## 2 Related Work
Regarding authentication, [PERSON] [21] proposes a detailed study comparing the advantages and disadvantages of public-key and symmetric cryptography in distributed environments, from the perspective of the cryptographic primitives used and in the case of signatures. This is a starting point for how parameterizations that balance anonymity with non-repudiation can be constructed. [PERSON] et al. [22] developed new criteria for assessing the security of key exchanges and proposed a way to highlight weaknesses in traditional methods, which can be described as a kind of audit of these models and is useful in designing the parameters of a particular signature. Other researchers, such as [PERSON] et al. [23] and [PERSON] et al. [24] investigated multi-factor authentication protocols, and therefore improved security, but did not address the subdomains of particular credentials used in scenarios that are specific to IoT. More recently, the works of [PERSON] [25] and [PERSON] et al. [26] extended the use of two-factor authentication in IoT and healthcare ecosystems and emphasize the importance of integrating a balance of anonymity and accountability for this type of signature. Their studies showed that current protocols are efficient as a general technique, but require customization for each class of applications. [PERSON] et al. [27] analyzed the time factors of multi-factor authentication and highlighted their influence on the perceived security and user satisfaction of such a module. This aspect is decisive in terms of the implementation domain in particular IoT ecosystems, but no concrete parameterization models are provided for such a case. The work of [PERSON] et al. [28] for blind biometric authentication offers an interesting approach for this class of problems, but its limitations come from the modules necessary to implement this technique as well as the complexity of biometric calculations, from the point of view of the particularities of the devices on which they are introduced, which may limit its use in practice. Recent works have also explored advanced features in signature schemes that align with future-proofing requirements. For example, lattice-based proxy signature schemes with message recovery [29] enable efficient verification and integrity preservation in constrained channels, a desirable feature for IoT. Similarly, research into quantum-secure blockchain systems [30] and threshold post-quantum cryptography [31] highlights the urgency of designing adaptable schemes that ensure both privacy and auditability in decentralized environments. Our proposal complements these directions by introducing a customizable anonymity parameter (\(T\)), which could potentially be extended into these frameworks with minimal structural modification. The analysis shows that, despite the numerous contributions in the specialized literature, there are discrepancies between anonymity and responsibility in the implementation in certain environments. In this sense, this paper presents a proposal for a scheme that has as its adaptability requirements for addressing the moderate integration of signature anonymity with the degree of security of the communication channel, designed for the specific case of vector subspaces with applicability in schemes that require the use of IoT.