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arXiv · 2601.18413

Fundamentals, Recent Advances, and Challenges Regarding Cryptographic Algorithms for the Quantum Computing Era

Darlan Noetzold·Valderi Reis Quietinho Leithardt
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Abstract

This book arises from the need to provide a clear and up-to-date overview of the impacts of quantum computing on cryptography. The goal is to provide a reference in Portuguese for undergraduate, master's, and doctoral students in the field of data security and cryptography. Throughout the chapters, we present fundamentals, we discuss classical and post-quantum algorithms, evaluate emerging patterns, and point out real-world implementation challenges. The initial objective is to serve as a guide for students, researchers, and professionals who need to understand not only the mathematics involved, but also its practical implications in security systems and policies. For more advanced professionals, the main objective is to present content and ideas so that they can assess the changes and perspectives in the era of quantum cryptographic algorithms. To that end, the text's structure was designed to be progressive: we begin with essential concepts, move on to quantum algorithms and their consequences (with emphasis on Shor's algorithm), present issues focusing on "families" of post-quantum schemes (based on lattices, codes, hash functions, multivariate, isogenies), analyze the state of the art in standardization (highlighting the NIST process), and finally, discuss migration, interoperability, performance, and cryptographic governance. We hope that this work will assist in the formation of critical thinking and informed technical decision-making, fostering secure transition strategies for the post-quantum era.

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Darlan Noetzold, Valderi Reis Quietinho Leithardt. 2026-01-26. Fundamentals, Recent Advances, and Challenges Regarding Cryptographic Algorithms for the Quantum Computing Era. https://arxiv.org/abs/2601.18413

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