Karatsuba-Ofman Multiplier with Integrated Modular Reduction for (2m )

In this paper a novel GF(2m) multiplier based on Karatsuba-Ofman Algorithm is presented. A binary field multiplication in polynomial basis is typically viewed as a two steps process, a polynomial multiplication followed by a modular reduction step. This research proposes a modification to the origin...

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Detalles Bibliográficos
Autores: Eduardo Cuevas Farfán, MIGUEL MORALES SANDOVAL, ALICIA MORALES REYES, CLAUDIA FEREGRINO URIBE, Ignacio Algredo Badillo, Paris Kitsos, RENE ARMANDO CUMPLIDO PARRA
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:México
Institución:Instituto Nacional de Astrofísica, Óptica y Electrónica
Repositorio:Repositorio Institucional del INAOE
Idioma:inglés
OAI Identifier:oai:inaoe.repositorioinstitucional.mx:1009/2396
Acceso en línea:http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/2396
Access Level:acceso abierto
Palabra clave:info:eu-repo/classification/Data security/Data security
info:eu-repo/classification/Cryptography/Cryptography
info:eu-repo/classification/Public key/Public key
info:eu-repo/classification/Algorithm design and analysis/Algorithm design and analysis
info:eu-repo/classification/Field programmable gate arrays/Field programmable gate arrays
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1203
Descripción
Sumario:In this paper a novel GF(2m) multiplier based on Karatsuba-Ofman Algorithm is presented. A binary field multiplication in polynomial basis is typically viewed as a two steps process, a polynomial multiplication followed by a modular reduction step. This research proposes a modification to the original Karatsuba-Ofman Algorithm in order to integrate the modular reduction inside the polynomial multiplication step. Modular reduction is achieved by using parallel linear feedback registers. The new algorithm is described in detail and results from a hardware implementation on FPGA technology are discussed. The hardware architecture is described in VHDL and synthesized for a Virtex-6 device. Although the proposed field multiplier can be implemented for arbitrary finite fields, the targeted finite fields are recommended for Elliptic Curve Cryptography. Comparing other KOA multipliers, our proposed multiplier uses 36% less area resources and improves the maximum delay in 10%.