This paper focuses on c≡x+by(mod N), the linear Diophantine equations over a finite field, and derives the general solution and the amount of solutions in the domain from the equations. Then demonstrates that this solution can partly reduce the amount of calculation which derive the signer's private key in some curve cryptography schemes to N/z (z is the smallest non-zero element of subgroup < -b >). Finally, lists five curve cryptography schemes that based on this type of equation, and takes the solution of the private key of a digital multi-signature scheme on the generalized conic curve over Z_n as an example to introduce the topic.