Steganographic information hiding via symmetric numerical semigroups

We introduce a steganographic information hiding scheme based on structural properties of numerical semigroups arising from the Frobenius coin problem. Instead of encoding data through representable integers, the proposed protocol embeds information into the gap structure of carefully chosen symmetric numerical semigroups. Symmetry guarantees a balanced gap density, ensuring that encoded values are statistically indistinguishable from uniform numerical noise to an observer lacking the private generating set. The security of the scheme relies on the assumed average-case hardness of numerical semigroup membership inference for hidden generators, offering a novel number-theoretic primitive for covert communication and post-quantum resilient information hiding.

💡 Research Summary

The paper introduces a novel steganographic information‑hiding scheme that leverages the gap structure of symmetric numerical semigroups, a concept rooted in the classical Frobenius coin problem. Instead of encoding data directly as representable integers, the authors embed information into the set of “gaps” (integers not belonging to the semigroup) of a carefully chosen symmetric semigroup. The key idea is that symmetric semigroups satisfy the duality property: for every integer z, z belongs to the semigroup S if and only if F(S) − z does not, where F(S) is the Frobenius number. Consequently, exactly half of the integers in the interval