Hierarchical Identity Based Cryptography With Authorized Delegation

When designing hierarchical identity based cryptosystems(HIBC),privacy and efficiency are two important factors which affect practicability of the HIBC systems being designed.Privacy problem in HIBC systems comes from the mechanism of private key delegation,that an entity's private key can usually be used to derive private keys for its descendants,i.e.,key escrow problem inherent in identity based cryptography,which does destroy encryption privacy of ciphertexts or authenticity and non-repudiation of signatures in HIBC systems.Efficiency concerns time complexity and space complexity in terms of cryptographic components(private keys,ciphertexts,signatures,etc.)and related cryptographic operations of the HIBC systems.It is desirable that size of cryptographic components is constant,and time complexity of cryptographic operations is also constant,i.e.,irrespective of depth of identities in hierarchical cryptosystems.Although key escrow problem is inherent in Identity Based Cryptography(IBC),resulting from the mechanism of private key generation,it is vital not to let the problem be exaggerated in Hierarchical IBC(HIBC)systems.It has been almost one and a half decades since the introduction of the concept of Hierarchical Identity-based Encryption(HIBE),however,how to solve key escrow problem and how to achieve targeted or independent delegation are still open.Aiming at solving inherent key escrow problem,realizing independent delegation,and achieving perfect privacy of ciphertexts and signatures,and constant time and space complexity of cryptographic components and operations,main contributions are as follows.Firstly,this dissertation concludes and analyzes mechanisms of private key delegation being implemented heretofore,i.e.,Unlimited Delegation and Limited Delegation,and points out that ways of constructing private keys,independent or integrated randomization with an identity's identifiers,exaggerate the key escrow problem and make independent delegation impossible in hierarchical systems.The dissertation proposes a new mechanism of independent authorization-based private key delegation for coping with key escrow problem and realizing independent private key delegation.That is called “Authorized Delegation”.Authorized delegation can achieve the following goals,(1)private keys are not valid delegation credentials for deriving private keys,(2)a credential is only valid for deriving private keys for those target identities,(3)and an entity intending to derive a private key for any one of its descendants should own a copy of valid delegation credential specific to the descendant delegated by the private key generator(PKG).Secondly,as “Authorized Delegation” being a conceptual mechanism,a new technique of constructing private keys – “Identifier Discrimination” is proposed,in order to build HIBC systems with authorized delegation.Specifically,with identifier discrimination,a private key for an entity is composed by differentiating between identifiers of the entity in terms of randomizing the master key of the HIBC system.Because the master key is randomized when generating a private key for an entity in a way different to that of randomizing the master key for generating private keys for its descendants,then the entity is prevented from deriving private keys for its descendants with its private key.Thirdly,the dissertation proposes a concrete method of discriminating an identity's identifiers for randomizing the master key,i.e.,defining a combined term on non-local identifiers of the identity and an independent term on local identifier of the identity;the combined term from non-local identifiers is key to depth-independence,while the independent term from local identifier is decisive factor of making key derivation with only use of private keys impossible.With the method,the dissertation constructs a Selective Identity(Selective-ID)secure HIBE system with authorized delegation under Decisional Bilinear Diffie-Hellman(DBDH)assumption without using random oracles.The HIBE is of constant size,i.e.,private key and ciphertext consist of constant number of group elements,and decryption requires only three bilinear map computations,regardless of the depth of identities.Fourthly,in order to avoid the breach of private key leakage in constructing Hierarchical Identity-based Signature from HIBE with Naor Transformation,the dissertation proposes a new method of constructing HIBS from HIBE,i.e.by introducing a virtual hierarchy level for signer's identity while treating the message intended to be signed as identifier of the level and randomizing the signer's private key independently with the newly introduced virtual level to get resulting signature.With the method,the dissertation constructs an Existential-Unforgeability under Adaptive Chosen Message and Identity Attacks(EUF-CMA)secure HIBS system out of the Selective-ID HIBE in standard security model under intractability assumption of Hybrid Gap Diffie-Hellman(HGDH)problem on bilinear group pair.Lastly,in order to create identity based anonymous signatures,the dissertation proposes an Anonymity under Chosen Plaintext Attacks and Full Traceability secure generic construction of Hierarchical Identity Based Group Signature(HIBGS)by integrating an EUF-CMA HIBS and the Groth-Sahai Proof.By introducing signature verification credential for anonymously(publicly)verifying group signatures,the HIBGS generic construction is instantiated with EUF-CMA secure HIBS constructed in the dissertation,and the Groth-Sahai proof is utilized for achieving anonymous signature proof,verification and signature opening.