Research Of Elliptic Curve Cryptosystem Based On ONB And Implementation Of FPGA

With the rapid development of telecommunications, more and more embedded devices begin to be connected to Internet, so those network security problems may appear in these devices. Elliptic Curve Cryptosystem (ECC) is a high-security public-key cryptography, and ECC based on Optimal Normal Basis (ONB) is more efficient. Therefore it is very necessary to research and implement ECC based on ONB.Based on deep analysis of ECC in the finite field on ONB and elliptic curve field, this thesis proposes an ECC digital signature solution which can be applied to embedded devices. By selecting the optimized Montgoment algorithm, the point multiplication in the elliptic curve field becomes low in time complexity. Where two steps in this algorithm are not dependent, they can be performed in parallel. And where two steps in this algorithm are the same operation, such as both multiplications in the finite field, only one module is in need. Through these optimization measures above, both time and resources can be reduced significantly in point multiplication. By linear feedback shift registers, the period of data generated from pseudo random number generator is (263-1); to decrease the data transferring time between different modules, serial- parallel function is designed in this generator. The point addition in elliptic curve field selects affine coordinate, and reuses finite field multiplication and finite field inverse modules. So, the point addition, finite field multiplication and finite field inverse can be integrated into one module. The modulo operation can be implemented by subtraction. The module called SHA can perform the basic calculation of hash according to SHA-256 algorithm.The simulation results show that the point multiplication is 462.234Kbit/s, and occupy 30K LEs in FPGA; pseudo random number generation is 4.38Mbit/s at least; point addition, 24.23Mbit/s; multiplication, 561.76Mbit/s; inverse, 26.45Mbit/s; modulo operation, 4.77Gbit/s; hash operation, 382.08Mbit/s, all under 50Mhz clock frequency.Finally, the efficiency of this thesis is analyzed and calculated. The result is that signature speed is 382 Mbit/s, and the verifying speed is 189 Mbit/s.