Researchs And Applications On Linearization Equation On Cryptanalysis Of Multivariate Public Key Cryptosystem

Linear equations is an important tool in cryptanalysis of multivariate public key cryptosystem. In this thesis, based on a matrix of cryptography with a new multivariate public key cryptosystem and Medium Field Equation system, we take multivariate public key cryptosystem as our research goal, which not only successfully break the first two public key cryptosystem, but also analyzing linearization feature about second-order matrix system in the Medium Field Equation system, but also describes in detail the principle, steps and features of linear equations in the process of multivariate analysis of public key cryptography.The first part of this thesis, summarize the method and steps to improve the linear equations attacks. Gives two features of linearization in multivariate public key cryptosystem, and vividly demonstrates the finding, iteration, elimination, and solution process of linear equations.1.In the design of center mapping structure, public key cryptography based on matrix is injected into cyclic matrix, the way that makes full use of the advantages of exchangeable cyclic matrix, reduces the amount of key objectives. The disadvantage of the idea is that not only key exchange method is similar to ElGamal method, but the public key satisfied linear equations, the method attacked by linear equations achieves the plaintext which decrypt from the legal ciphertext if an attacker obtains the equivalent private key by the way of analysis and calculation of given public key. Further, this thesis provide a middle attack method and give the procedure to this cryptography which is based on this cryptography is similar to Diffie-Hellman key exchange method.2.Based on a finite field of odd prime number, new multivariate public key cryptosystem, but we found the disadvantage through in-depth research that this kind of system is similar to Square cryptosystem, and its central idea is similar to the design of the mapping l-reversible cycle system. Some research show that this structure exists first-order linear equations. It can be convert to Square structure or the same structure if all the linear equations have been found. And differential attack which is useful to Square structure can decipher the legal ciphertext.3.The second-order matrix of center mapping structure of Medium Field Equation system public key cryptosystem is meeting all requirements of second-order linear equations. After this structure had been cracked, a lot of improvement have been done. This thesis found, all second-order matrix is meeting all requirements first-order or second-order linear equations when the structure is second-order multivariate polynomia and can be cracked.Two cryptosystem attacks mentioned in this article has been realized and verified with Magma software in the computer.