Hardware Factorization Based on Elliptic Curve Method

The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for factorization large integers is the General Number Field Sieve (GNFS). Recently, architectures for special purpose hardware for the GNFS have been proposed [5, 12]. One important step within the GNFS is the factorization of mid-size numbers for smoothness testing, an efficient algorithm for which is the Elliptic Curve Method (ECM). Since the smoothness testing is also suitable for parallelization, it is promising to improve ECM via special-purpose hardware. We show that massive parallel and cost efficient ECM hardware engines can improve the cost-time product of the RSA moduli factorization via the GNFS considerably. The computation of ECM is a classical example for an algorithm that can be significantly accelerated through special-purpose hardware. In this work, we present an efficient hardware implementation of ECM to factor numbers u...

• Type: Conference
• Year: 2005
• Where: FCCM
• Authors: Martin Simka, Jan Pelzl, Thorsten Kleinjung, Jens Franke, Christine Priplata, Colin Stahlke, Milos Drutarovský, Viktor Fischer
• Keywords: Efficient Ecm Hardware, FCCM 2005, GNFS, Hardware, Special-purpose Hardware