FPGA Implementation Of The ECC On GF(2～(163))

With the development of information technology, the advanced information security is eagerly desired. The cryptography is the key technology. Public key cryptosystem is adopted, but larger scale keys are required with the computing arts enhanced. RSA cryptosystem, a public-key cryptosystem being used widely today, seems to have difficulty in meeting the users'need of high security. However, the elliptic curve cryptosystem (ECC thereafter) is widely concerned due to the highest security of the same lengthbit. In addition, ECC also has many other merits such as less computation overheads, shorter key size, considerable bandwidth savings, and so on. So the ECC is, especially, suitable for situations which are limited by capability of calculation, space, bandwidth and requirement of high implementation. The rapid implementation of the ECC hardware has been a popular topic.In this paper, we study the implementation of the ECC algorithm by the FPGA from practical aspect. Based on mathematics and cryptography theory, integrated some specific relevant algorithm and FPGA, we ascertain the implementation of ECC for hardware project. The paper, which adopts Koblitz curve on GF(2163) recommended by P1363 and module of microprocessor, proves security of the ECC at FPGA. The article, whose every part introduces relevant basic theory and hardware implementation respectively, is achieved by three aspects as Finity Field, the ECC and Encryption Schemes.The circuit design is achieved at the Quartus II 5.0 produced by the Altera adopted the VHDL, and choose the EP2S130F1508C4 of Stratixâ…¡produced by the Altera. In order to high efficiency of hardware, elements of the GF(2163) are showed by the Normal Basis, and its key calculation, multiplication calculation, is introduced by the w-SMPOâ…¡through implementation of module of predicament. The ECC's key calculation----scalar quantity calculation adopts Montgomery's algorithms and is achieved by microprocessor module. Cryptography is acheved by the OPT-PSEC-3 whose security is able to be proved. The every part of the program which is combined with software programme ensures the correctness validity of the program. This project reaches the good target of performance. There are 8,830 ALUTs and...