Integer factorization based on elliptic curve method: towards better exploitation of reconfigurable hardware
(2007) 15th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM 2007) — Location: Napa, CA, USA (23.April.2007)
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- Abstract
- 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.
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de Meulenaer, G., Quisquater, J.-J., Gosset, F., & De Dormale, G. M. (2007). Integer factorization based on elliptic curve method: towards better exploitation of reconfigurable hardware. 15th Annual IEEE Symposium on Field-Programmable Custom ComputingMachines (FCCM 2007), p. 197-206. https://doi.org/10.1109/FCCM.2007.38