Digital Signature Schemes Based On Cubic Residues

Digital signature is one of the main contents of modern cryptology research.It plays an important role in network information security and it is also an important tool for e-commerce and electronic contract signing.The study of digital signature schemes is of theoretical and practical significance.To date,many identity-based ring signature schemes have been proposed.However,most schemes are based on bilinear pairing.Only a few identity-based ring signature schemes do not require pairing.In addition,there are some signature schemes based on quadratic residues in the literature.However,if the appropriate parameters are selected,the calculation efficiency of the cubic residues is better than that of the quadratic residues.In order to improve the efficiency of signature schemes,this paper uses the cubic residues to construct several digital signature schemes.Firstly,a novel method for calculating the cubic residues of cubic roots is given and some results about the cubic residues are proposed.Therefore,a theoretical basis is provided for the construction signature schemes based on the cubic residues.Secondly,an identity-based ring signature scheme on cubic residues is proposed.This scheme does not require any bilinear pairing problems that are difficult to calculate.The proposed scheme is proved to meetthe signer unconditional anonymity.The scheme is also secure against existing forgery on theadaptively chosen message and identity attack under assumption of the hardness of integerfactorization.Then,for the problem that a known scheme cannot withstand a conspiracy attack by users,a modified identity-basedsignature scheme based on cubic residues is proposed.The security analysis results show thatthe modified schemecan resist the conspiracy attack.Finally,in order to improve the efficiency of certificate-based signature scheme,a new certificate-based signature scheme based on cubic residue is proposed.The scheme is secure against existing forgery on the adaptively chosen message and identity attack under assumption of the hardness of integer factorization.A new signature scheme by using cubic residues is proposed.The secure of the scheme is based on both integer factorization and discrete logarithms on the finite field.