1CHES2006 2006/10/11

An Algorithm for η Ｔ　 Pairing Calculation in Characteristic Three and its Hardware

Implementation

Jean-Luc Beuchat, Masaaki Shirase, Tsuyoshi Takagi, and Eiji Okamoto

University of TsukubaFuture University-Hakodate

2CHES2006 2006/10/11

Context and Research• ηT pairing is

– a pairing on supersingular elliptic curves,– more efficient than Tate pairing.– but its algorithm has cube root operations.

• We research as follows :– New algorithm without cube root is proposed.– It is implemented on (low-cost) FPGA.

• Design board whose price is an entry level desktop PC.

3CHES2006 2006/10/11

ηT Pairing Algorithm

4CHES2006 2006/10/11

FPGA Implementation• Multiplier is based on an improvement of an

algorithm proposed by Song and Parhi.

• It has 9 parallel multipliers.

5CHES2006 2006/10/11

Implementation Result

6CHES2006 2006/10/11

See 　 J-L.Beuchat, M.Shirase, T.Takagi, and E.Okamoto, 　“ An Algorithm for η Ｔ　 Pairing Calculation in 　　　　　　　　　　　　 Characteristic Three and its Hardware Implementation‘’ 　 Cryptology ePrint Archive, Report 2006/327, 2006.

for details.

　　 

Thank You!