We propose a novel method to compute a cubic root of a cubic residue in Eisenstein ring.By applying our method,a new identity based signature scheme is proposed based on cubic residues.We formally prove that our scheme is secure against existential forgery on the adaptive chosen message and identity attacks assuming the hardness of factoring.Our scheme is the first identity based signature scheme based on cubic residues. We propose a novel method to compute a cubic root of a cubic residue in Eisenstein ring. By applying our method, a new identity based signature scheme is proposed based on cubic residues. We formally prove that our scheme is secure against existential forgery on the adaptive chosen message and identity measures assuming the hardness of factoring. Our scheme is the first identity based signature scheme based on cubic residues.