Performance and Efficiency Evaluation of M-SIDH
As the recent Castryck-Decru attack recovers the private key of SIDH in polynomial time, various methods have been proposed to prevent the attack. Among these, M-SIDH, proposed by Fouotsa et al., counters the Castryck-Decru attack by masking the torsion-point information transmitted during the key e...
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10786215/ |
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| author | Suhri Kim |
| author_facet | Suhri Kim |
| author_sort | Suhri Kim |
| collection | DOAJ |
| description | As the recent Castryck-Decru attack recovers the private key of SIDH in polynomial time, various methods have been proposed to prevent the attack. Among these, M-SIDH, proposed by Fouotsa et al., counters the Castryck-Decru attack by masking the torsion-point information transmitted during the key exchange process. In this paper, we implement M-SIDH and examine its performance. To the best of our knowledge, this is the first C language implementation of M-SIDH. In this regard, we propose a method for selecting parameters for M-SIDH and introduce a 2048-bit and a 4096-bit prime for the implementation, targeting the 48-bit and 94-bit classical security levels, respectively. We also optimize the square-root Velu formula in the context of SIDH. The original square-root Velu formula has been used in CSIDH-based systems, where an evaluation of a single point only needs to be performed. In this paper, we suggest an optimal method to use the square-root Velu formula in the SIDH environment, which requires multiple isogeny evaluations. Our implementation results show that MSIDH-2048 and MSIDH-4096 take 16.20s and 190.45s, respectively. |
| format | Article |
| id | doaj-art-a1546e32c3844e7e959342df6a27320b |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-a1546e32c3844e7e959342df6a27320b2024-12-20T00:01:40ZengIEEEIEEE Access2169-35362024-01-011218568618569410.1109/ACCESS.2024.351340510786215Performance and Efficiency Evaluation of M-SIDHSuhri Kim0https://orcid.org/0000-0003-2665-7142School of Mathematics, Statistics and Data Science, Sungshin Women’s University, Seoul, South KoreaAs the recent Castryck-Decru attack recovers the private key of SIDH in polynomial time, various methods have been proposed to prevent the attack. Among these, M-SIDH, proposed by Fouotsa et al., counters the Castryck-Decru attack by masking the torsion-point information transmitted during the key exchange process. In this paper, we implement M-SIDH and examine its performance. To the best of our knowledge, this is the first C language implementation of M-SIDH. In this regard, we propose a method for selecting parameters for M-SIDH and introduce a 2048-bit and a 4096-bit prime for the implementation, targeting the 48-bit and 94-bit classical security levels, respectively. We also optimize the square-root Velu formula in the context of SIDH. The original square-root Velu formula has been used in CSIDH-based systems, where an evaluation of a single point only needs to be performed. In this paper, we suggest an optimal method to use the square-root Velu formula in the SIDH environment, which requires multiple isogeny evaluations. Our implementation results show that MSIDH-2048 and MSIDH-4096 take 16.20s and 190.45s, respectively.https://ieeexplore.ieee.org/document/10786215/Isogenypost-quantum cryptographySIDHCastryck-Decru attackM-SIDH |
| spellingShingle | Suhri Kim Performance and Efficiency Evaluation of M-SIDH IEEE Access Isogeny post-quantum cryptography SIDH Castryck-Decru attack M-SIDH |
| title | Performance and Efficiency Evaluation of M-SIDH |
| title_full | Performance and Efficiency Evaluation of M-SIDH |
| title_fullStr | Performance and Efficiency Evaluation of M-SIDH |
| title_full_unstemmed | Performance and Efficiency Evaluation of M-SIDH |
| title_short | Performance and Efficiency Evaluation of M-SIDH |
| title_sort | performance and efficiency evaluation of m sidh |
| topic | Isogeny post-quantum cryptography SIDH Castryck-Decru attack M-SIDH |
| url | https://ieeexplore.ieee.org/document/10786215/ |
| work_keys_str_mv | AT suhrikim performanceandefficiencyevaluationofmsidh |