Construct And Implement On The Hidden Ergodic Matrix PKC

Commonly used encryption algorithm is public key encryption in Modern cryptography. Public key encryption in The matrix of Finite Fields and ergodic theory of cryptography is important in coding theory and application of research in it is extensive and practical, it continuously bring research and extension in the problem of matrix equation on the finite field.HEM-PKC public key cryptography is proposed by the HEM-PKC as an important theoretical basis on BMQ question. The BMQ problem has been shown to be NP-complete, so the security of it is understandable. As the present one of the few algorithms against quantum algorithms, the development potential of HEM-PKC is enormous. The key generation and encryption/decryption parts of HEM-PKC can be applied to the applications which need high-strength information technology. Be different from MQ-based public key cryptography, HEM-PKC use the relationship between the matrix and vector in finite fields and hybrid operation to design the trap door, and it is difficult to abstract its center map be a simple mathematical form.This article made the following several aspects:First, we show the introduction about modern cryptography technology research and development and status of MPKC algorithm, and summarize several types of existing algorithm and future development direction.Second, we specifically introduce five different types of MPKC, and analyze the differences and connections between them. MPKC mainly has the following five basic types:1. Unbalanced Oil and Vinegar Scheme (UOV)2. Stepwise Triangular Systems (STS)3. Matsumoto-Imai Scheme MIC*(MI)4. Hidden Field Equations (HFE)5. (?)-Invertible Cycles ((?)IC)These five programs have the same structure:ρ:x∈Fn(?)u(?)v(?)y∈FmNonlineal central mapφmingles in the two linear maps A, B, and F is the finite field, Φ(x) is the nonlinear mapping and A(x)=MS x+a and B(x)=MT x+b is linear or affine map. Public key is(F,ρ=[ρ1,(x1,…xn),…,ρm(x1,…xn)]), private key is(A,φ,B). The main difference is the construction in the nonlinear center maps.Finally, we introduce the design and implementation of HEM-PKC algorithms including the prerequisite, trapdoor construction methods and specific process of key generation and encryption and decryption process. Then we propose attack scenario for this algorithm.