Study on Factorization of n = p * q

• Main Authors: Yu-Hao Chang, 張煜�c
• Other Authors: Yi-Shiung Yeh
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/48362942165229681606

碩士 === 國立交通大學 === 資訊科學與工程研究所 === 95 === The RSA Cryptosystem is one of the most used public-key cryptosystems. The security it rests on the fact that it is computationally infeasible to factor a large integer into its component primes. This fact is referred to as the RSA assumption. It is believed that there is no deterministic Turing machines (DTM) that can break the RSA assumption in polynomial time. If a polynomial-time algorithm is found, the RSA Cryptosystem would be insecure. Owing to this, many scientists have devoted themselves to researching efficient factoring algorithms. So far, the quadratic sieve factoring algorithm (abbreviated to QS) is the fastest known general-purpose method for factoring numbers having less than about 110 digits. Restricted by time and computer hardware, we focus on one of the variants of the QS, called the multiple polynomial quadratic sieve (MPQS). To ensure the strength of the RSA assumption, we propose a scheme to enhance the sieving procedure of the MPQS. The experimental results are contributive to the analyses of the strength of the RSA assumption against the modern factoring technology and should be taken into consideration on future cryptographic implementations based on the RSA cryptosystem.