Design And Implementation Of Elliptic Curve Cryptography Over GF(2~m)

In 1985, Miller and Koblitz repectively proposed the Elliptic Curve Cryptography (ECC). It is an approach to public-key cryptography based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) in finite fields. ECC has been regarded as a public-key cryptography candidate with broaden prospective in comparison to RSA. 20 years after its birth, the advantages of ECC over classical cryptosystems in the fields of lower bandwith requirements, higher speed, less storage requirements and high demanding security assurance are still dominant.It is aimed to design a hardware implementation of a high speed ECC. Some of the algorithms of all the arithmetic layers will be compared and analyzed. Furthermore, some measures will be taken in order to optimize the performance of the algorithms for hardware implementation consideration.Our design will optimize the key operation unit of the binary finite field, the Galois field multiplier. Finally, Karatsuba Ofman Algorithm, Parallel Operating, and Pipeline thoughts are introduced to improve the original operation unit, which bright about 27% area reduction and 18% speed acceleration for the whole design.On the ECC arithmetic layer, our design adopts Montgomery point multiplication method which great reduces the overall time of performing single point multiplication. Meanwhile, it makes the design immune to side-channel attack.Our design follows a Top-Down design flow to carry out the work. The architecture are described in Verilog HDL and are verified by the FPGA developing software.