Information Hiding Model Based On The Coefficient Matrix Of Nonhomogeneous Linear Equations With Smallest Weight Solution On Binary Domain

Information hiding has been one important embranchment of information security. Almost all the methods analyzing information hiding are based on the change of some statistic characters of host data that happened after secret data being embedded into host data, and the quantum of host data modified is too big to change some statistic characters of host data. The quantum of host data modified in F5 algorithm is very small, so it is much hard to analyze F5 algorithm, and F5 was uased widely. But F5 algorithm has one shortcoming that its information hiding capacity is very small, so maybe some work should be done to make it perfect.After much investigation on F5 algorithm and the characters of Steganography, this thesis built information hiding mathematical model based on the coefficient matrix of nonhomogeneous linear equations with smallest weight solution on binary domain, and in the progress of finding the solutions of the mathematical model, the paper got four information hiding algorithm models. The four algorithm models with different parameter matrix have different characters: all the vectors of model one's algorithm matrix is one radix of vector space; model two's algorithm matrix is complementary matrix, and it is almost twice much capacity F5; model three's algorithm matrix has all vectors in vector space except zero vector and it described F5 algorithm in matrix operation; model four's algorithm matrix is one complementary matrix added with another L vectors, and its information hiding characters changed with different variable L. In the progress of building and finding the solutions of the mathematical model, some mathematical terms such as binary domain, complementary vector on binary domain, complementary matrix on binary domain were defined and the theorem that one vector has only one complementary vector on binary domain was given and was testified and the four algorithm models were strictly proved correct.This paper gave simulation experiment on model two with VC++, and the result indicated that model two has good imperceptibility and bigger capacity, so model two can be used widely in information hiding.