| Provable security is essentially an axiomatic research method, in which the securityof cryptographic schemes is reduced to a"well-known"basic theory or"an axiom", e.g.,some basic cryptographic algorithm or a number-theoretic assumption. Now it has alreadybecome an important theme of theoretical researches in modern cryptography, especiallyin the public key cryptography. Provable security is not only a method for proving thesecurity of the cryptographic schemes but also a method for constructing new schemes,which are also a theme of this dissertation. So our dissertation puts emphasis on boththe construction of public key cryptographic schemes and their security proof. The mainresults are specified as follows:1. New e?cient hierarchical identity-based encryption schemes are introduced in thestandard model. The first scheme is constructed in the selective-identity model. Ithas short ciphertexts and little computation at the phase of private keys generation.Furthermore, its security is reduced to the decision BDH assumption, which is morenatural than those in the available schemes. Based on the model 1 in the generalizedselective-identity model, the second scheme is obtained. Finally, we proposed themodified scheme of the second scheme. It achieves constant-size ciphertexts andprivate keys in this scheme shrink as the identity depth increases. It is worth notingthat the proposed schemes are constructed in the standard model.2. We propose some e?cient broadcast encryption schemes for ad hoc networks. Twoschemes are constructed under the random oracle model, the others are constructedunder the standard model. The schemes under the random oracles have short trans-missions and achieve low cost of users storage, which are important for a mobile adhoc network. To the best of our knowledge, very few works have dealt with theconstruction in the standard model. So the others are constructed in the standardmodel. The first scheme in the standard model is one of the most e?cient con-structions at present, which has short PKs and achieves constant-size ciphertextsas it consists of three group elements. Finally, we propose two broadcast encryp-tion protocols in the standard model, which are e?cient at the phase of group keysgeneration.3. Three efficient threshold broadcast encryption schemes are proposed. The thresholdbroadcast encryption is a dynamic threshold encryption, which is different withgeneral threshold encryption and especially useful in the mobile ad hoc networks.We first propose an identity-based threshold broadcast encryption in the standard model. However, the size of cipertexts and private keys relies on the numbers ofusers. Therefore, two e?cient modified schemes are introduced at last. It is worthnoting that three schemes are provable security without using random oracles.4. We construct three e?cient hierarchical identity-based signature schemes. Our pro-posed schemes are natural extensions of the existing schemes since their security isbased on the strong assumption or non-standard cryptographic assumption. Thefirst scheme is constructed under the CDH assumption. This assumption is morenatural than those in the available schemes. However, the size of private keys andciphertexts increases as the depth of identity increases. So two modified schemesare proposed. Both schemes achieve constant-size ciphertexts which consist of threegroup elements. Furthermore, their private keys shrinks as the identity depth in-creases.5. Two threshold signature schemes are presented. The first one is based on the Wa-ters's scheme and involves a PKG. The other is based on the Gennaro's distributedkey generation protocol.6. Finally, we first propose a strongly unforgeable signature. A transformation is pro-posed at first. It can convert any existentially unforgeable ID-Based signature whichis simulative-partitioned to a strongly unforgeable signature. Then based on Pater-son's scheme, a concrete construction of the strongly unforgeable ID-Based signatureis introduced in the standard model.
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