Multiplicative knapsack injectivity as condition of effective unauthorized access protection

Abstract

Abstract The mathematical modelling of data protection systems based on multiplicative knapsack is considered. In particular, development of cryptographic solution to hierarchic access control problem is represented. Previously in research the authors has formulated the requirements to knapsack in order to apply these to a hierarchic access control problem based on the requirements for similar models. Here in the article the possibility of practical implementation of the construction of such knapsacks is pointed. Based on special mathematical model for multiplicative knapsacks generalized sufficient condition of multiplicative knapsack injectivity is formulated and proved in the article. Known sufficient conditions of multiplicative knapsack injectivity are special cases of authors condition. The mathematical apparatus of additive knapsacks for building multiplicative vector is shown.