Compressed M-SIDH: an instance of compressed SIDH-like schemes with isogenies of highly composite degrees

Lin, Kaizhan; Lin, Jianming; Cai, Shiping; Wang, Weize; Zhao, Chang-An

doi:10.1007/s10623-024-01368-z

Des. Codes Cryptogr.

2024

DOI: 10.1007/s10623-024-01368-z

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Compressed M-SIDH: an instance of compressed SIDH-like schemes with isogenies of highly composite degrees

Kaizhan Lin,

Jianming Lin,

Shiping Cai

et al.

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Pairing Optimizations for Isogeny‐Based Cryptosystems

Cai,

Lin,

Zhao

2024

IET Information Security

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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.

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Pairing Optimizations for Isogeny‐Based Cryptosystems

Cai,

Lin,

Zhao

2024

IET Information Security

View full text Add to dashboard Cite

show abstract

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Compressed M-SIDH: an instance of compressed SIDH-like schemes with isogenies of highly composite degrees

Cited by 1 publication

References 30 publications

Pairing Optimizations for Isogeny‐Based Cryptosystems

Pairing Optimizations for Isogeny‐Based Cryptosystems

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