FPGA Implementation of Cryptographic Systems Based on Tate Pairing on Binary Field

Pairing-based cryptography is the use of a pairing between elements of two additive group on elliptic curve to a third multiplicative group on finite field to construct or analyze cryptographic systems. The Tate pairing is a common pairing and computed by use of Miller`s algorithm. Improved version for this algorithm on supersingular elliptic curve is named &etaT . Pairing is quite computationally expensive and time consuming. Therefore, it is more attractive to implement on hardware rather than software. In this paper we proposed a new architecture for computation of pairing on F2283. This architecture is resulted from merging two parts of algorithm including pairing and final exponentiation and using resource sharing technique. The base of Tate pairing is finite field arithmetic units. Design and synthesis of this implementation are conducted using Xilinx`s FPGA. Comparison between this result and other work shows that this implementation gains % 38 improvements on calculation time and %10 improvement on product of area and time. Also software implementation is done by SAGE mathematical software for justifying of the results and generating points on elliptic curve.