器（Multiple Pseudorandom Number Generator, MPNG）設計方法。該方法結合了混沌系統狀態的隨機特性與 RNS 的平行運算能力，能在每一次迭代中同時產生多達六組偽隨機數序列，大幅提升了產生效率。為驗證所生成序列的隨機性品質，本研究採用 NIST SP800-22 測試套件、Diehard 測試項目以及 Shannon 熵分析進行隨機性評估，評估結果顯示具有良好的統計特性。為進一步提升實際應用的安全性，本文設計一組 Tinkerbell 混沌系統的同步控制器，用以實現主僕系統之間的狀態同步，確保所產生的偽隨機亂數序列一致。此機制進一步擴展了 MPNG 的實際應用達成非對稱式加密方法架構。最後，本研究將 MPNG 整合至多代理系統（Multi-Agent System）中，並在資訊交換前進行混淆加密機制，有效保障分散式運算過程中的資料傳輸安全。所提出的方法經由三台輪式移動機器人進行硬體實作驗證，證實方法的可行性與實用性。

This study proposes a design method for a Multiple Pseudorandom Number Generator (MPNG) based on the Tinkerbell chaotic system and the Residue Number System (RNS). By exploiting the inherent randomness of chaotic state evolution and the parallel computation capability of RNS, the proposed method can simultaneously generate six pseudorandom sequences per iteration, significantly improving generation efficiency. The randomness quality of the generated sequences is validated using the NIST SP800-22 test suite, Diehard test items, and Shannon entropy analysis, demonstrating strong statistical properties. To further enhance application security, a synchronization controller for the Tinkerbell chaotic system is developed, enabling state synchronization between the master and slave systems and ensuring the generation of identical random sequences. This mechanism extends the proposed MPNG to an asymmetric encryption framework. Finally, the MPNG is integrated into a Multi-Agent System (MAS), where confusion-based encryption is applied before information exchange, effectively safeguarding data transmission in distributed computing environments. The proposed method was successfully validated through hardware implementation using three wheeled mobile robots, demonstrating its feasibility and practical applicability.

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