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題 名 | 解中國餘數定理公式法之不足--圖表法在Excel上的實作=A Novel Method for CRT Based on Simple Model |
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作 者 | 王中全; 陳東志; | 書刊名 | 中州學報 |
卷 期 | 26 2007.12[民96.12] |
頁 次 | 頁145-152 |
分類號 | 312.76 |
關鍵詞 | 中國餘數定理; RSA密碼系統; Chinese remainder theorem; CRT; RSA; Co-prime; Authentication; Broadcast; Access control; |
語 文 | 中文(Chinese) |
中文摘要 | 中國餘數定理 (Chinese Remainder Theorem, CRT) 流傳至今已相當久遠,無論理念上乃至公式上幾近完美,應用上更可說是繁不及備載,尤其在近代的密碼學及資料壓縮上皆有非常重要的應用 [1],例如在RSA密碼系統中,利用中國餘數定理可以使得解密速度快約四倍 [2],並可應用中國餘數定理解決安全廣播系統、通行碼確認、存取控制等問題,皆可利用中國餘數定理解決。唯中國餘數定理公式法仍然有弱點存在,特別是在模數彼此不互質時,即使有解,中國餘數定理公式法並不能做。而簡易圖表法正好足以彌補其不足,在論述及實作上,以更簡易的方法將中國餘數定理清楚表達,論述上分析簡單,作法直覺達到簡單的效果.實作上則以電子試算表Excel來達成清晰、易懂的目的。 |
英文摘要 | Chinese Remainder Theorem (CRT) is a popular theorem for most engineering and scientific applications. CRT is wildly applies to many fields, like RSA cryptographic system employs CRT to achieve four times faster than usual in decompression, CRT also applies to secure broadcast system, authentication and access control, ...,etc. For algorithm, CRT is traditionally applied to several modular numbers with relatively prime numbers to get the result with formulas. On many conditions, the modular numbers are not co-prime numbers but these questions should have answers. However, the traditional CRT with formula does not resolve these questions. In this paper, we propose a simple and clear method to solve these questions with tables and figures. In practice, we apply to Excel work sheet on both methods to compare the results. The results show our method achieves the goals of intuition and efficiency. |
本系統中英文摘要資訊取自各篇刊載內容。