Research And Implementation Of Elliptic Curve Cryptography Algorithm

Security issues are playing an important role in the modern communication and computer networks. As the Internet becomes more and more accessible for the public to understand and employ, many kinds of commercial and social transactions can be performed electronic form in the network. Using all kinds of cryptographic algorithms can insure security of these activities. Elliptic Curve Cryptography (ECC) systems, which are a series of public-key systems, are presented first by Miller and Koblitz independently. Elliptic curves cryptography algorithm has a high safety property and faster speed, allows for shorter key lengths, requires fewer computational resources for implementation than other traditional public-key algorithms based on the discrete logarithm in finite fields and the integer factorization problem. The theory of ECC is being studied a lot and it is the focus of the cryptography and the industrial estate, especially the technique of the implementation of ECC.The fundamental theory of the modem cryptology is firstly researched, three sorts of existed public-key algorithms and elliptic curves cryptography algorithm are introduced too. Secondly, Galois field theory and finite group theory related with elliptic curve cryptography are discussed. Then the structure of ECC is expatiated in detail, the algorithms of modular multiplication, modular squaring, modular inversion based on Galois field and point addition, point multiplication, double point based on finite group are focus on too. This tesis ascertain the implementation of elliptic curves cryptography algorithm for hardware project: according to the design idea of hiberarchy and modularization, we adopt very high speed IC hardware description language (Verilog) as design input, simulation and synthesis the design in every level and every model for the correction of the fundamental design. After that, finish the top design. Using MATLAB verifies all of these designs. When implementation modular multiplication based on Galois field, a kind of modular multiplication based on look-up table is presented. On the case of consumption some hardware resource, calculating speed of modular multiplication is increased, the efficiency of elliptic curves cryptography is increased too.