The Implementation Of FPGA Over Elliptic Curves Cryptography Based On GF(2～n)

Elliptic Curve Cryptography (ECC) was the one of the known public crypto methods that provided the best strength-per-bit.Under the same secure conditions,the ECC has the advantages such as less computation amounts,shorter length of documents adopted by many international standard institutions and regarded as the most universally used public key system.An implementation of ECC based on FPGA was discussed in this paper after researching the cryptography and some relevant algorithm.According to the design, under the idea of hiberarchy and modularization, we simulated the designing in every level and every model for the correct of whole simulation.At last, we carryed out the timing simulation after the logic synthesis and layout. The design was very flexible and universal ,and it was suitable for implementation of the FPGA.Firstly, the advantages and present research of Elliptic Curve Crytography was generalized;Secondly, we particularized the hardware design of ECC core modules.A mixed parallel-serial multiplier was designed, which makes the areas and the resources match balanced.In order to reduce the resources, the multiplicative inverse and multiple were placed in the same ALU;Thirdly we realized the ECC on two secure elliptic curves,one was the 191 bit secure curve ,the other was 233 bit secure curve.The design process,hardware architecture and results analysis were offered;Fourthly, the ECC system based on the FPGA was simulated and the test result and analysis were given, the results as in software implementation showed the design was exactness.Finally, the conclusion summarized the whole paper and previewed the further developments we have done.