Research And Application On Indistinguishability Obfuscation

In the field of cryptography, the research on obfuscation theory began in the late 1980 s, it was not until 2001 that Barak et al. gave out the formal cryptographic definition of obfuscation. Briefly, the goal of obfuscation is to make the program “unintelligible” while preserving its functionality. In recent years, especially since 2013, the first candidate indistinguishability obfuscation construction for all circuits proposed by Garg et al. makes the application of obfuscation theory possible. Thereafter, cryptologists worked on many hard problems in many aspects including whether the general purpose obfuscation actually exists and how to construct secure obfuscation, they obtained many important achievements and promoted the development of cryptography.According to the new development of obfuscation theory in recent years, we introduce all kinds of distinct obfuscation, such as virtual black box obfuscation, average-case virtual gray box obfuscation, best-possible obfuscation, indistinguishability obfuscation and differing-input obfuscation. We describe and summarize the definition and property of different obfuscation in detail. We focus on the candidate indistinguishability obfuscation construction for all circuits, and construct a new two-branch obfuscator using the candidate for the first time, then design a new secure obvious transfer protocol, and analyzes its security. Following on the definition, we propose a multi-encryption scheme and a multi-branch obfuscation. The main research of this thesis is as follows:1.Research on the first candidate indistinguishability obfuscation for all circuits proposed by Garg et al. This work is a landmark breakthrough for the research of obfuscation theory, and can be divided into two steps: Firstly, they construct a candidate indistinguishability obfuscation for 1NC circuits, the security of the candidate is based on a new algebraic hardness assumption, using a simplified variant of multilinear maps, which we call Multilinear Jigsaw Puzzles; afterwards, bootstrap the candidate indistinguishability obfuscation for 1NC circuits into the candidate indistinguishability obfuscation for all circuits. The construction also employs branch programs, multilinear maps, graded encoding scheme and other theories. Finally, they give out the security proof of the candidate construction using a series of security games.2.Research on the application of candidate indistinguishability obfuscation for all circuits. After the candidate construction was proposed, cryptologists studied it and obtained many interesting applications, including multiparty non-interactive key exchange protocol, recipient-private broadcast encryption, and traitor tracing with short parameters, functional encryption scheme and so on. We study the applications introduced above and describe them in this thesis briefly, and study the way which they used to employ the candidate indistinguishability obfuscation construction.3.Using the first candidate indistinguishability obfuscation for all circuits, we construct a two-branch obfuscator for the public key cryptosystem based on DDH assumption. Another technique tool of the obfuscator is a dual-mode cryptosystem, the security of the obfuscator mainly relies on the indistinguishability of the two branches. Then, based on the new obfuscator, we combined the obfuscator with the definition of obvious transfer functionality to construct a secure k-out-of- l obvious transfer protocol and analyze its security. Finally, we extend the concept of the two-branch obfuscator and give out the definition of multi-branch obfuscation.4.Research on the obfuscation of different function classes, and the provable security theory, the computational complexity theory, the random oracle model, the standard model and other theories which used in the process of the research. We also study the correlation of different obfuscation security definition by combining researches on obfuscation theory inland and abroad with our own achievements.