Uma Análise Física e Computacional do Impacto da Computação Quântica na Criptografia

Abstract

This work consists of a bibliographic and introductory review on the intersection between classical cryptography and quantum computing. The text is structured from the formulation of symmetric and asymmetric encryption methods, emphasizing the RSA algorithm and its limiting basis on the mathematical problem of integer factorization. To substantiate the quantum paradigm, the postulates of quantum mechanics are reviewed through Dirac notation, highlighting essential operational properties, such as superposi- tion and interference. In the computational scope, the study describes reversible logic gates and the concept of quantum parallelism based on the Deutsch-Jozsa algorithm. Next, the theoretical structure of Shor’s algorithm and the use of the Quantum Fourier Transform in the drastic reduction of the time complexity of factorization are detailed. The text concludes with a brief compilation of the empirical obstacles for the construction of viable hardware, based on the challenge imposed by the fast decoherence rates against the time necessary for the execution of logical operations on the qubits.