1. CHES2006 2006/10/11 1 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 Tsukuba Future University-Hakodate

2. CHES2006 2006/10/11 2 Context and Research η T 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.

3. CHES2006 2006/10/11 3 ηT Pairing Algorithm

4. CHES2006 2006/10/11 4 FPGA Implementation Multiplier is based on an improvement of an algorithm proposed by Song and Parhi. It has 9 parallel multipliers.

5. CHES2006 2006/10/11 5 Implementation Result

6. CHES2006 2006/10/11 6 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!