## Integer Factorization Based on Elliptic Curve Method: Towards Better Exploitation of Reconfigurable Hardware

Citations: | 6 - 0 self |

### BibTeX

@MISC{Meulenaer_integerfactorization,

author = {Giacomo De Meulenaer and François Gosset and Guerric Meurice De Dormale and Jean-jacques Quisquater},

title = {Integer Factorization Based on Elliptic Curve Method: Towards Better Exploitation of Reconfigurable Hardware},

year = {}

}

### OpenURL

### 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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(Show Context)
Citation Context ...ing mid-size numbers [8]. While those numbers are easily factorizable, the challenge lies in the amount of computation: factorization of 1014 125-bit numbers for a 1024-bit modulus is required (using =-=[3]-=-). For this task, the Elliptic Curve Method (ECM) appears as an attractive solution. Up to now, the best successful factorization attempts were for RSA-200 (663-bit) and RSA-640, solved in 2005 by Bah... |

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Citation Context ...m for factorizing RSA modulus is the Number Field Sieve (NFS), introduced by Pollard in 1991. It is composed of a sieving and a matrix step, the former being the most expensive part for 1024-bit keys =-=[6]-=-. The reader is referred to [15] for an introduction to the NFS and to [10] for the details. This paper focuses on the sieving step and more precisely on the relation collection step. This task is usu... |

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(Show Context)
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2 |
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(Show Context)
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2 |
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(Show Context)
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2 |
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Citation Context ...pose hardware came out to lower the cost of both machine and power consumption. Such proposals in the context of the NFS sieving step are the TWINKEL device, mesh-based sieving, TWIRL and SHARCS (see =-=[17]-=- for an overview and references). ECM is one of the building block of SHARCS [3] and it was proposed to combine it with TWIRL in [5]. For the design of a hardware machine a platform has first to be ch... |