Skip to main content

Abstract

Post-quantum encryption schemes use variants of the Fujisaki-Okamoto transformation in order to construct a highly secure key encapsulation mechanism from a weakly secure public key encryption scheme. In the third round of the NIST post-quantum cryptography standardization call, all the candidates for the key encapsulation mechanism category use some of these transformations. This work studies how the mentioned transformations are applied in the code-based candidates of the NIST third round. These are Classic McEliece (finalist), BIKE (alternative) and HQC (alternative). Studying the differences between the transformations gives a better understanding of these candidates.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aguilar Melchor, C., et al.: HQC (Hamming Quasi-Cyclic) (2021). https://pqc-hqc.org/

  2. Albrecht, M.R., et al.: Classic McEliece: conservative code-based cryptography (2020). https://classic.mceliece.org/nist.html

  3. Aragon, N., et al.: BIKE (Bit Flipping Key Encapsulation) (2021). https://bikesuite.org

  4. Bernstein, D.J., Persichetti, E.: Towards KEM unification. Cryptology ePrint Archive, Report 2018/526 (2018). https://eprint.iacr.org/2018/526

  5. Coron, J.S., Handschih, H., Joye, M., Pailier, P., Pointcheval, D., Tymen, C.: GEM: a generic chosen-ciphertext secure encryption method. In: Proceeding Topics in Cryptology - CT-RSA 2002, Lecture Notes Computer Science, vol. 2271, pp. 263–276 (2002). https://doi.org/10.1007/3-540-45760-7_18

  6. Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. Cryptology ePrint Archive, Report 2001–108 (2001). http://eprint.iacr.org/2001/108

  7. Dent, A.W.: A designer’s guide to KEMs. In: Proceding 9th IMA International Conference on Cryptography and Coding, Lecture Notes in Computer Science, vol. 2898 (2003). https://doi.org/10.1007/978-3-540-40974-8_12

  8. Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Proceeding 19th Annual International Cryptology Conference, Advances in Cryptology - CRYPTO 1999, Lecture Notes Computer Science, vol. 1666, pp. 537–554 (1999). https://doi.org/10.1007/3-540-48405-1_34

  9. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997). https://doi.org/10.1103/PhysRevLett.79.325

    Article  Google Scholar 

  10. Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Proceeding 15th International Conference Theory of Cryptography TCC 2017, Lecture Notes Computer Science, vol. 10677, pp. 341–371 (2017). https://doi.org/10.1007/978-3-319-70500-2_12

  11. Jiang, H., Zhang, Z., Chen, L., Wang, H., Ma, Z.: IND-CCA-secure key encapsulation mechanism in the quantum random oracle model, revisited. Cryptology ePrint Archive, Report 2017/1096 (2017). http://eprint.iacr.org/2017/1096

  12. NIST: Post-quantum cryptography (2016). https://csrc.nist.gov/Projects/Post-Quantum-Cryptography

  13. Saito, T., Xagawa, K., Yamakawa, T.: Tightly-secure key-encapsulation mechanism in the quantum random oracle model. Cryptology ePrint Archive, Report 2017/1005 (2017). https://doi.org/10.1007/978-3-319-78372-7_17, http://eprint.iacr.org/2017/1005

  14. Saito, T., Xagawa, K., Yamakawa, T.: Tightly-secure key-encapsulation mechanism in the quantum random oracle model. In: Proceeding Annual International Conference on the Theory and Applications of Cryptographic Techniques, Advances in Cryptology - EUROCRYPT 2000, Lecture Notes Computer Science, vol. 10822, pp. 520–551 (2018). https://doi.org/10.1007/978-3-319-78372-7_17

  15. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999). https://doi.org/10.1137/S0036144598347011

    Article  MathSciNet  MATH  Google Scholar 

Download references

This work was supported in part by project P2QProMeTe (PID2020-112586RB-I00/AEI/10.13039/501100011033), ORACLE Project, with reference PCI2020-120691-2, funded by MCIN/AEI/10.13039/501100011033 and European Union “NextGenerationEU/PRTR”, in part by the Spanish State Research Agency (AEI) of the Ministry of Science and Innovation (MCIN), and in part by the EU Horizon 2020 research and innovation programme, project SPIRS (Grant Agreement No. 952622).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miguel Ángel González de la Torre .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

González de la Torre, M.Á., Hernández Encinas, L. (2023). About the Fujisaki-Okamoto Transformation in the Code-Based Algorithms of the NIST Post-quantum Call. In: García Bringas, P., et al. International Joint Conference 15th International Conference on Computational Intelligence in Security for Information Systems (CISIS 2022) 13th International Conference on EUropean Transnational Education (ICEUTE 2022). CISIS ICEUTE 2022 2022. Lecture Notes in Networks and Systems, vol 532. Springer, Cham. https://doi.org/10.1007/978-3-031-18409-3_8

Download citation

Publish with us

Policies and ethics