Methods of Speeding Up Secret Computations With Insecure Auxiliary Computer

Currently, the problem of speeding up secret computations with the help of an auxiliary computer changed and was enriched by numerous problems of computational mathematics, where a solution means an approximate solution. The main goal of this paper is to demonstrate the different methods of computing approximate solutions of some equations with help of an auxiliary computer. To show methods, we chose the certain classes of algebraic and differential equations because in most cases modern computing problems are reduced to solving such systems of equations (differential equations, linear programming, etc.).