Conic curve cryptosystem was first introduced by CAO Zhenfu in 1998.By now

the previous study on conic curve cryptosystem has been based on conic curve group in finite field

GF(p).

Since the hardware circuits are suitable for performing addition

multiplication

squaring and the inversion operations in a finite field

GF(2

n

)

the operations in finite field

GF(2

n

) are typically easier to implement in hardware and software than their counterpart in finite field

GF(p)

.In order to speed up the computation of conic curve cryptosystem

the conic curve group is extended from finite field

GF(p)

to fini

te field

GF(2

n

)

and the order of the conic curve group in finite field

GF(2

n

) is given.In addition

this paper suggests to use conic curve group in finite field

GF(2

n

) for realizing public-key cryptosystem

and presents the basic ElGamal public-key encryption scheme and the Digital Signature Algorithm (DSA) based on conic curve in finite field

GF(2

n

)

.Security of public-key cryptosystem based on conic curve in finite field

GF(2

n

)

is analyzed.