Research On Public Key Cryptography Based On Quasi-cyclic Parity Check Code

In today's society,informatization has become an inevitable trend under the rapid economic development,dominating and permeating all aspects of society,forming a strong network of relationships.Meanwhile,security issues in communications have also brought huge challenges to the cyber world.Information security technology has become a key technology in the development of information networks in recent years,and cryptography is the core of information security.The continuous development of quantum computing has brought progress and convenience to the physical application of quantum computers in various fields.However,it also threatens some current cryptosystems based on NP problems that general computers cannot solve.The approaching pace of practical quantum computers forces cryptographers to prepare in advance,and to set about discussing public key cryptography(PKC)which can resist quantum attacks.The PKC scheme based on QC-LDPC/QC-MDPC is currently the promising scheme for the standardization of post-quantum cryptography which the National Institute of Standards and Technology(NIST)is soliciting.According to the comprehensive comparison and analysis of this scheme with others,it has good performance characteristics like both the key size and the algorithm complexity are low.But a key recovery attack can crack the scheme against its security.Attacker could collect feedback information of the decoding failure from the receiver by adding specific error patterns to the massage,then somehow reconstructed the secret key.To copy with this attack,this paper proposed two countermeasures which utilize different techniques of error controlling.The first solution combined automatic repeat-request(ARQ)and pseudo-random sequence to obtain a security model that can encrypt feedback information.The second solution used fountain code to generate abundant encrypted packets to substitute for the ARQ structure,and then came up with a new PKC scheme based on cascaded QC-MDPC code.According to theoretical and simulation analysis,both countermeasures can effectively defend against key recovery attack,and it can maintain better resistance to other attacks.But the key size and the complexity of the scheme relatively increased a lot instead.Therefore,to obtain a compromise scheme between security and practicality is the focus of future related research.