Abstract
Recently, Galvez et al. submitted McNie, a new public key encryption scheme to NIST as a candidate for the standard of post-quantum cryptography. They claimed that their parameters achieve 128-bit security with small key size by using Quasi-Cyclic Low Rank Parity Check codes (QC-LRPC) and block circulant matrices as the public key and secret key for the encryption. However, McNie based on QC-LRPC has several limitations in its design. In addition, Gaborit suggested an attack against the McNie encryption, which reduces the security levels of Galvez et al.’s proposals. Moreover, McNie based on LRPC codes has decryption failure. We propose a key recovery attack which recovers the secret key of their encryption of the claimed security level for all the proposed parameters. Even Galvez et al. revised their parameters against Gaborit’s attack, we are still able to recover the secret key for the revised parameters by our key recovery attack. We propose a new McNie encryption based on Gabidulin codes with appropriate choices of secret key. Our McNie based on Gabidulin codes has error free decryption.
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References
Aragon, N., Gaborit, P., Hauteville, A., Tillich, J.P.: Improvement of Generic Attacks on the Rank Syndrome Decoding Problem (2017). \(<\)hal-01618464\(>\)
Faugère, J.-C., Levy-dit-Vehel, F., Perret, L.: Cryptanalysis of MinRank. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 280–296. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_16
Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. J. Cryptology 26(1), 80–101 (2013)
Gabidulin, E.M.: Theory of codes with maximum rank distance. Problemy Peredachi Informatsii 21(1), 3–16 (1985)
Gaborit, P.: Attack on McNie. In: Post-Quantum Cryptography, Round 1 Submmisions, McNie, Official Comments. https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/round-1/official-comments/McNie-official-comment.pdf
Gaborit, P., Hauteville, A., Phan, D.H., Tillich, J.-P.: Identity-based encryption from codes with rank metric. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 194–224. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_7
Gaborit, P., Ruatta, O., Schrek, J.: On the complexity of the rank syndrome decoding problem. IEEE Trans. Inf. Theory 62(2), 1006–1019 (2016)
Gaborit, P., Murat, G., Ruatta, O., Zémor, G.: Low Rank Parity Check codes and their application to cryptography. In: The Proceedings of Workshop on Coding and Cryptography (WCC) 2013, Borgen, Norway, pp. 168–180 (2013)
Gaborit, P., Zémor, G.: On the hardness of the decoding and the minimum distance problems for rank codes. IEEE Trans. Inf. Theory 62(12), 7245–7252 (2016)
Galvez, L., Kim, J., Kim, M.J., Kim, Y., Lee, N.: McNie: Compact McEliece-Niederreiter Cryptosystem. https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/round-1/submissions/McNie.zip
Galvez, L., Kim, J., Kim, M.J., Kim, Y., Lee, N.: New McNie parameters. In: Post-Quantum Cryptography, Round 1 Submmisions, McNie, Official Comments. https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/round-1/official-comments/McNie-official-comment.pdf
Goubin, L., Courtois, N.T.: Cryptanalysis of the TTM cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 44–57. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44448-3_4
Levy-dit-Vehel, F., Perret, L.: Algebraic decoding of rank metric codes. In: Proceedings of YACC 2006, pp. 142–152 (2006)
Otmani, A., Kalachi, H.T., Ndjeya, S.: Improved Cryptanalysis of Rank Metric Schemes Based on Gabidulin Codes. CoRR abs/1602.08549 (2016)
Ourivski, A.V., Johansson, T.: New technique for decoding codes in the rank metric and its cryptography applications. Probl. Inf. Trans. 38(3), 237–246 (2002)
Overbeck, R.: Structural attacks for public key cryptosystems based on Gabidulin codes. J. Cryptology 21(2), 280–301 (2008)
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Lau, T.S.C., Tan, C.H. (2018). Key Recovery Attack on McNie Based on Low Rank Parity Check Codes and Its Reparation. In: Inomata, A., Yasuda, K. (eds) Advances in Information and Computer Security. IWSEC 2018. Lecture Notes in Computer Science(), vol 11049. Springer, Cham. https://doi.org/10.1007/978-3-319-97916-8_2
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DOI: https://doi.org/10.1007/978-3-319-97916-8_2
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