Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers
Identifieur interne : 003950 ( Main/Exploration ); précédent : 003949; suivant : 003951Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers
Auteurs : Jean-Luc Beuchat [Japon] ; Jérémie Detrey [France] ; Nicolas Estibals [France] ; Eiji Okamoto [Japon] ; Francisco Rodríguez-Henríquez [Mexique]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
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.
Url:
DOI: 10.1007/978-3-642-04138-9_17
Affiliations:
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Instituto Politécnico Nacional No. 2508, 07300, México City</wicri:regionArea><wicri:noRegion>México City</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><affiliations><list><country><li>France</li><li>Japon</li><li>Mexique</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Villers-les-Nancy Cédex</li></settlement></list><tree><country name="Japon"><noRegion><name sortKey="Beuchat, Jean Luc" sort="Beuchat, Jean Luc" uniqKey="Beuchat J" first="Jean-Luc" last="Beuchat">Jean-Luc Beuchat</name></noRegion><name sortKey="Okamoto, Eiji" sort="Okamoto, Eiji" uniqKey="Okamoto E" first="Eiji" last="Okamoto">Eiji Okamoto</name></country><country name="France"><region name="Grand Est"><name sortKey="Detrey, Jeremie" sort="Detrey, Jeremie" uniqKey="Detrey J" first="Jérémie" last="Detrey">Jérémie Detrey</name></region><name sortKey="Estibals, Nicolas" sort="Estibals, Nicolas" uniqKey="Estibals N" first="Nicolas" last="Estibals">Nicolas Estibals</name></country><country name="Mexique"><noRegion><name sortKey="Rodriguez Henriquez, Francisco" sort="Rodriguez Henriquez, Francisco" uniqKey="Rodriguez Henriquez F" first="Francisco" last="Rodríguez-Henríquez">Francisco Rodríguez-Henríquez</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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