A Fast FPGA Implementation of Tate Pairing in Cryptography over Binary Field

Tate pairing is a bilinear map used in identity based cryptography schemes. In this paper, we propose an efficient FPGA implementation of the Tate pairing computation on supersingular elliptic curve in GF(2). Because Tate pairing is quite computationally expensive, it is more suitable to implement it using hardware than using software. In this work, we have designed and synthesized all the arithmetic units as well as the Tate pairing module using Xilinx’s FPGA. The results of our experiments demonstrate that the FPGA implementation can speed up the Tate pairing computation by 152 times compared to a software based implementation. Keyword: Tate pairing, public key cryptography, FPGA, Binary field, identity based cryptography.

[1]  G. Frey,et al.  A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curves , 1994 .

[2]  Keshab K. Parhi,et al.  Low-Energy Digit-Serial/Parallel Finite Field Multipliers , 1998 .

[3]  Christof Paar,et al.  Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes , 2002, Des. Codes Cryptogr..

[4]  D. Diamond,et al.  Low-Energy Finite Field Arithmetic Primitives for Implementing Security in Wireless Sensor Networks , 2006, 2006 International Conference on Communications, Circuits and Systems.

[5]  Steven D. Galbraith,et al.  Implementing the Tate Pairing , 2002, ANTS.

[6]  Elisabeth Oswald,et al.  Introduction to Elliptic Curve Cryptography , 2002 .

[7]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1991, STOC '91.

[8]  Christof Paar,et al.  Efficient Multiplier Architectures for Galois Fields GF(2 4n) , 1998, IEEE Trans. Computers.

[9]  Paulo S. L. M. Barreto,et al.  Efficient Implementation of Pairing-Based Cryptosystems , 2004, Journal of Cryptology.

[10]  Soonhak Kwon,et al.  Efficient Tate Pairing Computation for Elliptic Curves over Binary Fields , 2005, ACISP.

[11]  Kris Gaj,et al.  FPGA accelerated tate pairing based cryptosystems over binary fields , 2006, 2006 IEEE International Conference on Field Programmable Technology.

[12]  Paulo S. L. M. Barreto,et al.  Efficient pairing computation on supersingular Abelian varieties , 2007, IACR Cryptol. ePrint Arch..

[13]  T. Itoh,et al.  A Fast Algorithm for Computing Multiplicative Inverses in GF(2^m) Using Normal Bases , 1988, Inf. Comput..

[14]  Kenneth G. Paterson,et al.  ID-based Signatures from Pairings on Elliptic Curves , 2002, IACR Cryptol. ePrint Arch..

[15]  W. Marnane,et al.  FPGA implementation of a GF(2/sup 2M/) multiplier for use in pairing based cryptosystems , 2005, International Conference on Field Programmable Logic and Applications, 2005..

[16]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.