| Research on the elliptic curve over finite field F2m that is suitable for constructing the cryptosystem, analyze the security basis of the elliptic curve cryptosystem and the common attacks to it. Because the security of elliptic curve only has relation to the elliptic curve itself, it is important to select the suited elliptic curve. Indicate that making operation on the elliptic curve is very complicated. Analyze some correlation problem of using elliptic curve over finite field F2m to construct cryptosystem. The elliptic curve through affine transformation can be used to construct public-key cryptosystem and the operation through mapping transformation can facilitate the design of the algorithm and implementation in the elliptic.Expatiate on the ideas and methods of constructing elliptic curve cryptosystem over finite field F2m, build an elliptic curve cryptosystem which is easy to implement and secure. Design a user identity authentication scheme based on the elliptic curve cryptosystem. Up to now, there is no efficient attack found to the elliptic curve discrete logarithm of non-supersingular elliptic curve over finite field, so the scheme is secure in theory and practical. Additional the operation of it is convenient and the implementation is easier as well, so it is suitable for some practice such as electronic business and electronic voting etc.The most time consuming operation of the elliptic curve cryptosystems is the operation elliptic scalar multiplication, kP. We provide an efficient and fast algorithm for computing elliptic scalar multiplication on non-supersingular elliptic curves defined over finite field F2m. Our algorithm is easy to implement in both hardware and software, works for any elliptic curve over finite field F2m,requires no precomputed multiples of a point, needs less memory, and is faster on average than the addition-subtraction method. Therefore, the method possesses many desirable features for implementing elliptic curves in restricted environments. |
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