Zero-knowledge Identification Scheme Based On Coding Difficulty Problem

Nowadays,network communication occupies an important position in daily life,but brings a series of information security problems.In order to prevent malicious third parties in the network from impersonating normal users,identity authentication is usually required,that is,to confirm the identity of users in the network through certain technical means.There are also many construction methods for identity authentication schemes,such as authentication based on cryptographic knowledge,authentication based on biological characteristics,and so on.Comparatively speaking,the application of constructing an identity authentication scheme based on cryptographically difficult problems is more extensive.At present,the construction of a large number of identity authentication schemes is based on traditional difficult problems in cryptography,such as the integer factorization problem,the discrete logarithm problem on finite fields,and so on.However,such identity authentication schemes have shortcomings: on the one hand,the key’s growth rate increases with the increase of the security requirements of the system,which leads to the increasing computational overhead of the scheme? on the other hand,traditional problems are difficult to resist quantum computer attacks,which makes the security of the identity authentication scheme easy to be destroyed.Aiming at the shortcomings of existing identity authentication schemes,this paper builds a secure,efficient,and low cost zero-knowledge authentication protocol based on coding difficulties.Aiming at the problem that some interactive identity authentication schemes have a high probability of reasonable deception,this paper proposes a zero-knowledge MCZK identity authentication scheme based on the difficult problem of matrix completition.Based on the problem of low-rank matrix completition difficulty,this paper constructs a five-round interactive identity authentication protocol,adding random numbers and random matrices between the verifier and the prover,so that the original attacker’s probability successfully impersonates the prover’s identity is reduced from 2/3 to 1/2,which reduces the number of protocol executions to achieve the same required system security.This paper also proves that the MCZK scheme,as a zero-knowledge proof protocol,satisfies completeness,soundness,and zero-knowledge.Through the data simulation analysis,the MCZK scheme in this paper has the advantages of less communication overhead,less total protocol times and resistance to quantum attacks when selecting the 11 × 11 dimensional matrix.Aiming at the problems of high communication overhead and low efficiency in some identity authentication schemes based on the Hamming coding problems,this paper proposes a zero-knowledge RSDZK identity authentication scheme based on rank syndrome decoding.This paper designs a commitment algorithm,which covers the prover’s private key through two random vectors,assists in constructing an interactive zero-knowledge proof scheme,and proves that the scheme satisfies three properties: completeness,soundness and zeroknowledge.In the experimental simulation,this paper implements the RSDZK scheme on the rank metric and the comparison scheme on the Hamming metric respectively,and compares their secret value’s length,average communication overhead,etc.And the results show that the average communication overhead of this paper’s scheme is reduced by about 58%,while it has obvious advantages in the selection of common parameters.In addition,this paper tests the running time of the two schemes in each interaction phase in one concordance,and verifies the superiority of the RSDZK scheme in this paper in terms of time efficiency.Finally,combined with theoretical analysis and simulation experiments,this paper verifies the security and higher efficiency of the two interactive zero-knowledge authentication schemes,and makes an outlook on the research direction of constructing identity authentication scheme based on coding difficulties problems.