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@inproceedings{2273651,
author = {Bock, Estuardo Alpirez and Chmielewski, Lukasz Michal and Miteloudi, Konstantina},
address = {Jaipur},
booktitle = {12th International Conference on Security, Privacy, and Applied Cryptography Engineering, SPACE 2022},
doi = {http://dx.doi.org/10.1007/978-3-031-22829-2_7},
keywords = {ECC; Montgomery Ladder; Curve25519; Complete addition formulas; Side-channel analysis},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Jaipur},
isbn = {978-3-031-22828-5},
pages = {118-137},
publisher = {Springer},
title = {Protecting the Most Significant Bits in Scalar Multiplication Algorithms},
year = {2022}
}
TY - JOUR
ID - 2273651
AU - Bock, Estuardo Alpirez - Chmielewski, Lukasz Michal - Miteloudi, Konstantina
PY - 2022
TI - Protecting the Most Significant Bits in Scalar Multiplication Algorithms
PB - Springer
CY - Jaipur
SN - 9783031228285
KW - ECC
KW - Montgomery Ladder
KW - Curve25519
KW - Complete addition formulas
KW - Side-channel analysis
N2 - The Montgomery Ladder is widely used for implementing the scalar multiplication in elliptic curve cryptographic designs. This algorithm is efficient and provides a natural robustness against (simple) side-channel attacks. Previous works however showed that implementations of the Montgomery Ladder using Lopez-Dahab projective coordinates easily leak the value of the most significant bits of the secret scalar, which led to a full key recovery in an attack known as LadderLeak [3]. In light of such leakage, we analyse further popular methods for implementing the Montgomery Ladder. We first consider open source software implementations of the X25519 protocol which implement the Montgomery Ladder based on the ladderstep algorithm from Dull et al. [15]. We confirm via power measurements that these implementations also easily leak the most significant scalar bits, even when implementing Z-coordinate randomisations. We thus propose simple modifications of the algorithm and its handling of the most significant bits and show the effectiveness of our modifications via experimental results. Particularly, our re-designs of the algorithm do not incurring significant efficiency penalties. As a second case study, we consider open source hardware implementations of the Montgomery Ladder based on the complete addition formulas for prime order elliptic curves, where we observe the exact same leakage. As we explain, the most significant bits in implementations of the complete addition formulas can be protected in an analogous way as we do for Curve25519 in our first case study.
ER -
BOCK, Estuardo Alpirez, Lukasz Michal CHMIELEWSKI a Konstantina MITELOUDI. Protecting the Most Significant Bits in Scalar Multiplication Algorithms. In \textit{12th International Conference on Security, Privacy, and Applied Cryptography Engineering, SPACE 2022}. Jaipur: Springer, 2022, s.~118-137. ISBN~978-3-031-22828-5. Dostupné z: https://dx.doi.org/10.1007/978-3-031-22829-2\_{}7.
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