SCIS 2022
2022 Symposium on
Cryptography and Information Security
Osaka, Japan & Online, Jan. 18 – 21, 2022
The Institute of Electronics,
Information and Communication Engineers

Copyright ©2022 The Institute of Electronics,
Information and Communication Engineers

Implementations on identity-based signature schemes based on
variants of CSIDH
Hyungrok Jo ∗Junji Shikata †Keywords:
post-quantum cryptography, isogeny-based cryptography, identity-based signaturescheme, CSIDH, CsiIBS, forward-secure signature

Abstract

curve isogenies,”, Journal of Mathematical Cryptology, 8(3), pp. 209-247, 2014.

Identity-based cryptography are one of main highfunctional applications for a modern society. The necessity for these proposals are enlarging especially as
growing the pie of IoT (Internet of Things) among
electronics industry. Recently, there are some suggestions of identity based identification schemes or signature schemes based on even isogeny walk problems,
which are known as one of promising candidates forpost-quantum cryptography (PQC for short).
In this paper, we measure the performances of two
identity-based signature schemes, which are recently
proposed by Peng et al. [8] CsiIBS (2020) and Shawand Dutta [9] (ProvSec2021), respectively. Especially,
since in Shaw and Dutta’s work, there are no implementation results, we try to measure the proper parameter sets of their schemes. We also consider the best
possibilities of each scheme by switching the underlying isogeny problems (CSIDH) to variants (CSURF)
of CSIDH or other isogeny problems such as endomorphism computation problem towards high efficiencies.

[4] Eisenträger, K., Hallgren, S., Lauter, K., Morrison,T., & Petit, C., “Supersingular isogeny graphs andendomorphism rings: reductions and solutions,”
In Annual International Conference on the Theoryand Applications of Cryptographic Techniques, pp.
329-368, Springer, Cham., 2018.
[5] Fan, X., Tian, S., Xu, X., & Li, B., “CSURF-TWO:CSIDH for the Ratio (2: 1),”, In International
Conference on Information Security and Cryptology, pp. 148-156, Springer, Cham., 2020.
[6] Galbraith, S. D., Petit, C., & Silva, J., “Identification protocols and signature schemes based onsupersingular isogeny problems,” In International
Conference on the Theory and Application of Cryptology and Information Security, pp. 3-33, Springer,Cham., 2017.
[7] Kim, S., “On the Use of Twisted Montgomery
Curves for CSIDH-Based Cryptography.” Journalof the Korea Institute of Information Security &Cryptology, 31(3), pp. 497-508, 2021.

References[1] Castryck, W., Lange, T., Martindale, C., Panny,L., & Renes, J., “CSIDH: an efficient postquantum commutative group action.” In International Conference on the Theory and Application ofCryptology and Information Security, pp. 395-427,Springer, Cham, 2018.

[8] Peng, C., Chen, J., Zhou, L., Choo, K. K. R., &He, D., “CsiIBS: A post-quantum identity-based
signature scheme based on isogenies,” Journal ofInformation Security and Applications, 54, 102504,2020.

[2] Castryck, W., & Decru, T., “CSIDH on thesurface.” In International Conference on PostQuantum Cryptography (PQCrypto 2020), Vol.
12100, pp. 111-129, Springer, 2020.

[9] Shaw, S., & Dutta, R., “Identification Scheme andForward-Secure Signature in Identity-Based Setting from Isogenies,” In International Conference
on Provable Security, pp. 309-326, Springer, Cham,2021.

[3] De Feo, L., Jao, D., & Plût, J.,“Towards quantumresistant cryptosystems from supersingular elliptic∗Yokohama National University, Institute of Advanced
Sciences,79-5 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa(jo-hyungrok-xz@ynu.ac.jp)† Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku,
Yokohama, Kanagawa (junji-shikata-rb@ynu.ac.jp)1