Abstract
HQC (Hamming Quasi-Cyclic) cryptosystem, proposed by Aguilar Melchor et al., is a code-based key encapsulation mechanism (KEM) running for standardization to NIST’s competition in the category “post-quantum public key encryption scheme”. The underlying hard mathematical problem of HQC is presented as the s-DQCSD (Decision Quasi-Cyclic Syndrome Decoding) problem, which refers to the question of distinguishing whether a given instance came from the s-QCSD distribution or the uniform distribution. Under the assumption that 2-DQCSD and 3-DQCSD are hard, HQC, viewed as a PKE scheme, is proven to be IND-CPA secure, and can be transformed into an IND-CCA2 secure KEM. However, in this paper, we are going to show that s-DQCSD problem is actually not intractable. More precisely, we can efficiently distinguish the s-QCSD distribution instances from the uniform distribution instances with at least a constant advantage. Furthermore, with a similar technique, we show that HQC can not attain IND-CPA security with all the proposed parameter sets.
This work was supported in part by the NNSF of China (No. 61572490, and No. 11471314), the National Center for Mathematics and Interdisciplinary Sciences, CAS.
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
Aguilar, C., et al.: HQC Submission (2017). https://csrc.nist.gov/Projects/Post-Quantum-Cryptography/Round-1-Submissions
Aguilar, C., Blazy, O., Deneuville, J.C., Gaborit, P., Zémor, G.: Efficient encryption from random quasi-cyclic codes. arXiv preprint arXiv:1612.05572 (2016)
Chen, L., Jordan, S., et al.: Report on post-quantum cryptography (2016). http://nvlpubs.nist.gov/nistpubs/ir/2016/NIST.IR.8105.pdf
Dennis Hofheinz, K.H., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. Cryptology ePrint Archive Report 2017/604 (2017)
Katz, J., Lindell, Y.: Introduction to Modern Cryptography. Chapman & Hall/CRC, Boca Raton (2007)
Lin, S., Costello, D.J.: Error control coding. Princ. Mob. Commun. 44(2), 607–610 (1983)
Mceliece, R.J.: A public-key cryptosystem based on algebraic coding theory. Coding Thv 4244, 114–116 (1978)
Misoczki, R., Tillich, J.P., Sendrier, N., Barreto, P.S.L.M.: MDPC-McEliece: new McEliece variants from moderate density parity-check codes. In: IEEE International Symposium on Information Theory Proceedings, pp. 2069–2073 (2013)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: 37th STOC, pp. 84–93 (2005)
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 1994 Proceedings of 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Acknowledgments
We very thank the anonymous referees for their valuable suggestions on how to improve the presentation of this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Liu, Z., Pan, Y., Xie, T. (2018). Breaking the Hardness Assumption and IND-CPA Security of HQC Submitted to NIST PQC Project. In: Camenisch, J., Papadimitratos, P. (eds) Cryptology and Network Security. CANS 2018. Lecture Notes in Computer Science(), vol 11124. Springer, Cham. https://doi.org/10.1007/978-3-030-00434-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-00434-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00433-0
Online ISBN: 978-3-030-00434-7
eBook Packages: Computer ScienceComputer Science (R0)