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FPGA Implementation and Optimization Design of ECC Cryptographic Algorithm

2014-03-05
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　　This paper mainly studies the implementation and optimization design of elliptic curve cryptography based on FPGA chip. Since the point multiplication operation greatly affects the encryption/decryption speed of the elliptic curve cryptography system, this paper focuses on optimizing the FPGA design of the point multiplication operation. First, three point multiplication algorithms are compared and analyzed, and the Montgomery algorithm is determined to be the most conducive to FPGA chip implementation from the perspective of computational complexity. Then, according to the Montgomery algorithm, the basic operations (modular addition, modular multiplication, modular square and modular inverse) in the elliptic domain based on the FPGA chip are implemented using the VerilogHDL language. Through the implementation of the three modular multiplication algorithms on FPGA, a serial-parallel hybrid multiplier is designed to achieve the best match between area and speed. This paper uses Modelsim to simulate the hardware system designed in this project, and verifies that the designed hardware system completes the implementation of the elliptic curve cryptography algorithm on FPGA. Finally, SynplifyPro is used for synthesis and layout and routing. The synthesis report file proves that the ECC encryption system designed in this project has achieved the purpose of optimizing chip speed and area.

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