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題 名 | Advanced Fast Binary Modular Arithmetic Algorithms Design and Number Theory Analyses for Public-Key Cryptosystems=公開金鑰密碼學加速演算法進階設計運算應用與數學理論分析研究 |
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作 者 | 吳嘉龍; | 書刊名 | 航空技術學院學報 |
卷 期 | 10:1 2011.08[民100.08] |
頁 次 | 頁15-22 |
分類號 | 312.76 |
關鍵詞 | 公開金鑰密碼系統; 複雜度; 數論研究; 演算法設計; 數值分析; Public-key cryptosystem; Computation complexity; Number theory; Algorithm design; Numerical analysis; |
語 文 | 英文(English) |
中文摘要 | 高效能模指數運算演算法設計分析在公開金鑰密碼學應用與複雜度分析性數論的研究上(包括RSA密碼系統與DSS簽章系統)有相當重要的地位。在此論文中,將深入分析探討快速模運算演算法中之計點演算法( dot counting method)、查表演算法(look-up table method)、模乘數演算法(modular multiplication)、模平方演算法(modular squaring)以及模反運算演算法(modular inverse)技術,基於這些數學理論分析並探討現在最新演算法中演算法的運算複雜度,基於以上數學理論來深入研究分析這些演算法,並找出各演算法優缺點,進一步加以改進現存的快速演算法或者設計出更加快速有效進階的模運算演算法。由於查表法與計點演算法特性可以減少運算重複出現,利用這個優點,得以有效的減少在模算術運算過程中的冗餘乘法運算量,進而減少了整體模運算演算法的計算複雜度。 |
英文摘要 | The modular exponentiation is a common operation for scrambling secret message and is used by RSA public-key cryptosystem and DSS digital signature. Some methods of fast modular exponentiation have been proposed and applied to the above mentioned cryptosystems in past years. The computation of large modular exponentiation is a time-consuming arithmetic operation used in cryptography. The security of RSA cryptography ultimately lies on our inability to effectively factor large integers. Therefore, modular exponentiation can be time consuming, and is often the dominant part of modern cryptographic algorithms for key exchange, electronic signature, and authentication. “Binary algorithm”is the basic method for fast modular multiplication and squaring. New algorithms including “dot counting method”,“look-up table method”, “modular multiplication”,“modular squaring” and “modular inverse” will be full investigated in this paper. I can therefore incorporate modular arithmetic and modern techniques to further effectively reduce the number of multiplications for modern cryptographic applications. |
本系統中英文摘要資訊取自各篇刊載內容。