Disclosed herein are a finite-field division operator, an elliptic curve cryptosystem having the finite-field division operator, and a method for operating the elliptic curve cryptosystem. The method for operating an elliptic curve cryptosystem may include, setting, by a key setting unit, a length of a key of a cryptographic algorithm, generating, by the key setting unit, first setup information that indicates a number of words corresponding to the key length, and generating, by the key setting unit, second setup information that indicates a number of repetitions of an operation by a finite-field division operator corresponding to the key length.