Research On New Variants Of Lossy Trapdoor Functions And Their Applications

Lossy trapdoor functions(LTF)is a powerful extension of one-way trapdoor functions(OWF)which is a fundamental primitive in public key cryptography.LTF has excellent flexibility to create new variants and inner relations to many other primitives.So it is convenient to incorporate different properties into variants of LTF to solve many problems left by OWF.Since its appearance,LTF has shown its high importance in various areas in cryptography including public key encryption(PKE)secure against chosen cipheitext attack(CCA),leakage resilient(LR)PKE,oblivious transfer etc.However,analysis of existing LTF works indicates that some problems still don't have a satisfying solution.And there are many new problems in other areas which can be solved by LTF.This thesis focuses on those problems which are not solved completely in LR cryptography and discovering new applications of LTF.The main content are listed as follows:(1)To solve the problem that existing LTF works can only achieve LR-LTF in weakened security model,this thesis presents a new variant of LTF which is called branch hidden ABO-LTF.This novel primitive can not only preserve the functionality as original version,but also achieve LR property in common model.Further,LR-CCA secure PKE scheme in common model can be constructed via this variant.(2)To solve the problem that all existing works about post challenge leakage resilient(PCLR)CCA security use non-interactive zeroknowledge proofs(NIZK)which leads to inefficiency of application,this thesis first presents an LR-LTF in spit-state model based on entropy leakage resilient PKE.Then a PCLR CCA secure PKE scheme is built via this LR-LTF in split state model without NIZK proofs.(3)To solve the problem that it is difficult to achive CCA security directly from IBE schemes which are designed by dual system encryption(DSE)technique,this thesis presents the definition of ciphertext characteristic and a relaxed CCA security model called DSE-CCA model.With these tools DSE-CCA secure IBE scheme and LR-DSE-CCA secheme can be smoothly constructed via classic approaches.(4)In the field of public key encryption with keyword search(PEKS),keyword guessing attack(KGA)is always a threat.Existing works can only resist offline KGA but fail in online environment.This thesis combines non-interactive key exchange(NIKE)protocol and ABO-LTF to create a new variant of lossy encryption,which is called branch hidden ABO-LPKE.This kind of PKE can make certain users incapable of encrypting messages in public key environment.With this new scheme,the server aided PEKS secure against offline KGA can be upgraded to resist online attacks.