Integer Factorization Based on Elliptic Curve Method: Towards Better Exploitation of Reconfigurable Hardware
Giacomo de Meulenaer, François Gosset, Guerric Meurice de Dormale, Jean-Jacques Quisquater · 2007
Currently, the best known algorithm for factorizing modulus of the RSA public key cryptosystem is the Number Field Sieve. One of its important phases usually combines a sieving technique and a method for checking smoothness of mid-size numbers. For this factorization, the Elliptic Curve Method (ECM) is an attractive solution. As ECM is highly regular and many parallel computations are required, hardware-based platforms were shown to be more cost-effective than software solutions. The few papers dealing with implementation of ECM on FPGA are all based on bit-serial architectures. They use only general-purpose logic and low-cost FPGAs which appear as the best performance/cost solution. This work explores another approach, based on the exploitation of embedded multipliers available in modern FPGAs and the use of high-performances FPGAs. The proposed architecture - based on a fully parallel and pipelined modular multiplier circuit - exhibits a 15-fold improvement over throughput/hardware cost ratio of previously published results.