Design and Implementation of ECM-based Distributed Integer Factorization Tools with GMP-ECM

• Main Authors: Bin-Hui Chou, 周秉慧
• Other Authors: Chung-Huang Yang
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/52698327559186554866

碩士 === 國立高雄師範大學 === 資訊教育研究所 === 94 === Among public key cryptosystems, RSA is considered a secure and practical cryptosystem. The way to generate keys in RSA is to pick two primes, p and q, and to multiply p by q to produce n which is public while p and q are private. Factoring n or finding the factors of n is called integer factorization. The security of RSA depends on the difficulty of integer factorization. Integer factorization algorithms can be divided into two categories. One is that the complexity depends on the size of n, and the other is that the complexity depends on the size of the factor found; ECM, which is highlighted in this thesis, is the best known method in the second category. Most of current factorization tools are console programs on the Linux environment, which does not correspond to the Windows graphical environment accepted by most users. Therefore, two factorization tools are implemented in this thesis. GFactor, the first one, is a GUI tool with multiple factorization algorithms on the Windows and Linux platform. Since the integer factorization is the problem of exponential complexity, a big number is hardly factored by any individual computer. Thus, the second tool of a distributed system with cluster architecture—ECMcontroller is provided. ECMcontroller sends commands to all nodes; nodes perform GMP-ECM command respectively and return results back to the controller as if just one computer were at work.