The invention discloses a novel procuration signature and verification method based on integer factorization problems. The novel procuration signature and verification method based on the integer factorization problems includes the steps: before a network operates, firstly generating personal public keys and private keys by original signature people and procuration signature people, and issuing the public keys; when signature requests are provided, generating authorization letters by the original signature people, and calculating signature authorization based on a chameleon hash function and an ordinary digital signature algorithm, sending the signature authorization to the procuration signature people, carrying out validity verification on the received signature authorization by the procuration signature people, if the signature authorization is effective, generating the procuration signature based on collision property of the chameleon hash function, and digital signature does not need to be carried out on information, when a verifier receives the authorization letters and the procuration signature, firstly, verifying whether the authorization letters are effective or not, after the authorization letters are verified to be effective, and then verifying validity of the procuration signature. According to the application of the novel procuration signature and verification method based on the integer factorization problems, processing efficiency of the procuration signature is high, and the length of the procuration signature is short. The novel procuration signature and verification method based on the integer factorization problems is suitable for environments such as mobile networks and the wireless networks where computing power and network bandwidth are limited.