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

Elliptic Curves Cryptography (ECC) is evolving as a popular public-key cryptosystems by offering the smaller key size and the highest strength per bit. At one time, the reconfigurable ECC has attracted many researchers because of its flexibility and expansibility in application area.According to hierarchical structure of ECC and involved different operation,this thesis in-depth researches the design theory of reconfigurable ECC. Based on design theory, the entire architecture of reconfigurable ECC is introduced,and the structure and operation flow of each component in entire architecture are studied. In realization of low level operation,a mixed parallel-serial structure is accomplished,which makes the area and the performance to achieve reasonable tradeoff. And the structure of multiplier and squarer is realized,which can be used in arbitrary binary fields and irreducible polynomials. Modular multiplicative inversion is achieved with repeated multiplication and squaring based on the Fermat's theorem. The format of input data is controlled by data interface to satisfy the requirement of point multiplication for different finite fields. In realization of high level operation,different point multiplication arithmetic is analyzed in this thesis, it is concluded that the Montgomery point multiplication algorithm using projective coordinates is easily implemented with FPGA,and implementation result of algorithm is given. Based on implementation of point multiplication operation, the asymmetric cryptographic algorithms on elliptic curve are realized, and their correctness is proved.The architecture is described by VHDL and synthesized by FPGA devices of Altera. Compared with other design, the proposed architecture in this paper can be provided with better selectivity of system parameters and higher operation performance.