Research On Hardware Design Method Of Elliptic Curve Cryptography Based On GF(2~m)

Since Koblitz proposed the ECDLP(Elliptic Curve Discrete Logarithm Problem)based on the Abel addition group which is composed by the point of Elliptic Curve,the ECC(Elliptic Curve Cryptography)is favored by people because of the shorter key and higher safety strength.As for the encryption strength,ECC encryption system 163-bit key is equivalent to the RSA algorithm 1024 bit.ECC has been widely used in the field of network security and remote communications,so it's implementation on hardware has significant practical significance.In this paper,the elliptic curve cryptography algorithm based on binary finite field is discussed,and the arithmetic operations in finite fields are further analyzed and improved.On the basis of all,the hardware implementation method of point multiplication is designed,and finaly verified on FPGA hardware platform.To realize the Elliptic Curve Cryptography(ECC)effectively,the Montgomery point multiplication under projection coordinates is adopted in this paper.By the study of the binary finite fields,paralleled modular multiplication algorithm and inversion algorithm which is based on Euclidean algorithm were presented.The two algorithms are optimized during the process and then realized the fast evaluation of point multiplication by adopting Montgomery algorithm.ECC hardware implementation design is proposed based on the method,and converted to logic designs using Verilog RTL,and then synthesized,apr and timing analysis by ISE Design Suit 14.7,finally it works on the XC7A100 T FPGA platform of Xilinx.The result shows that the clock frequency of the circuit could reach up to 105 MHz and the operating rate attained to 24.3?s which demonstrate the feasibility and the effectiveness of the project.