DocumentCode :
3344624
Title :
Integer Factorization Based on Elliptic Curve Method: Towards Better Exploitation of Reconfigurable Hardware
Author :
de Meulenaer, G. ; Gosset, Francois ; de Dormale, G.M. ; Quisquater, Jean-Jacques
Author_Institution :
Univ. Catholique de Louvain, Louvain-La-Neuve
fYear :
2007
fDate :
23-25 April 2007
Firstpage :
197
Lastpage :
206
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.
Keywords :
digital arithmetic; embedded systems; field programmable gate arrays; multiplying circuits; parallel architectures; pipeline processing; public key cryptography; reconfigurable architectures; RSA public key cryptosystem; bit-serial architecture; elliptic curve method; embedded multiplier; general-purpose logic; high-performance FPGA; integer factorization; number field sieve; parallel architecture; parallel modular multiplier circuit; pipelined modular multiplier circuit; reconfigurable hardware; Circuits; Computer architecture; Concurrent computing; Costs; Electrochemical machining; Elliptic curves; Field programmable gate arrays; Hardware; Logic; Public key cryptography; FPGA; Factorization; elliptic curve; parallel modular multiplier.;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Field-Programmable Custom Computing Machines, 2007. FCCM 2007. 15th Annual IEEE Symposium on
Conference_Location :
Napa, CA
Print_ISBN :
978-0-7695-2940-0
Type :
conf
DOI :
10.1109/FCCM.2007.12
Filename :
4297256
Link To Document :
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