Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition method

The mathematical model of cryptosystem based on the method of gamma superposition, in which the algorithm of the inverse transformation of the closed text is reduced to the impossibility of problem solution is developed. The multiplicative knapsack task is generalized and the problem of working out of alphabetic cryptosystems mathematical models is considered. The mathematical models of such cryptosystems are offered in the article. The investigation is based on the C. Shannon, who considered, that cryptosystems containing Diophantine difficulties, possesses the greatest uncertainty of key selection process. Necessary and suffitient conditions at which generalized multiplicative knapsack is injective on Zp, p . 2, are established. The problem of building the isomorphic additive and multiplicative knapsacks is also considered.