針對現代密碼學資訊安全應用探討快速模指數運算與數論分析研究

Modular Exponentiation Arithmetic and Number Theory for Modern Cryptographic Security Applications

　　本文之目的為利用非熱電漿之放電系統來處理青黴菌生物氣膠，以探討及評估放電技術運用於室內空氣品質改善及提升生物安全之可行性。本研究針對電漿功率、頻率、相對溼度及停留時間等變因來探討非熱介電質放電電漿系統對生物氣膠殺菌效果。研究結果發現非熱電漿系統對於生物氣膠具有殺菌效果，殺菌效果隨生物氣膠在電漿反應系統停留時間增加而增加；相對濕度對愈高，殺菌效果愈好。另外，電漿殺菌效率皆隨電漿功率增加而增加，且在高電壓低頻率比低電壓高頻率下之殺菌效果好。在放電頻率為60Hz、反應停留時間1.5秒、功率10W及相對溼度70%下，為非熱DBD電漿系統之最佳殺菌條件。本研究顯示非熱電漿放電系統具有高殺菌能力，未來若能加以評估試驗，將可運用於室內空調系統改善室內空氣品質及做為生物恐怖攻擊之危機處理技術，以提升生物安全及降低生物危害。

　　Most modern cryptographic protocols, which require a large number of processing steps, are based on modular arithmetic. This paper proposes a new fast technique to fast evaluate modular exponentiation which combines a binary exponentiation method, a complement representation method, and a signed-digit representation method. Modular exponentiation is one of the most time-consuming operations for many cryptosystems. Base on the research, we can incorporate modular arithmetic and some novel methods (such as hardware and software designs) to efficiently reduce the number of multiplications for modern cryptographic applications in the future.

Keywords: Signed-digit representation, modular exponentiation, number theory, RSA public key cryptography.