Research On Theory And Application Of Obfuscation In Public Key Cryptography

As a new research field, obfuscation in cryptography preserves its ideology in code obfuscation:making code elusive while keeping the original functionality. For the sake of proving the availability and possibility of obfuscation in cryptography, many related researches and discussions have been carried out. Recently, several important results of obfuscation have been proposed, including the possibility of obfuscation using point function, the comparison between obfuscating general-purpose functionality and special constructed functionality, the relevance of obfuscation and probabilistic encryption and the discussion in security of obfuscation based on certain kind of Virtual Black-box Property, all of the above at last lead to the study on obfuscation divided into two directions:One is the study on constructing obfuscation using Point Function and Point Functions With Multibit Output in abstract sense. Another one is on finding more appropriate cryptographic protocols and algorithms, including Encryption, Digital Signature, Access Control Model, and then we make some new special functionality based on them and formalize the obfuscation. In this paper, we reviewed the development history of obfuscation and made some conclusions on it. More importantly, we make some useful obfuscation applied to the Public Key Cryptography (PKC) for the first time and give out some definitions on security of obfuscating PKC in order to introduce the definitions to the PKC schemes. Our mainly work are as follows:1. We proposed a special proxy Recrypt-Identity Based on Encryption (Recrypt-IBE) scheme and give out the security proving of obfuscation. Our construction is based on the Boneh et.’s Hierarchical Identity Based Encryption scheme (HIBE), it divided the dID which generated by the main secret key of PKG and the Bob’s public key is extended, then we use the Hohenberger’s obfuscation of Re-encryption to make a secure circuit obfuscation. We can give this obfuscated circuit to any third party to execute the original functionality, the resulting ciphertext is in form of been encrypted by recipient’s public key. Our obfuscated circuit does not reveal any secret of both communicators, and the PKG cannot make any efficient computation of plaintext m meanwhile the decryption algorithm is efficient. With the guarantees of securely keys’transfer and efficient key escrow, we give out a new method to solve the problem which PKG always has the overmuch authority.2. We provided a special signature scheme which has a two-step verifying process, and finally get a1-out-of-n oblivious signature scheme through the secure obfuscation. Our obfuscation of this special functionality is based on the Pedersen’s VSS, which makes use of Waters’signature scheme and Boneh et.’s linear encryption scheme. We proved there exists an adversary whose breaking our scheme is equivalent to solve the certain complexity assumption used in PKC, for example:Strong Diffle-Hellman Indistinguishability Assumption (SDHI) and Decision Linear Assumption (DL). Moreover, we give out a comparison between Average-Case Virtual Black-Box Property (ACVBP) and oblivious property involved in Zero Knowledge Proof (ZKP), and the core is focused on the possibility of extending the concept of indistinguishability (IND) to some applications in ZKP, which will certainly develop a new direction of researching the obfuscation in ZKP protocol.3. In summarized of the study and research results from both interiors and externals, combined with my positive results, we make some analysis on the relationship about security definitions between PKC scheme and obfuscation. We discuss the method that talks about how to create special functionality using existing algorithm. At last, the relation with PKC scheme is provided by proving the possibility of achieving some functionality in PKC using appropriately constructed obfuscation. Specially, the IND property which implied by virtual black-box property gives out the security proving method according to the ideology of PKC scheme.