Pairing Optimizations for Isogeny-Based Cryptosystems
In isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing computations is unsatisfactory due to the hig...
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| Format: | Article |
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Wiley
2024-01-01
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| Series: | IET Information Security |
| Online Access: | http://dx.doi.org/10.1049/2024/9631360 |
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| author | Shiping Cai Kaizhan Lin Chang-An Zhao |
| author_facet | Shiping Cai Kaizhan Lin Chang-An Zhao |
| author_sort | Shiping Cai |
| collection | DOAJ |
| description | In isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function. Reducing the computational expense of the Miller function is crucial for enhancing the overall performance of pairing computations in isogeny-based cryptography. This paper addresses this efficiency bottleneck. To achieve this, we propose several techniques for a better implementation of pairings in isogeny-based cryptosystems. We use (modified) Jacobian coordinates and present new algorithms for Miller function computations to compute pairings of order 2∙ and 3∙. For pairings of arbitrary order, which are crucial for key compression in some SIDH-based schemes (such as M-SIDH and binSIDH), we combine Miller doublings with Miller additions/subtractions, leading to a considerable speedup. Moreover, the optimizations for pairing applications in CSIDH-based protocols are also considered in this paper. In particular, our approach for supersingularity verification in CSIDH is 15.3% faster than Doliskani’s test, which is the state-of-the-art. |
| format | Article |
| id | doaj-art-83484ecb4c654e178274487a1cbcc586 |
| institution | Kabale University |
| issn | 1751-8717 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Information Security |
| spelling | doaj-art-83484ecb4c654e178274487a1cbcc5862025-02-02T23:18:51ZengWileyIET Information Security1751-87172024-01-01202410.1049/2024/9631360Pairing Optimizations for Isogeny-Based CryptosystemsShiping Cai0Kaizhan Lin1Chang-An Zhao2School of MathematicsSchool of MathematicsSchool of MathematicsIn isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function. Reducing the computational expense of the Miller function is crucial for enhancing the overall performance of pairing computations in isogeny-based cryptography. This paper addresses this efficiency bottleneck. To achieve this, we propose several techniques for a better implementation of pairings in isogeny-based cryptosystems. We use (modified) Jacobian coordinates and present new algorithms for Miller function computations to compute pairings of order 2∙ and 3∙. For pairings of arbitrary order, which are crucial for key compression in some SIDH-based schemes (such as M-SIDH and binSIDH), we combine Miller doublings with Miller additions/subtractions, leading to a considerable speedup. Moreover, the optimizations for pairing applications in CSIDH-based protocols are also considered in this paper. In particular, our approach for supersingularity verification in CSIDH is 15.3% faster than Doliskani’s test, which is the state-of-the-art.http://dx.doi.org/10.1049/2024/9631360 |
| spellingShingle | Shiping Cai Kaizhan Lin Chang-An Zhao Pairing Optimizations for Isogeny-Based Cryptosystems IET Information Security |
| title | Pairing Optimizations for Isogeny-Based Cryptosystems |
| title_full | Pairing Optimizations for Isogeny-Based Cryptosystems |
| title_fullStr | Pairing Optimizations for Isogeny-Based Cryptosystems |
| title_full_unstemmed | Pairing Optimizations for Isogeny-Based Cryptosystems |
| title_short | Pairing Optimizations for Isogeny-Based Cryptosystems |
| title_sort | pairing optimizations for isogeny based cryptosystems |
| url | http://dx.doi.org/10.1049/2024/9631360 |
| work_keys_str_mv | AT shipingcai pairingoptimizationsforisogenybasedcryptosystems AT kaizhanlin pairingoptimizationsforisogenybasedcryptosystems AT changanzhao pairingoptimizationsforisogenybasedcryptosystems |