Study Of Provably Secure Certificateless Public Key Cryptosystems

The theory of provably secure is an important research branch in public cryptog-raphy.The method of random oracle model still plays an important role in the security proof of public key cryptography.Therefore,it is important to design provably secure public key cryptography scheme by a random oracle.This paper studies three provably secure certificateless public key cryptosystems under the random oracle model,these schemes are the research hotspots of current public key cryptography,The main re-sults obtained are as follows:An efficient certificateless anonymous multi-receiver encryption scheme is pro-posed using elliptic curve cryptography(ECC).In proposed scheme,no bil:inear pair-ings or probabilistic hash-to-point(HTP):function is involved the in the process of en-cryption and decryption,and then address the troubles of private key escrow in multi-receiver encryption scheme based on ID-PKC.First,we describe the formal defini-tion and secure model of certificateless anonymous multi-receiver encryption scheme.Then the proposed scheme is described in detail.Finally,the performance and se-curity of the proposed scheme are analyzed.Performance analysis shows that our scheme has less running time and higher efficiency than the recent literature scheme.It is proved that the proposed CLAMRE scheme provides message confidentiality and receiver anonymity under the random oracle model with the difficulties of Decision Diffie-Hellman problem and against the adversaries defined in CL-PKC system.A provably secure certificateless multi-receiver threshold decryption scheme in random oracle is proposed.Threshold decryption is achieved using Lagrangian in-terpolation polynomial key sharing system.The proposed scheme does not need to establish key share in advance,the information directly is encrypted using the user's public key and the shared secret value.The proposed scheme effectively solve the problem which hard to share any private keys corresponding to the public keys under mobile network featured with dynamic character.Compare with the existing some threshold decryption schemes,the proposed scheme has more efficiency because the bilinear pairings and probabilistic hash-to-point(HTP)function in the process of en-cryption and decryption are not involved.Finally,under the random oracle model,it is proved that our scheme is the indistinguishability of information encryption and the anonymity of the receiver,and the security are reduced to the decision Diffie-Hellman(DDH)problem.A forward secure certificateless proxy multi-signature scheme is studied under random oracle model.Combining forward secure technique with certificateless prox-y multi-signature,we propose a forward secure certificateless proxy multi-signature scheme.The all signature before the key is exposed are still valid even if the proxy signature key in a time period is exposed.So the proposed scheme efficiently limit the damage of key exposure.Key update of the proposed scheme is easy implemented,so it is suitable to apply the mobile network setting.In security analysis,we consider a extreme case in which adversary A(A1 or A2)is working against a single honest,and remaining users are corrupted by adversary A.It is proved that the proposed scheme is existentially unforgeable against an adaptively chosen-message attack and an adap-tively chosen-warrant attack.The difficult problem depends on the computational Diffie-Hellman(CDH)problem.