At the bedrock of cryptosystems lie trapdoor functions, serving as the fundamental building blocks that determine the security and efficacy of encryption mechanisms. These functions operate as one-way transformations, demonstrating an inherent asymmetry: they are designed to be easily computable in one direction, while proving computationally challenging, if not infeasible, in the opposite direction. This paper contributes to the evolving landscape of cryptographic research by introducing a novel trapdoor function, offering a fresh perspective on the intricate balance between computational efficiency and security in cryptographic protocols.
The primary objective of this paper is to present and scrutinize the proposed trapdoor function, delving into a comprehensive analysis that unveils both its strengths and weaknesses. By subjecting the function to rigorous examination, we aim to shed light on its robustness as well as potential vulnerabilities, contributing valuable insights to the broader cryptographic community. Understanding the intricacies of this new trapdoor function is essential for assessing its viability in practical applications, particularly in securing sensitive information in real-world scenarios.
Moreover, this paper does not shy away from addressing the pragmatic challenges associated with deploying the proposed trapdoor function at scale. A thorough discussion unfolds, highlighting the potential hurdles and limitations when attempting to integrate this function into large-scale environments. Considering the practicality and scalability of cryptographic solutions is pivotal, and our analysis strives to provide a clear understanding of the circumstances under which the proposed trapdoor function may encounter obstacles in widespread implementation.
In essence, this paper contributes to the ongoing discourse surrounding trapdoor functions by introducing a new entrant into the cryptographic arena. By meticulously exploring its attributes, strengths, and limitations, we aim to foster a deeper understanding of the intricate interplay between cryptographic theory and real-world applicability.

An earlier research project that dealt with converting ASCII codes into 2D Cartesian coordinates and then applying translation and rotation transformations to construct an encryption system, is improved by this study. Here, we present a variation of the Cantor Pairing Function to convert ASCII values into distinctive 2D Coordinates. Then, we apply some novel methods to jumble the ciphertext generated as a result of the transformations. We suggest numerous improvements to the earlier research via simple tweaks in the existing code and by introducing a novel key generation protocol that generates an infinite integral key space with no decryption failures. The only way to break this protocol with no prior information would be brute force attack. With the help of elementary combinatorics and probability topics, we prove that this encryption protocol is seemingly infeasible to overcome by an unwelcome adversary.

This paper outlines an encoding schematic that is dependent on simple Cartesian coordinate transformations. Namely, the change of axes and the rotation of axes. A combination of these two is incorporated after turning singular ASCII values into 2D points. This system is based on multiple private keys that can also act as a potential candidate for threshold cryptography. Comprehensive initial testing has been performed on certain parameters by altering their values within a range. Further testing is required for more insights about the system. For now, the list of parameters that amounts to successful decryption is to be noted down for future use with this system.