Abstract
In the NIST Post-Quantum Cryptography (PQC) standardization process, among 17 candidates for code-based public-key encryption (PKE), signature or key encapsulation mechanism (KEM), only three are in the 4th evaluation round. The remaining code-based candidates are Classic McEliece [CCUGLMMNPP+20], BIKE [ABBBBDGGGM+17] and HQC [MABBBBDDGL+20]. Cryptographic primitives from coding theory are some of the most promising candidates and their security is based on the well-known problems of post-quantum cryptography. In this paper, we present an efficient implementation of a secure KEM based on binary quasi-dyadic generalized Srivastava (QD-GS) codes. With QD-GS codes defined for an extension degree \(m>2\), this key establishment scheme is protected against the attacks of Barelli-Couvreur Bardet et al.. We also provide parameters that are secure against folding technique and FOPT attacks. Finally, we compare the performance of our implementation in runtime with the NIST finalists based on codes for the 4th round.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aragon, N., et al.: BIKE: Bit Flipping Key Encapsulation (2017). https://bikesuite.org/files/v4.2/BIKE_Spec021.09.29.1.pdf. Accessed 09 Dec 2022
Banegas, G., et al.: DAGS: key encapsulation using dyadic GS codes. J. Math. Cryptol. 12(4), 221–239 (2018)
Banegas, G., et al.: DAGS: reloaded revisiting dyadic key encapsulation. In: Baldi, M., Persichetti, E., Santini, P. (eds.) CBC 2019. LNCS, vol. 11666, pp. 69–85. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25922-8_4
Bardet, M., Bertin, M., Couvreur, A., Otmani, A.: Practical algebraic attack on DAGS. In: Baldi, M., Persichetti, E., Santini, P. (eds.) CBC 2019. LNCS, vol. 11666, pp. 86–101. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25922-8_5
Banegas, G., Barreto, P.S., Persichetti, E., Santini, P.: Designing efficient dyadic operations for cryptographic applications. J. Math. Cryptol. 14(1), 95–109 (2020)
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
Berger, T.P., Cayrel, P.-L., Gaborit, P., Otmani, A.: Reducing key length of the McEliece cryptosystem. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 77–97. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02384-2_6
Chou, T., et al.: Classic McEliece: conservative code-based cryptography (2020). https://classic.mceliece.org/nist/mceliece-20201010.pdf. Accessed 09 Dec 2022
Faugère, J.-C., Otmani, A., Perret, L., De Portzamparc, F., Tillich, J.-P.: Folding alternant and Goppa codes with non-trivial automorphism groups. IEEE Trans. Inf. Theory 62(1), 184–198 (2015)
Faugère, J.-C., Otmani, A., Perret, L., De Portzamparc, F., Tillich, J.-P.: Structural cryptanalysis of McEliece schemes with compact keys. Des. Codes Cryptography 79(1), 87–112 (2016)
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
Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic cryptanalysis of compact McEliece’s variants- toward a complexity analysis. In: Conference on Symbolic Computation and Cryptography, p. 45 (2013)
Jabri, A.A.: A statistical decoding algorithm for general linear block codes. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 1–8. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45325-3_1
Melchor, C.A., et al.: Hamming quasi-cyclic (HQC) (2020). https://pqc-hqc.org/doc/hqc-specification_2020-10-01.pdf. Accessed 09 Dec 2022
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
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes, vol. 16. Elsevier (1977)
Persichetti, E.: Compact McEliece keys based on quasidyadic Srivastava codes. J. Math. Cryptol. 6(2), 149–169 (2012)
Prange, E.: The use of information sets in decoding cyclic codes. IRE Trans. Inf. Theory 8(5), 5–9 (1962)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Seck, B. et al. (2023). Software Implementation of a Code-Based Key Encapsulation Mechanism from Binary QD Generalized Srivastava Codes. In: Deneuville, JC. (eds) Code-Based Cryptography. CBCrypto 2022. Lecture Notes in Computer Science, vol 13839. Springer, Cham. https://doi.org/10.1007/978-3-031-29689-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-29689-5_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-29688-8
Online ISBN: 978-3-031-29689-5
eBook Packages: Computer ScienceComputer Science (R0)