(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Undeniable signatures are a special kind of digital signature that need the active cooperation of the signer in the verification process, granting properties such as completeness, soundness, unforgeability, and invisibility. Moreover, these schemes techniques allow controlled verification in contrast to traditional signatures, meaning that they are perfect in situations when secrecy and selective disclosure are important. Over the years, undeniable signatures have undergone substantial evolution from the transition from classical encryption such as discrete logarithms to modern algorithms that include lattice-based, hash-based, and code-based post-quantum. In this article, focused on classification and taxonomy of undeniable signature schemes through evolution from early concepts to solutions that are resistant to quantum alterations. Unlike previous surveys, our taxonomy highlights distinctions between classical, convertible, and designated confirmer variants, while also introducing a post-quantum perspective rooted in lattice-based and code-based constructions. We analytically classify key properties for undeniable signature schemes whence inspect their strengths and weaknesses, also offer a methodical framework for comprehending the differences between them. Our contributions comprise a comprehensive taxonomy of undeniable signatures, considering various aspects such as security, efficiency, and practical applicability, as well as insights into potential areas future research paths, especially in terms of post- quantum systems. By displaying our views in this regard, our goal is to provide a more profound comprehension and guide ongoing and effective research in undeniable signature schemes.