Providing a security proof is always an important issue in the process of designing a cryptographic scheme or protocol. We often show the security of a cryptosystem via ¡§problem reduction.¡¨ In this thesis, lots of emphasis was put on the review of techniques for proving the security of cryptosystems. These techniques consist of Random Oracle Model and Forking Lemma. We also introduced some well-known cryptographic schemes which can be proved secure using these techniques. Then we offered a security proof of a blind signature scheme based on the one proposed by Fan. In the end, we made a comparison between our proof and the proof of another blind signature scheme provided by David Pointcheval and Jacques Stern. Some arguments and discussions about using the Random Oracle Model to prove the security of a cryptosystem were also included.