FPGA Implementation And Optimization Design Of Algorithms For Elliptic Curve Cryptosystem(ECC)

With the rapid development of the computing speed of computer and the power of Internet distributed calculating, some classical cipher system such as RSA, Diffie-Hellman .etc are more and more insecure when the length of cryptographic key less than 512 bit. Though lengthen cryptographic key may enhance security, encrypt will be more and more inefficiency, in addition the demand for system increasingly higher. Hence, Elliptic Curve Cryptosystem (ECC) has exhibits its advantage fully in "Short Cryptographic Key". ECC tend to substitute RSA as the universal public key cryptographic system.This thesis analyzed Elliptic Curve Cryptosystem along with the arithmetic base of elliptic curve and studied the material algorithms for FPGA implementation of Elliptic Curve Cryptosystem in details. I will present a feasible scheme for hardware implementation of elliptic curve cryptographic system.A mixed parallel-serial multiplying unit is designed, which makes the area and the velocity of the calculation of multiplication match best. Extended Euclidean Algorithm is selected to realize inversion from the standpoint of saving time. Some fast algorithms in allusion to given elliptic curve are abandoned considering diversity of Elliptic Curve Cryptosystem.Four types of the point multiplication algorithms are analyzed in this thesis. Considering the characteristics of subjacent operation, it is concluded that the Montgomery algorithm is easily implemented with FPGA.Through the complete design environment of Quartus II, subjacent operation and point multiplication of Elliptic Curve Cryptosystem are realized by VHDL. These modules are tested by the examples of elliptic curve in ANXI X9.62 and there correctness was proved.Test results show that the processor can work out the whole flow of Elliptic Curve Cryptosystem effectively. Computing KP needs 15.15ms on the average Result in operating frequency is about 20MHz. This processor that has choice parameter and high speed can apply to discretional elliptic curve based on finite field f_l with mless than 256.