Complexity and the Transition to Post-Quantum Security: Cryptographic Challenges regarding Shor’s and Grover’s Algorithms
Fabián Alexis Aburto Moccia, Eduardo Recabarren Domínguez, Gustavo Gatica, Berenice Guerra-Tamara, Germán Herrera Vidal, Jorge Mario Karam Rozo, Alfonso R. Romero-Conrado, Jairo R. Coronado-Hernández · Procedia Computer Science · 2025
Quantum computing has become one of the most important emerging technologies, with the potential to compromise traditional cryptographic systems such as RSA and ECC, which are widely used for information security. This study proposes a strategic roadmap to help organizations transition to post-quantum security systems, mitigating the risks generated by advanced quantum algorithms like Shor’s and Grover’s. The methodology includes a review of scientific literature and a comparative analysis of emerging cryptographic technologies, including lattice-based cryptography, code-based cryptography, and quantum key distribution (QKD). The results allowed evidence of the need for proactive and structured planning, including a gradual implementation of post-quantum cryptographic solutions, updating security policies, and specialized training programs for technical and executive personnel. This paper provides a comprehensive framework to help organizations anticipate quantum threats and ensure the resilience of their cryptographic security infrastructure.