Signature on conic curve over Z_n based on two hard problems

The security of the digital signature scheme (Xiao06 scheme) on conic curve C_n (a, b) over the residue class ring Z_n was analyzed. The analysis result indicates that the published parameters can make the modulus n be factorized using the Weda's theorem, and shows that the Xiao06 scheme is not a scheme whose security based on the integer factorization problem. To address this issue, an improved digital signature scheme on conic curve over Z_n was proposed. Some parameters were kept secretly, and the verification algorithm was modified in the improved scheme. Furthermore, the numerical simulation of the improved scheme was given. The analysis shows that the improved scheme is a digital signature scheme based on two hard problems in computing discrete logarithm and factorizing integer simultaneously, and that the improved scheme has not only the merits (convenience for plaintext embedding, quickness for the inverse operation, and easiness for element order and points computing in curve) of the Xiao06 scheme, but also the advantage of strong anti-cracking ability.