Research On Design And Applications Of Cryptography Obfuscation

At first,obfuscation comes from field of computer,namely,code obfuscation.The purpose of obfuscation is to protect software.Software program can keep the original functionality use obfuscation,but it make the program“unintelligible”,so,the adversary can not get code.In 2001,Barak et al.gave out the formal cryptographic definition of obfuscation.This is foundation of research.At the beginning,they design“virtual black box”property,but it can not achieve.At the same time,they defined notion of indistinguishability obfuscation.In 2013,the first candidate indistinguishability obfuscation construction for all circuits proposed by Garg et al.makes the apply of obfuscation theory possible.According to the new research of obfuscation theory in recent years,we summarize 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.In this paper,we focus on the candidate indistinguishability obfuscation construction for all circuits,and application,based on indistinguishability obfuscation,we construct a IND-CCA public key encryption,and prove the security.The main research of this thesis is as follows:1.Introduce the basic knowledge of cryptography obfuscation,such as computational complexity theory,provable security theory,random oracle model,and standard model.Summarize all kinds of distinct obfuscation,such as virtual black box obfuscation,best-possible obfuscation,indistinguishability obfuscation and differing-input obfuscation.2.Research on the candidate indistinguishability obfuscation for all circuits.It is foundation of obfuscaton.The construct process as follows:Firstly,they construct a candidate indistinguishability obfuscation forNC¹circuits,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 forNC¹circuits into the candidate indistinguishability obfuscation for all circuits.The security prove by series of hybrids.At last,we give application of indistinguishability obfuscation,namely,deniable encryption.3.Research on obfuscation cryptanalysis.Recent obfuscation is based on multilinear maps,there have some attack on multilinear maps,this threat the security of obfuscation.We introduce a notion of multilinear maps,then,give an attack on GGH13 multilinear maps.Finally,we introduce the cryptanalysis ofHyb₂,it can distinguish two obfuscated program which functionality equivalent.4.Using the first candidate indistinguishability obfuscation for all circuits and punctured technology,we construct two obfuscator,base this,we construct IND-CCA public key encryption.The scheme encrypt bit-by-bit.For improve efficiency,with single-bit to multi-bit technology,we translate the scheme to multi-bit encryption.