Compact and Flexible Microcoded Elliptic Curve Processor for Reconfigurable Devices

This paper presents a very compact and flexible processor to support Elliptic Curve (EC) cryptosystems based on GF(2^m) finite fields. This processor can be customized with a two-level microinstruction hierarchy that allows for customization of both field operations and EC algorithms. It was specially designed to benefit from reconfiguration capabilities to scale arithmetic units for different sizes and to replicate processing units to enhance performance. The flexibility resulting from these characteristics was not found in the related art. The proposed processor was implemented and thoroughly tested in a Xilinx Virtex XC4VSX35, supporting a real EC algorithm for point multiplication for a GF(2^163) field, requiring 1.35ms, and using up to 15 times less area than related implementations.

[1]  Philip Heng Wai Leong,et al.  A microcoded elliptic curve processor using FPGA technology , 2002, IEEE Trans. Very Large Scale Integr. Syst..

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

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

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

[5]  Ricardo Chaves,et al.  Efficient FPGA elliptic curve cryptographic processor over GF(2m) , 2008, 2008 International Conference on Field-Programmable Technology.

[6]  G. Seroussi Compact Representation of Elliptic Curve Points over F 2 , 1998 .

[7]  Ingrid Verbauwhede,et al.  Elliptic-Curve-Based Security Processor for RFID , 2008, IEEE Transactions on Computers.

[8]  Sorin A. Huss,et al.  FPGA based hardware acceleration for elliptic curve public key cryptosystems , 2004, J. Syst. Softw..

[9]  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..

[10]  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).

[11]  Andreas Curiger,et al.  On Computing Multiplicative Inverses in GF(2^m) , 1993, IEEE Trans. Computers.

[12]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[13]  Zoya Dyka,et al.  Area efficient hardware implementation of elliptic curve cryptography by iteratively applying Karatsuba's method , 2005, Design, Automation and Test in Europe.

[14]  Theerayod Wiangtong,et al.  International Conference on Field Programmable Technology , 2006 .

[15]  Mohammed Benaissa,et al.  Fast Elliptic Curve Cryptography on FPGA , 2008, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.