Digital signature with elliptic curves over the finite fields.

Let x3 + ax + b be an irreducible cubic polynomial over p. Then by using transformations x → x + j and x → j–1x, where j ∈ F*p, we can generate new irreducible cubic polynomials. In this paper, we use the elliptic curve equation y2 = x3 + ax + b and some transformations to generate an irreducible cubic polynomial, say Q. We generate the public and private keys in the elliptic curve digital signature algorithm (ECDSA), by defining the isomorphism between.Finally, we discuss the security of keys and the validity of signature. [ABSTRACT FROM AUTHOR]