Abstract
Recently, Chen et al. proposed a framework for authenticated key exchange (AKE) protocols (referred to as CMYSG scheme) in Designs, Codes and Cryptography (available at http://link.springer.com/article/10.1007/s10623-016-0295-3). It is claimed that the proposed AKE protocol is secure in a new leakage-resilient eCK model w.r.t. auxiliary inputs (AI-LR-eCK). The main tool used for the generic construction is the smooth projective hash function (SPHF). In this note, we revisit the CMYSG scheme and point out a subtle flaw in the original security proof. Precisely, we show that the AI-LR-eCK security of the proposed construction cannot be successfully reduced to a pseudo-random SPHF and thus the CMYSG scheme is not secure as claimed. To restore the security proof, we replace the underlying typical SPHF with a 2-smooth SPHF, and show that such a replacement combined with a \(\pi \hbox {PRF}\) suffices to overcome the subtle flaw.
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References
Chen R., Mu Y., Yang G., Susilo W., Guo F.: Strong authenticated key exchange with auxiliary input. Des. Codes Cryptogr. 1–29 (2016). doi:10.1007/s10623-016-0295-3.
Chen R., Mu Y., Yang G., Susilo W., Guo F.: Strongly leakage-resilient authenticated key exchange. In: CT-RSA, pp. 19–36 (2016).
Chen R., Mu Y., Yang G., Susilo W., Guo F.: Strong authenticated key exchange with auxiliary inputs. Cryptology ePrint Archive, Report 2017/418. http://eprint.iacr.org/2017/418 (2017).
Okamoto T.: Authenticated key exchange and key encapsulation in the standard model. In: ASIACRYPT, pp. 474–484 (2007).
Acknowledgements
We would like to thank Colin Boyd for his helpful suggestions in improving this note.
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Communicated by C. Boyd.
The paper titled “Strong Authenticated Key Exchange with Auxiliary Inputs” has been published in the Designs, Codes and Cryptography (available at http://link.springer.com/article/10.1007/s10623-016-0295-3). This note is mainly to point out a subtle flaw in the original security proof, and provide a fixing solution to restore the security proof.
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Chen, R., Mu, Y., Yang, G. et al. A note on the strong authenticated key exchange with auxiliary inputs. Des. Codes Cryptogr. 85, 175–178 (2017). https://doi.org/10.1007/s10623-017-0386-9
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DOI: https://doi.org/10.1007/s10623-017-0386-9