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Code-Based Cryptography Workshop

CBC 2019: Code-Based Cryptography pp 69–85Cite as

DAGS: Reloaded Revisiting Dyadic Key Encapsulation

Part of the Lecture Notes in Computer Science book series (LNSC,volume 11666)

Abstract

In this paper we revisit some of the main aspects of the DAGS Key Encapsulation Mechanism, one of the code-based candidates to NIST’s standardization call for the key exchange/encryption functionalities. In particular, we modify the algorithms for key generation, encapsulation and decapsulation to fit an alternative KEM framework, and we present a new set of parameters that use binary codes. We discuss advantages and disadvantages for each of the variants proposed.

Keywords

  • Post-quantum cryptography
  • Code-based cryptography
  • Key exchange

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  • DOI: 10.1007/978-3-030-25922-8_4
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Notes

  1. 1.

    If A is not invertible, abort and go back to 1.

  2. 2.

    This is mostly a formal difference, since \(\tilde{H}\) is in fact the public key.

  3. 3.

    In alternant form.

  4. 4.

    See next section for details.

References

  1. Banegas, G., et al.: DAGS: key encapsulation using dyadic GS codes. J. Math. Cryptol. 12, 221–239 (2018)

    MathSciNet  CrossRef  Google Scholar 

  2. Banegas, G., Barreto, P.S.L.M., Persichetti, E., Santini, P.: Designing efficient dyadic operations for cryptographic applications. IACR Cryptology ePrint Archive 2018, p. 650 (2018)

    Google Scholar 

  3. Bardet, M., Bertin, M., Couvreur, A., Otmani, A.: Practical algebraic attack on DAGS. To appear

    Google Scholar 

  4. Barelli, É., Couvreur, A.: An efficient structural attack on NIST submission DAGS. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11272, pp. 93–118. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03326-2_4

    CrossRef  Google Scholar 

  5. Bernstein, D.J., Persichetti, E.: Towards KEM unification. IACR Cryptology ePrint Archive 2018, p. 526 (2018)

    Google Scholar 

  6. Cayrel, P.-L., Hoffmann, G., Persichetti, E.: Efficient Implementation of a CCA2-Secure Variant of McEliece Using Generalized Srivastava Codes. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 138–155. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_9

    CrossRef  Google Scholar 

  7. https://classic.mceliece.org/

  8. http://www.dags-project.org

  9. Faugere, J.-C., Otmani, A., Perret, L., De Portzamparc, F., Tillich, J.-P.: Structural cryptanalysis of McEliece schemes with compact keys. DCC 79(1), 87–112 (2016)

    MathSciNet  MATH  Google Scholar 

  10. Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic cryptanalysis of McEliece variants with compact keys. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 279–298. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_14

    CrossRef  Google Scholar 

  11. Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P:. Algebraic cryptanalysis of McEliece variants with compact keys - towards a complexity analysis. In: Proceedings of the 2nd International Conference on Symbolic Computation and Cryptography, SCC 2010, pp. 45–55. RHUL, June 2010

    CrossRef  Google Scholar 

  12. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC), pp. 212–219, May 1996

    Google Scholar 

  13. Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_12

    CrossRef  MATH  Google Scholar 

  14. https://keccak.team/kangarootwelve.html

  15. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. Elsevier, Amsterdam (1977). North-Holland Mathematical Library

    MATH  Google Scholar 

  16. Misoczki, R., Barreto, P.S.L.M.: Compact McEliece keys from Goppa codes. In: Jacobson, M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 376–392. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05445-7_24

    CrossRef  Google Scholar 

  17. https://csrc.nist.gov/projects/post-quantum-cryptography/post-quantum-cryptography-standardization

  18. Nojima, R., Imai, H., Kobara, K., Morozov, K.: Semantic security for the McEliece cryptosystem without random oracles. Des. Code. Cryptogr. 49(1–3), 289–305 (2008)

    MathSciNet  CrossRef  Google Scholar 

  19. Persichetti, E.: Compact McEliece keys based on quasi-dyadic Srivastava codes. J. Math. Cryptol. 6(2), 149–169 (2012)

    MathSciNet  CrossRef  Google Scholar 

  20. Sarwate, D.: On the complexity of decoding Goppa codes. IEEE Trans. Inf. Theory 23(4), 515–516 (1977)

    MathSciNet  CrossRef  Google Scholar 

  21. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    MathSciNet  CrossRef  Google Scholar 

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Author information

Authors and Affiliations

  1. Tecnische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gustavo Banegas

  2. University of Washington Tacoma, Tacoma, USA

    Paulo S. L. M. Barreto

  3. Laboratoire d’Algebre, de Cryptographie, de Géométrie Algébrique et Applications, Université Cheikh Anta Diop, Dakar, Senegal

    Brice Odilon Boidje, Gilbert Ndollane Dione, Cheikh Thiécoumba Gueye, Jean Belo Klamti & Ousmane N’diaye

  4. Laboratoire Hubert Curien, Université Jean Monnet, Saint-Etienne, France

    Pierre-Louis Cayrel

  5. George Mason University, Fairfax, USA

    Kris Gaj, Richard Haeussler & Duc Tri Nguyen

  6. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, USA

    Edoardo Persichetti

  7. Universidade de São Paulo, São Paulo, Brazil

    Jefferson E. Ricardini

Authors
  1. Gustavo Banegas
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  2. Paulo S. L. M. Barreto
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  3. Brice Odilon Boidje
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  4. Pierre-Louis Cayrel
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  5. Gilbert Ndollane Dione
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  6. Kris Gaj
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  7. Cheikh Thiécoumba Gueye
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  8. Richard Haeussler
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  9. Jean Belo Klamti
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  10. Ousmane N’diaye
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  11. Duc Tri Nguyen
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  12. Edoardo Persichetti
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  13. Jefferson E. Ricardini
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Corresponding author

Correspondence to Edoardo Persichetti .

Editor information

Editors and Affiliations

  1. Marche Polytechnic University, Ancona, Italy

    Prof. Marco Baldi

  2. Florida Atlantic University, Boca Raton, FL, USA

    Dr. Edoardo Persichetti

  3. Marche Polytechnic University, Ancona, Italy

    Paolo Santini

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Banegas, G. et al. (2019). DAGS: Reloaded Revisiting Dyadic Key Encapsulation. In: Baldi, M., Persichetti, E., Santini, P. (eds) Code-Based Cryptography. CBC 2019. Lecture Notes in Computer Science(), vol 11666. Springer, Cham. https://doi.org/10.1007/978-3-030-25922-8_4

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  • DOI: https://doi.org/10.1007/978-3-030-25922-8_4

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