Research And Application On Theory Of Obfuscation In Cryptographic Protocol

Obfuscation theory comes from code obfuscation and developed very fast in recent years. Briefly, obfuscator takes a program(Turing machine or circuit) as input and output another program which have same functionality as the origenal one, but it is “unintelligible”. Cryptoloists make deep study on a series problems about obfuscation, such as if there exist general obfuscation, how to construct secure obfuscator etc, and they get significant achievements.According to the different security of obfuscation, we divide obfuscation into two parts. The first is based on black-box simulation, the definition proposed by Hada and requires attackers that any information learns by obfuscation program only can simulate this information by access to black-box. If this kind of obfuscation can be achieved, it will solve many hardness problem in cryptography. But the research is still in a state of the bottleneck, they turn to study indistinguishability obfuscation whose security is weaker.As the new development of obfuscation, we reclassify the obfuscation and describe it in more detail. It’s the first time to construct a secure obfuscator for encrypted blind signature, we analyze its security. The main research of this article as follows:1.We proposed a secure obfuscator for encrypted blind signature, which want to conceal the interactive information and make the interactive process unintelligible. we firstly use Schnorr’s blind signature scheme and linear encryption scheme as blocks to construct obfuscator. To prove the security of obfuscator, we present two new security definition: blindness and one-more unforgeability(EBS) w.r.t encrypted blind signature(EBS) obfuscator. Under the DL assumption and the hardness of discrete logarithm, we construct different adversaries and prove the blindness, one-more unforgeability and average-case virtual black box property(ACVBP) w.r.t dependent oracle.2.Study indistinguishability obfuscation. We transform any MPC protocol into 2-round protocol in CRS model which use Garg’s indistinguishability obfuscation. Parties entrust their input and randomness in the first round and in the second round parties provide their obfuscation of “next-message” function in base MPC protocol. Then each party calculate the obfuscation of “next-message” function and obtain the output. Weprove the MPC protocol against static malicious adversary in UC set at last.3.We study the obfuscation of point function. We construct the elements of key firstly and make it an obfuscator for multi-bit point function(MBPF). The first construction is based on a chosen plaintext secure PKE scheme and an MBPF obfuscator satisfying the AIND security in the presence of computationally hard-to-invert auxiliary input. Our second construction is based on a lossy encryption scheme and an MBPF obfuscator satisfying the AIND security in the presence of statistically hard-to-invert auxiliary input. Then we show the relations among security notions for MBPF obfuscators.4.We study obfuscations of different kinds of functions, and briefly describe computational complexity theory, provable security, random oracle model and standard model. We classify the definition and security of obfuscation, and study the relations among the security definitions combined with our results.