Research On Lossy Trapdoor Function And Its Application In Encryption

Lossy trapdoor-function(LTDF)is a powerful extension of trapdoor functions,which can be realized from the hardness of decisional Deffie-Hellman(DDH)problem in cyclic groups and the hardness of worst-case problems on lattices.LTDF has pow-erful function and flexibility.It is a very useful tool to construct many advanced cryptography primitives.It has been widely used in many cryptography fields,including injective trapdoor functions,collision-resistant hash functions,chosen-ciphertext attack-secure public-key encryption,selective-opening attack-secure public-key encryption,deterministic public-key encryption,hedged public-key encryption and oblivious transfer,etc.The analysis shows that there are still some deficiencies in the leakage-resilience of the previous constructions of LTDF and its application in deterministic public-key encryption.Therefore,to obtain better performances and applications for LTDF.This thesis focuses on study the leakage-resilient LTDF and its applications in the hedge public-key encryption and CCA-secure deterministic public-key encryption.The main content are as follows.1)To resist the trapdoor leakage attacks form adversaries,this thesis presents a two-key continual leakage-resilient LTDF and proves its security under the deci-sional linear(DLIN)assumption.To solve the problem that existing leakage-resilient LTOFs can only be achieved in weakened security model,we propose a new con-struction of continual leakage-resilient all-but-one trapdoor function(ABO-TDF).Our construction can not only preserve the functionality in the application,but also achieve leakage-resilience in common model.2)The security of existing hedge public-key encryption schemes is dependent of the assumption that the internal secret states are completely inaccessible to the ad-versary,little research on hedged public-key encryption in the presence of key-leakage was done.Therefore,in this thesis,based on our continual leakage-resilient ABO-TDF,we propose two generic constructions of continual leakage-resilient hedged public-key encryption and prove their security in common leakage security model.3)Existing CCA-secure deterministic public-key encryption(D-PKE)schemes are designed based on a lossy trapdoor function(LTDF)and an all-but-one trap-door function(ABO-TDF).Inspired by various construction methods of CCA-secure PKE scheme,we pre'sent an alternative paradigm to design CCA-secure D-PKE.Our approach is a simple generic construction based on the identity-based lossy trapdoor function(IB-LTDF).Moreover,our approach can be considered as another applica-tion of the CHK transformation.4)To solve the problem that all existing deterministic identity-based encryption D-IBE schemes can only resist CPA but-fail in CCA setting.This thesis introduces a notion of identity-based ABO-TDF,and proposes the construction of identity-based ABO-TDF under the DLIN assumption.Based on an IB-LTDF and an IB-ABO-TDF,we design a generic construction of CCA-secure D-IBE scheme in the standard model.