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Efficient ηT Pairing Calculation Algorithm and FPGA Implementation for Characteristic Three Curves

This research presents a novel ηT pairing algorithm that eliminates cube root operations, enhancing efficiency compared to traditional Tate pairing techniques on supersingular elliptic curves. Our implementation targets low-cost FPGA boards, comparable to entry-level desktop PCs, featuring a design based on an improved multiplication algorithm with nine parallel multipliers. This advancement offers a robust hardware solution for cryptographic applications. Detailed results and methodology can be found in our publication: J-L. Beuchat et al., "An Algorithm for ηT Pairing Calculation in Characteristic Three and its Hardware Implementation," Cryptology ePrint Archive, 2006.

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Efficient ηT Pairing Calculation Algorithm and FPGA Implementation for Characteristic Three Curves

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  1. An Algorithm for ηＴPairing 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. 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.

  3. ηT Pairing Algorithm

  4. FPGA Implementation • Multiplier is based on an improvement of analgorithm proposed by Song and Parhi. • It has 9 parallel multipliers.

  5. Implementation Result

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

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