Implementation And Application Of HFMS In Real Number Field

Implementation and Application of HFMS in Real Nmber FieldAs we all know, with the development of science and technology, network security is more and more attention has been paid. Sudden case in recent years, such as CSDN has been blasting library events remind us that the emphasis on information security, otherwise we would have to bear the irreparable loss. Although quantum computer age has not yet come, but it already constitutes a new threat to the existing crypto systems, presented a new challenge. The past, many are considered to be very safe crypto system will no longer be safe, including ECC, RSA and EIGamal convert generalized discrete Fourier transform of public key cryptography in polynomial time quantum computers are compromised. We can not resist quantum computer era, to the contrary, we should adopt a positive attitude to meet it. If we can field in quantum computers are not good at specially constructed some password, then these passwords will be a lot of chance to resist the attack of quantum computers. The hidden field research on the matrix collection of public key cryptography (HFMS) is a classification based on BMQ problem with matrix algebra finite field are MPKC, a new public-key cryptosystemconstructed programIn this paper, a graph G3-coloring problem of the BMQ problem on the finite field of q elements is NP-Complete Problem and HFMS public key cryptography scheme conceived:①A={A1,…,An}∈Fq2×n linearly independent②B={B1,…,Bn}∈Fqn×n linearly independent, C={C1,…,Cn}∈Fqn×n linearly independent and b∈Vs(B)\{0}(?) b∈Ln(Fq)∧b-1∈Vs (C)\{0};③Rank(A·B)=2n;Meet not only achieve the DPS-HFMS the key point is how to find the corresponding constraint matrix set (A, B,C), gives the method of how to find the ergodic matrix to meet the constraints of the DPS-HFMS specific finding structure, also DPS-HFMS constraint conditions (A,B,C) is further weakened, no longer requires none of the singular in the matrix Vs(b)\{0},Vs(b)\{0} the non-singular matrix is only required inverse Vs(C)\{0}, gives the NPS-HFMS constructor method, as well as how to find and configured to meet the NPS-HFMS constraints traverse the matrix (A,B,C) of its critical point (B,C) of the structure. Number of a non-singular matrix of Fqn×n, the proportion of the non-singular matrix relationship with the HFMS the decryption success rate is derived out of the HFMS the formula decryption success rate. Found either M∈Fqn×n whether or not a singular matrix, the majority of the success of the HFMS the decryption rate in△n(Fq) around the fluctuations, which shows the HFMS Average decryption success rate with△n(Fq), so, if q is large, we can guarantee HFMS having a high success rate of the average decryption.Finally, the concrete realization of the NPS-HRMS, we found that in the process of matrix operations, can’t always avoid the loss of accuracy, the final result decryption failed. To this end, we limited the value of the real matrix elements, the tolerable error NPS-HRMS structure, and confirmed by specific experimental feasibility and correctness of the program to achieve the desired objectives.