Análise experimental da ameaça quântica à criptografia clássica pelo Algoritmo de Shor em simuladores ideais vs. hardware real na Arquitetura Heron
Resumo
O algoritmo de Shor ameaça a criptografia assimétrica (RSA, ECC), mas restrições da era NISQ como ruído e decoerência limitam sua execução prática. Neste artigo é avaliado empiricamente o algoritmo de Shor no processador IBM Heron (ibm_fez), contrastando a complexidade teórica com a viabilidade física. Para N = 55 (número a fatorar, com L = 6 bits), a arquitetura padrão com registrador de medição m = 2L gerou mais de 96,667 portas CNOT, degradando o sinal para ruído estatístico. Como mitigação, avaliou-se uma arquitetura otimizada com m = L, o que reduziu as portas de emaranhamento em ≈ 49% e preservou picos discerníveis sob ruído térmico. Conclui-se que barreiras tecnológicas rigorosas limitam a ameaça imediata, oferecendo uma base factual para o planejamento da migração pós-quântica (PQC) com urgência mas sem alarmismos.
Palavras-chave:
ameaça quântica, algoritmo quântico de Shor, criptografia assimétrica, criptografia pós-quântica (PQC), era NISQ, portas de emaranhamento
Referências
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Dubey, V. M. and Varshney, G. (2026). Measurement study of post-quantum readiness of internet: 2026.
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Kavitha, S. S. et al. (2025). Quantum shor’s algorithm vs. classical general number field sieve (gnfs) approach for large integer factorization. In 2025 International Conference on Next Generation Communication & Information Processing (INCIP), pages 1–6. IEEE.
Lee, Y., Choi, M., Min, Y., Bae, E., and Bae, S. (2025). Two variations of quantum phase estimation for reducing circuit error rates: Application to the harrow-hassidim-lloyd algorithm. arXiv preprint arXiv:2507.06711.
Lenstra, A. K. and Lenstra, H. W. (1993). The development of the number field sieve. Springer-Verlag, Berlin.
Mallick, T., Zeldin, M., Cenk, M., and Nita-Rotaru, C. (2025). Quantum disruption: An sok of how post-quantum attackers reshape blockchain security and performance.
National Institute of Standards and Technology (2024). Post-quantum cryptography standardization. NIST Computer Security Resource Center.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.
Rassekhnia, J. (2026). Quantum encryption resilience score (qers) for computer system processes, iot, and iiot devices across mqtt, [link], and [link].
Robertson, R. and Ventura, D. (2024). Introducing unique: The unconventional noiseless intermediate quantum emulator. arXiv preprint arXiv:2409.07000.
Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th Annual Symposium on Foundations of Computer Science, pages 124–134. IEEE.
Skosana, U. and Tame, M. (2022). Demonstration of shor’s factoring algorithm for n = 21 on ibm quantum processors. arXiv preprint arXiv:2103.13855.
Su, T. H. et al. (2026). Scalable quantum reinforcement learning on nisq devices with dynamic-circuit qubit reuse. arXiv preprint arXiv:2509.16002v2.
Zelenovic, J., Taghizadeh, L., Pena-Gonzalez, E., García, J. G., and Preneel, B. (2026). Post-quantum discovery as a governance capability: Evidence-based cryptographic visibility and exposure prioritisation in a critical service provider.
Amico, M. (2026). Exponentially cheaper coherent phase estimation via uncontrolled unitaries. arXiv preprint arXiv:2603.27858v2.
Amico, M., Saleem, Z. H., and Kumph, M. (2019). An experimental study of shor’s factoring algorithm on ibm q. Physical Review A, 100(1):012305.
Bagourd, P. et al. (2026). Practical challenges in executing shor’s algorithm on existing quantum platforms. arXiv preprint arXiv:2512.15330v3.
Dubey, V. M. and Varshney, G. (2026). Measurement study of post-quantum readiness of internet: 2026.
Dutkiewicz, A. et al. (2025). Error mitigation and circuit division for early fault-tolerant quantum phase estimation. arXiv preprint arXiv:2410.05369v2.
Gidney, C. (2025). How to factor 2048 bit rsa integers with less than a million noisy qubits.
Gidney, C. and Ekerå, M. (2021). How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum, 5:433.
Kahanamoku-Meyer, G. D. et al. (2025). A log-depth in-place quantum fourier transform that rarely needs ancillas. arXiv preprint arXiv:2505.00701.
Kavitha, S. S. et al. (2025). Quantum shor’s algorithm vs. classical general number field sieve (gnfs) approach for large integer factorization. In 2025 International Conference on Next Generation Communication & Information Processing (INCIP), pages 1–6. IEEE.
Lee, Y., Choi, M., Min, Y., Bae, E., and Bae, S. (2025). Two variations of quantum phase estimation for reducing circuit error rates: Application to the harrow-hassidim-lloyd algorithm. arXiv preprint arXiv:2507.06711.
Lenstra, A. K. and Lenstra, H. W. (1993). The development of the number field sieve. Springer-Verlag, Berlin.
Mallick, T., Zeldin, M., Cenk, M., and Nita-Rotaru, C. (2025). Quantum disruption: An sok of how post-quantum attackers reshape blockchain security and performance.
National Institute of Standards and Technology (2024). Post-quantum cryptography standardization. NIST Computer Security Resource Center.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.
Rassekhnia, J. (2026). Quantum encryption resilience score (qers) for computer system processes, iot, and iiot devices across mqtt, [link], and [link].
Robertson, R. and Ventura, D. (2024). Introducing unique: The unconventional noiseless intermediate quantum emulator. arXiv preprint arXiv:2409.07000.
Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th Annual Symposium on Foundations of Computer Science, pages 124–134. IEEE.
Skosana, U. and Tame, M. (2022). Demonstration of shor’s factoring algorithm for n = 21 on ibm quantum processors. arXiv preprint arXiv:2103.13855.
Su, T. H. et al. (2026). Scalable quantum reinforcement learning on nisq devices with dynamic-circuit qubit reuse. arXiv preprint arXiv:2509.16002v2.
Zelenovic, J., Taghizadeh, L., Pena-Gonzalez, E., García, J. G., and Preneel, B. (2026). Post-quantum discovery as a governance capability: Evidence-based cryptographic visibility and exposure prioritisation in a critical service provider.
Publicado
01/09/2026
Como Citar
LIMA, Luis; FREITAS, Rosiane.
Análise experimental da ameaça quântica à criptografia clássica pelo Algoritmo de Shor em simuladores ideais vs. hardware real na Arquitetura Heron. In: SIMPÓSIO BRASILEIRO DE CIBERSEGURANÇA (SBSEG), 26. , 2026, Armação dos Búzios/RJ.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 143-158.
DOI: https://doi.org/10.5753/sbseg.2026.29318.
