MNT curves security level in PBC

[tha061]

Hi everyone,

Could anyone please let me know what is the security level of MNT curves mentioned in this: https://github.com/JHUISI/charm/blob/bbb7e62c8f79549e8d843dafa09802caefcf2e89/charm/toolbox/pairingcurves.py

I found that MNT159 supports an 80-bit security level claimed in few papers. However, I can't find any reference to this information as well as other curves like MNT224, MNT201.

Thank you for your help.

[flagUpDown]

According to [1], these four curves (SS512, MNT159, MNT201, MNT224) provide security levels of 80-bit, 80-bit, 100-bit, and 112-bit, respectively. But the expression of the security level of the same curve is inconsistent in different papers.
In addition, I can't find any reference to this information as well as other curves like SS1024. I hope the official can add a table to explain the security level of all curves.

[1] H. Cui, Z. Wan, R. H. Deng, G. Wang and Y. Li, "Efficient and Expressive Keyword Search Over Encrypted Data in Cloud," in IEEE Transactions on Dependable and Secure Computing, vol. 15, no. 3, pp. 409-422, 1 May-June 2018, doi: 10.1109/TDSC.2016.2599883.