In the year 2007, a slightly nerdy girl fell in love with all things math. Even though she only was exposed to a small part of the immense field of mathematics, she knew that math would always have a place in her heart. Ten years later, that passion for math is still burning inside. She never thought she would be interested in anything other than strictly mathematics. However, she discovered a love for computer science her sophomore year of college. Now, she is graduating college with a double major in both mathematics and computer science.\nThis nerdy girl is me. It was my first semester, freshman year at Ouachita Baptist University when I discovered an interest in cryptography. Discrete Mathematics had a small portion of the class that discussed various types of cryptosystems. These were the simplified versions that were easier to comprehend so that we could truly grasp the underlying concepts of cryptography. However, I craved more. I wanted to delve further into the advanced world of cryptography. It was not until my Honors Directed Study that I was able to do so.\nDuring my directed study, I was able to research the history of cryptography and what it has transformed into today. While it was fascinating to look at all the various cryptosystems that have been created throughout time, one cryptosystem caught my eye in particular—Elliptic Curve Cryptography, commonly referred to as ECC. I had heard of a few cryptosystems but never the ECC. As such, my interest was piqued. Having the opportunity to research Elliptic Curve Cryptography, I was ready to try and understand a new mathematical concept. I was ready to further expand my love and passion for mathematics, and I was not disappointed. Learning even the basics of elliptical curves proved challenging. The math behind ECC is immense and quite frankly, intimidating. Nevertheless, I do not back down from a challenge…at least not a mathematical one.\nMy research of elliptic curves, the basis of Elliptic Curve Cryptography, opened up my eyes to an entirely new field of mathematics. The challenges that arose during my studies, while frustrating at times, are well worth the wealth of knowledge I was able to acquire. The research in my study of elliptical curve cryptography only increased the ten-year passion for mathematics that is still inside the slightly nerdy girl.\nThis paper is the culmination of all my research over elliptic curves. It reflects the knowledge that I was able to acquire while studying elliptic curve cryptography and quantum computers.
Abstract The notion of a quantum computer is no longer just theoretical. It is the most significant technology in the world, and nations are competing to become the leaders in quantum computing. The computing time will be cut down from years to hours or even minutes thanks to technology. The scientific community will greatly benefit from the capabilities of quantum computing. It does, however, represent severe risks to cyber security. All encryption algorithms are theoretically prone to damage. Compared to RSA-based cryptosystems, elliptic curve cryptography (ECC) is quicker, more effective, and more sensitive to quantum attacks. Standard ECC is still unworthy of establishing a secure network connection, nonetheless. The improved ECC method is used to extend the communication strategy, reconfiguring the message with the number of cipher-text from both sides. Therefore, we need to carefully evaluate the quantum security of EECC to prepare for the advent of quantum computers. In this, work a new strategy (CQAEECC) known as a collaborative quantum-assisted Extended Elliptic Curve Cryptography (EECC) to protect the transmission of information across networks. The mechanism of merging cryptographic methods and the private key is retrieved from the Quantum Cryptography used by Extended Elliptic Curve Cryptography to ensure greater security over networks. The novel cryptography is compared with standard algorithms and the results show that it is one of the most efficient public key cryptosystems (PKC) for desirable security. Thereupon, the proposed method has the ability to ensure confidentiality, integrity, and availability over the network.
Quantum computing poses an existential threat to public-key cryptography, with Shor's algorithm capable of breaking RSA and elliptic curve systems once cryptographically relevant quantum computers (CRQCs) emerge. While post-quantum cryptography (PQC) offers algorithmic solutions, organizational readiness extends beyond technical implementation to encompass governance, interoperability, and adaptive capacity. This review synthesizes the quantum threat landscape, evaluates NIST-standardized PQC algorithms through quantitative performance analysis, and examines global standardization dynamics. We introduce a novel Quantum Readiness Maturity Model (QRMM) that enables organizations to assess and advance their preparedness across five dimensions: cryptographic infrastructure, governance frameworks, sectoral adaptation, interoperability resilience, and strategic agility. Applying this model to finance, telecommunications, and defense sectors reveals systematic gaps in migration planning and crypto-agility. Our analysis demonstrates that quantum readiness requires treating cryptographic transformation as a strategic enterprise capability rather than a purely technical upgrade. The proposed framework provides actionable pathways for practitioners while identifying critical research directions in hybrid deployment strategies, post-quantum PKI architectures, and algorithmic diversity.