由於網際網路的興起，許多重要的資料開始經由網路傳輸，但如何保護傳輸資料不被他人竊取，便成為一個相當重要的議題。傳統的對稱式加密系統已不能滿足網際網路環境的需求，這使得公開金鑰密碼系統的需求日增。目前主流的公開金鑰密碼系統為 RSA，而 RSA 的理論安全性是建構在因數分解的難度上。因此， RSA 中的大數到底需要多大才算安全，自然就成為 RSA 系統安全的研究重點。到目前為止，分解 100 位數以上的 RSA 數最有效率的分解法為通用型數域篩選因式分解法。在本篇論文中，我們在一台 Linux Server 上實作該分解法，並藉由觀察參數調整的結果，以作為改進分解效能的建議。 With the explosive growth rate of the Internet, there are more and more data transferred by Internet. Therefore, the ability to conduct electronic communications and transactions securely has become an issue of vital concern. The public key cryptosystem arises because the conventional secret-key cryptosystem can not meet the needs of distribution application. RSA is a very popular public key cryptosystem and its security relies on the difficulty of factoring a large number. Because of the popularity of this algorithm, much research has gone into this problem. As we know, the General Number Field Sieve(GNFS) is the asymptotically fastest factoring algorithm for large integers. In this thesis, we will implement this algorithm on a Linux server and discuss how to tune its parameters to get better performance.
