Digital signature with elliptic curves over the finite fields

Abstract

Let x³ + ax + b be an irreducible cubic polynomial over 𝔽_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.

Subject Classification:

• 11T71
• 11G05
• 14H52

Keywords:

• Finite field
• Transformation
• Elliptic curve
• Digital signature