An FPGA implementation of elliptic curve cryptography for future secure web transaction

Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. So it would be more attractive to implement this unit using hardware than using software. In this paper, we propose an efficient FPGA implementation of the elliptic curve point multiplication in GF(2). We have designed and synthesized the elliptic curve point multiplication with Xilinx’s FPGA. Experimental results demonstrate that the FPGA implementation can speedup the point multiplication by 31.6 times compared to a software based implementation.

[1]  Alfred Menezes,et al.  Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.

[2]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[3]  Dan S. Wallach,et al.  Performance analysis of TLS Web servers , 2006, TOCS.

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

[5]  N. Koblitz Elliptic curve cryptosystems , 1987 .

[6]  Francisco Rodríguez-Henríquez,et al.  A parallel architecture for fast computation of elliptic curve scalar multiplication over GF(2/sup m/) , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[7]  Jean-Jacques Quisquater,et al.  High-speed hardware implementations of Elliptic Curve Cryptography: A survey , 2007, J. Syst. Archit..

[8]  Christof Paar,et al.  A High Performance Reconfigurable Elliptic Curve Processor for GF(2m) , 2000, CHES.

[9]  M. Anwar Hasan,et al.  High-Performance Architecture of Elliptic Curve Scalar Multiplication , 2008, IEEE Transactions on Computers.

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

[11]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[12]  Douglas Stebila,et al.  Performance analysis of elliptic curve cryptography for SSL , 2002, WiSE '02.

[13]  Ricardo Dahab,et al.  Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation , 1999, CHES.

[14]  Tarek A. El-Ghazawi,et al.  Low latency elliptic curve cryptography accelerators for NIST curves over binary fields , 2005, Proceedings. 2005 IEEE International Conference on Field-Programmable Technology, 2005..

[15]  Wai Keung Wong,et al.  FPGA implementation of a microcoded elliptic curve cryptographic processor , 2000, Proceedings 2000 IEEE Symposium on Field-Programmable Custom Computing Machines (Cat. No.PR00871).

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

[17]  Miguel Morales-Sandoval,et al.  On the hardware design of an elliptic curve cryptosystem , 2004, Proceedings of the Fifth Mexican International Conference in Computer Science, 2004. ENC 2004..

[18]  Sorin A. Huss,et al.  Rapid prototyping for hardware accelerated elliptic curve public-key cryptosystems , 2001, Proceedings 12th International Workshop on Rapid System Prototyping. RSP 2001.