High-Performance Integer Factoring with Reconfigurable Devices

Ralf Zimmermann, Tim Güneysu, Chris­tof Paar

International Conference on Field Programmable Logic and Applications, FPL 2010, August 31 2010 - September 2, 2010, Milano, Italy


Abstract

We present a novel FPGA-based implementation of the Elliptic Curve Method (ECM) for the factorization of medium-sized composite integers. More precisely, we demonstrate an ECM implementation capable to determine prime factors of up to 2,424 151-bit integers per second using a single Xilinx Virtex-4 SX35 FPGA. Using this implementation on a cluster like the COPACOBANA is beneficial for attacking cryptographic primitives like the well-known RSA cryptosystem with advanced methods such as the Number Field Sieve (NFS).

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Tags: copacobana, elliptic curve method, Factorization, reconfigurable hardware