Abstract
We discuss side-channel attacks on CRT-RSA encryption or signature scheme (the RSA scheme with the Chinese remainder theorem) implemented via the sliding window method. The sliding window method calculates exponentiations through repeated squaring and multiplication. These square-and-multiply sequences can be obtained by side-channel attacks, and there is the risk of recovering CRT-RSA secret keys from these sequences. Especially, in CHES 2017, it is proved that we can recover secret keys from the correct square-and-multiply sequences in polynomial time when the window size w is less than 4. However, there are errors in the obtained sequences. Oonishi and Kunihiro proposed a method for recovering secret keys from noisy sequences when \(w=1\). Although this work only addresses the case with \(w=1\), it should be possible to recover secret keys for larger values of w. In this paper, we propose a new method for recovering secret keys from noisy sequences in the sliding window method. Moreover, we clarify the amount of errors for which our method works.
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Acknowledgements
The first author is supported by a JSPS Fellowship for Young Scientists. This research was partially supported by JSPS Grant-in-Aid for JSPS Fellows 20J11754 and JST CREST Grant Number JPMJCR14D6, Japan.
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Oonishi, K., Kunihiro, N. (2020). Recovering CRT-RSA Secret Keys from Noisy Square-and-Multiply Sequences in the Sliding Window Method. In: Liu, J., Cui, H. (eds) Information Security and Privacy. ACISP 2020. Lecture Notes in Computer Science(), vol 12248. Springer, Cham. https://doi.org/10.1007/978-3-030-55304-3_34
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