Based On Public Key Cryptography Algorithm Analysis And Design Of Error Correction Code

The McEliece and Niederreiter public key schemes are the most popular code-based public key cryptosystems,which are considered as one of the few systems that can resist the attack from quantum computer.Their security are based on two assumptions of difficult problems.The first is the hard of decoding an arbitrary linear code;the other is the hard of recovering the structre of the underlying code which is generated by an arbitrary generator matrix over a finite field,and its public key that formed by the generator matrix is a random-looking algebraic code.The scheme has remarkably fast encryption and decryption speeds with a strong ability of key reduction.However,it is not suitable to apply to practical for the disadvantage of its large key size.In order to resolve this problem,a effective method is indispensable to be found for constructing the practical code-based pulic key cryptosystem.In this paper,the first section rests on the Niederreiter type public key cryptosystem,a new structral attack is constructed by making use the nature of the rank metric.The idea of the structural attack is tring to recover the secret key of the system by analysing the characteristic of the public key over the Niederreiter type public key cryptosystem based on rank metric,and reachs the plaintext from the secret key.Then,the relations is given between the powerful of attack and the system parameters.Under the relations,the modified Niederreiter type public key scheme based on rank metric is provided.The content of the second part is about the McEliece encryption scheme based on rank metric.Take advantage of linear transformation and hash function,a new transformation is constructed in the McEliece type public key cryptosystem,By the introducing of the new transformation,the cipertext information with error encodin can be hided in the multiple transformations.So the transformation plays an important role in hiding the structure of the code.This method increases the error code number applied to the public key cryptosystem through the process of encoding the error information vector into a kind of error code family. By the analyzing to the most strong attacks toward the new transformation,the McEliece public key cryptosystem based on rank metric is feasible and security.