The security of Canard-Traore fair e-cash system scheme was believed to depend on the strong-RSA as sumption and the Decision Diffie-Hellman assumption in groups of unknown order. But it is not the case. The ryptanalysis on Canard-Traore fair e-cash system was presented. An algorithm was designed to show that Canard Traore fair e-cash system is insecure: It is forgeability. Further, two drawbacks on Canard-Traore fair e-cash system scheme were pointed out. One is that those integer intervals for si(i= 1,…, 9) are unappropriate. The other is that the datum s3 in signature data is redundant. Moreover, a minute description of the technique to shun the challenge in the scheme was presented. The technique is helpful for designing new group signature schemes in the future.