Research On Theory And Applications Of Obfuscation In Provable Security

In recent years, obfuscation problem has been one of the hottest and most difficultpoints in cryptography. Obfuscation originated in code obfuscation, at first, it was usedto protect the intellectual property rights of software and to prevent softwares fromstatic analysis, tampering or reverse engineering attack, so as. In recent years, throughthe research and discussion of cryptography specialists such as Barak, Canetti,Goldwasser et. al，obfuscation has developed as a special cryptography problem. Thepurpose of obfuscation is to make the original program “unintelligible” by sometechniques while keeping the original program’s functionality. Up to now, obfuscationhas made significant progress in many fields, such as the possibility of obfuscationusing point function, the relevance of probabilistic encryption and obfuscation, thediscussion in security of obfuscation based on different kinds of Virtual Black-BoxProperty, the comparison between obfuscating general-purpose functionality and specialconstructed functionality and so on. Above conclusions divide the study on obfuscationinto two directions: one is to research on discussing Point Functions and PointFunctions with Multibit Output and constructing and abstract obfuscation of simplealgorithms; the other is the research on discussion the combination of complexalgorithm protocols and constructing secure obfuscation of special functionality, such assecure obfuscation of re-encryption, encrypted signatures and so on. The main researchof our paper is as follows:1. we introduce the concept, purpose and several ways of code obfuscation,including appearance obfuscation, data obfuscation, prevention confusion, controllingconstruction obfuscation;2. we introduce the basic idea, difficult assumptions of provable security, securemodels of digital signature scheme and public key encryption scheme, and the methodof standard model and random oracle model;3. we introduce the scope of application and three properties of obfuscation incryptography, the definitions of Turing Machine obfuscator and Circuit obfuscator andcompare their similarities and differences and also relationships;4. we sum up the existed secure obfuscations of special functionalities, includingre-encryption secure obfuscation, encrypted signature secure obfuscation, and functionalre-encryption and collusion-resistant obfuscation and their research backgrounds,specific algorithms and security analysis; 5. we present an algorithm called Secure Obfuscation for TightlyStructure-Preserving Encrypted Proxy Signatures, when we don’t know weather thethird party could be trusted or not, we obfuscate the scheme in the process ofexchanging secret keys in proxy signature. As a result, we successfully prevent thesecret key from being eavesdropped or decepted and ensure that the proxy signature isdelivered smoothly. We use DL assumption and DBDH assumption and combine withACVBP to demonstrate the security. The obfuscation procedure expand the single userof secure obfuscation of encrypted signature to multi-user setting of that, while itssecurity won’t be influenced by ciphertexts and the number of users. It not only retainsthe advantages of efficient operation efficiency of Tightly Structure-PreservingSignatures, but also gets a solution on the fact that the third party who might not betrusted, reducing the threat of a third party collusion attack.