Paper 2022/707

Efficiently Masking Polynomial Inversion at Arbitrary Order

Markus Krausz, Ruhr University Bochum
Georg Land, Ruhr University Bochum, German Research Centre for Artificial Intelligence
Jan Richter-Brockmann, Ruhr University Bochum
Tim Güneysu, Ruhr University Bochum, German Research Centre for Artificial Intelligence

Physical side-channel analysis poses a huge threat to post-quantum cryptographic schemes implemented on embedded devices. Still, secure implementations are missing for many schemes. In this paper, we present an efficient solution for masked polynomial inversion, a main component of the key generation of multiple post-quantum KEMs. For this, we introduce a polynomial-multiplicative masking scheme with efficient arbitrary order conversions from and to additive masking. Furthermore, we show how to integrate polynomial inversion and multiplication into the masking schemes to reduce costs considerably. We demonstrate the performance of our algorithms for two different post-quantum cryptographic schemes on the Cortex-M4. For NTRU, we measure an overhead of 35% for the first-order masked inversion compared to the unmasked inversion while for BIKE the overhead is as little as 11%. Lastly, we verify the security of our algorithms for the first masking order by measuring and performing a TVLA based side-channel analysis.

Available format(s)
Publication info
PQC Masking Polynomial Inversion Higher-order Masking
Contact author(s)
markus krausz @ rub de
georg land @ rub de
jan richter-brockmann @ rub de
tim gueneysu @ rub de
2022-06-06: approved
2022-06-03: received
See all versions
Short URL
No rights reserved


      author = {Markus Krausz and Georg Land and Jan Richter-Brockmann and Tim Güneysu},
      title = {Efficiently Masking Polynomial Inversion at Arbitrary Order},
      howpublished = {Cryptology ePrint Archive, Paper 2022/707},
      year = {2022},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.