Title: A flexible processor for the characteristic 3 η_T pairing

Authors: Robert Ronan, Colin Murphy, Tim Kerins, Colm O.hEigeartaigh, Paulo S.L.M. Barreto

Addresses: Department of Electrical Engineering, University College Cork, Ireland. ' Department of Electrical Engineering, University College Cork, Ireland. ' Department of Electrical Engineering, University College Cork, Ireland. ' School of Computing, Dublin City University, Ireland. ' Escola Politecnica, Sao Paulo, Brazil

Abstract: The η_T pairing is an efficient method for the calculation of the Tate pairing. In this paper, we describe the hardware implementation of the η_T pairing on a supersingular elliptic curve of characteristic 3. All characteristic 3 operations required for the computation of the pairing are outlined in detail. We describe how the required extension field operations can be performed in terms of subfield operations, many of which can be computed in parallel in hardware. The hardware architectures required for pairing computation are also described. An efficient and reconfigurable processor utilising these hardware architectures is presented and discussed. The processor is highly reconfigurable and can easily be tailored for a low area implementation, or for a high throughput implementation or for a desired balance between the two. Results are provided for various configurations of the processor when implemented over the field F397 on an FPGA.

Keywords: η_T pairing; characteristic 3; elliptic curves; reconfigurable processors; flexible processors; Tate pairing; hardware architectures; FPGA.

DOI: 10.1504/IJHPSA.2007.015393

International Journal of High Performance Systems Architecture, 2007 Vol.1 No.2, pp.79 - 88

Published online: 14 Oct 2007 *

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