The Construction Of One-way Function From Indistinguishability Obfuscation

One-way function is a special function,its unique property of one-way makes it possible for many cryptographic designs.The proof of the existence of one-way function implies a solution to the NP-complete problem.It means that it is difficult to use the existing theoretical knowledge to prove the existence of one-way function,but it is the basic assumption in cryptography to assume that one-way function exists.Trapdoor one-way function has a secret message that makes it possible to calculate effectively in both directions,and its calculation method can be made public.There is a close relationship between trapdoor one-way function and public key cryptography.Since the concept of indistinguishability obfuscation has been proposed by Barak et al,Garg et al.put forward the first construction of indistinguishability obfuscation by using multilinear maps until 2013.Its security mainly relies on an algebraic hardness assumption.The construction first achieves indistinguishability obfuscation for NC1 circuit,and then uses indistinguishability obfuscation for NC1 together with fully homomorpic encryption to achieve indistinguishability obfuscation for all circuits.The circuit obfuscated by indistinguishability obfuscator has the same function with the original circuit,and it has a higher security.Indistinguishability obfuscation is widely used because of its powerful functions.This paper contructs one-way function based on indistinguishability obfuscation,and analyzes the security of this one-way function.It mainly gets the following two achievements:1.This paper constructs the self-multilinear map with auxiliary information on the basis of self-bilinear map.The auxiliary information contains important parameters,and it is obfuscated by indistinguishability obfuscator to prevent those parameters from being leaked.This paper also analyzes probability,time complexity and security of self-multilinear map to ensure that the computational Diffie-Hellman assumption holds while the map satisfying eocoding division problem.2.This paper proposes the concept of scrambled circuit and describes the properties and construction method of scrambled circuit in detail.And it also analyzes the function of scrambled circuit.Then it constructs one-way function scheme by using self-multilinear map from indistinguishability obfuscation and scrambled circuit which is obfuscated by indistinguishability obfuscator.This paper also analyzes the scheme and obtains that this scheme satisfies the basic properties of one-way function,and there is a trapdoor which can make the inverse operation become efficient in this scheme.By analyzing,this scheme has efficiency and the use of indistinguishability obfuscation greatly increases the security of this scheme.Finally,it applies this one-way function to other cryptographic schemes according to its properties.