Studies On Provably Secure Public-Key Cryptosystems

With the rapid development of computation and communication,many computer application systems have been quite widespread,such as cloud computing,wireless sensor networks,PDAs,cell phones and smartcards.On account of openness,information security problem has gradually become a bottleneck of the further development and applications of these systems.As one of the most significant security measures,public key cryptography is playing an important role in these systems.In addition,confidentiality,integrity,availability and non-repudiation of the messages can be achieved when messages are transmitted over a public channel.In this paper,provably secure public key cryptography is mainly studied.Our contributions to this work are detailed as follows:1.As we known,resource-limited systems cannot execute complex applications very well due to the limitations of computing resource,storage space and communication bandwidth.We propose three pairing-free certificateless signature schemes which may be practicably implemented in resource-limited systems and we give the corresponding formal security proof for every scheme in the random oracle model.The first scheme is proposed based on our newly defined variant of RSA problem and the well known discrete logarithm problem.As far as I known,this is the first provably secure RSA-based certificateless signature scheme.The second scheme is proposed based on discrete logarithm problem.The third scheme is modified from Yeh et al.'s scheme published in Multimedia Tools and Applications,which is more practical than Yeh et al.'s scheme and can achieve the same security level as theirs.2.Although some public key cryptography schemes have been published,we can still find some weaknesses of the schemes.First we review Chen et al.'s certificateless aggregate signature scheme published in Security and Communication Networks and provide two attacks to indicate their scheme cannot achieve the security levels they claimed.Then we review Li et al's certificateless online/offline signcryption scheme published in Security and Communication Networks and give a concrete attack algorithm to indicate their scheme cannot achieve the strong existential unforgeability they claimed.Last we review Lin et al.'s forward-backward secure signature scheme published in Journal of Information Science and Engineering and show an attack to point out that their scheme doesn't satisfy backward security.3.We creatively study the combination of fuzzy identity-based signature and certificateless public key cryptography to try to eliminate the key escrow problem inherently existed in fuzzy identity-based signature.We first propose the concept of fuzzy certificateless signature and define the syntax and security model of fuzzy certificateless signature.Then we propose the first concrete fuzzy certificateless signature scheme which may be practicably implemented in biometric identification.In addition,we provide a formal security proof to demonstrate that in the random oracle model,our newly proposed scheme is existentially unforgeable against Type I and Type II chosen message attacks formalized in the security model under the computational Diffie-Hellman assumption.4.In current cloud computing system,large amounts of sensitive data are shared to other cloud users.To keep these data confidentiality,data owners should encrypt their data before outsourcing.Proxy re-encryption can be chosen to satisfy the requirement of the secure data sharing in cloud environment.A pairing-free certificateless proxy re-encryption scheme is first proposed in the random oracle model,which is more efficient than other existing certificateless proxy re-encryption schemes.Then a new RSA-based unidirectional proxy reencryption scheme is proposed in the random oracle model,which is the first RSA-based unidirectional proxy re-encryption scheme with chosen-ciphertext security.