Abstract
We present an optimized, constant-time software library for commutative supersingular isogeny Diffie-Hellman key exchange (CSIDH) proposed by Castryck et al. which targets 64-bit ARM processors. The proposed library is implemented based on highly-optimized field arithmetic operations and computes the entire key exchange in constant-time. The proposed implementation is resistant to timing attacks. We adopt optimization techniques to evaluate the highest performance CSIDH on ARM-powered embedded devices such as cellphones, analyzing the possibility of using such a scheme in the quantum era. To the best of our knowledge, the proposed implementation is the first constant-time implementation of CSIDH and the first evaluation of this scheme on embedded devices. The benchmark result on a Google Pixel 2 smartphone equipped with 64-bit high-performance ARM Cortex-A72 core shows that it takes almost 12 s for each party to compute a commutative action operation in constant-time over the 511-bit finite field proposed by Castryck et al. However, using uniform but variable-time Montgomery ladder with security considerations improves these results significantly.
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- 1.
M and S stand for field multiplication and field squaring, respectively.
- 2.
The optimal value for k is directly related to the prime and the trade-off between memory usage and performance.
- 3.
Our library is publicly available at: https://github.com/amirjalali65/ARMv8-CSIDH.
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Acknowledgment
This work is supported in parts by NSF CNS-1801341, NIST-60NANB17D184, NIST-60NANB16D246, and ARO W911NF-17-1-0311, as well as NSERC, CryptoWorks21, Public Works and Government Services Canada, Canada First Research Excellence Fund, and the Royal Bank of Canada.
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Jalali, A., Azarderakhsh, R., Kermani, M.M., Jao, D. (2019). Towards Optimized and Constant-Time CSIDH on Embedded Devices. In: Polian, I., Stöttinger, M. (eds) Constructive Side-Channel Analysis and Secure Design. COSADE 2019. Lecture Notes in Computer Science(), vol 11421. Springer, Cham. https://doi.org/10.1007/978-3-030-16350-1_12
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