Inferring Bivariate Polynomials for Homomorphic Encryption Application

Inspired by the advancements in (fully) homomorphic encryption recent decades and its practical applications, we conducted a preliminary study on underlying mathematical structure of corresponding schemes. Hence, this paper focuses investigating challenge deducing bivariate polynomials constructed using operations, namely repetitive additions multiplications. To begin with, introduce an approach for solving previously mentioned problem Lagrange interpolation evaluation univariate polynomials. This method is well-established determining that satisfy specific set points. Moreover, propose second based modular knapsack resolution algorithms. These algorithms are designed to address optimization problems which objects with weights values involved. Finally, provide recommendations how run our order obtain better results terms precision.