# Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

2 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier. Thanks to a careful selection of algorithms for computing the tower field arithmetic associated to the Tate pairing, we manage to keep the pipeline busy. We also describe the strategies we considered to design our parallel multiplier. They are included in a VHDL code generator allowing for the exploration of a wide range of operators. Then, we outline the architecture of a coprocessor for the Tate pairing over $\mathbb{F}_{3^m}$. However, a final exponentiation is still needed to obtain a unique value, which is desirable in most of the cryptographic protocols. We supplement our pairing accelerator with a coprocessor responsible for this task. An improved exponentiation algorithm allows us to save hardware resources. According to our place-and-route results on Xilinx FPGAs, our design improves both the computation time and the area-time trade-off compared to previoulsy published coprocessors.
Type de document :
Communication dans un congrès
Christophe Clavier and Kris Gaj. 11th International Workshop on Cryptographic Hardware and Embedded Systems - CHES 2009, Sep 2009, Lausanne, Switzerland. Springer, 5747, pp.225-239, 2009, Lecture Notes in Computer Science. 〈10.1007/978-3-642-04138-9_17〉
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https://hal.inria.fr/inria-00424011
Contributeur : Jérémie Detrey <>
Soumis le : mardi 13 octobre 2009 - 16:46:51
Dernière modification le : jeudi 11 janvier 2018 - 06:21:04
Document(s) archivé(s) le : mardi 16 octobre 2012 - 12:11:26

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bdeor_ches2009.pdf
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### Citation

Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals, Eiji Okamoto, Francisco Rodríguez-Henríquez. Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers. Christophe Clavier and Kris Gaj. 11th International Workshop on Cryptographic Hardware and Embedded Systems - CHES 2009, Sep 2009, Lausanne, Switzerland. Springer, 5747, pp.225-239, 2009, Lecture Notes in Computer Science. 〈10.1007/978-3-642-04138-9_17〉. 〈inria-00424011〉

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