The article presents the so-called coin bag problem, which is modeled by linear Diophantine equations. The problem in question involves assessing the contents of a set of coins based on its weight. Since this type of problem is undecidable, a special variant of the problem was proposed for which effective problem-solving algorithms can be developed. In this paper, an original heuristic is presented (an algorithm based on problem decomposition) which allows to solve the coin bag problem in fewer steps compared to a brute force algorithm. The proposed approach was verified in a series of computational experiments. Additionally, an authentication scheme making use of the approach was proposed as an example of potential practical use.

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