Protecting the Most Significant Bits in Scalar Multiplication Algorithms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00129801" target="_blank" >RIV/00216224:14330/22:00129801 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-031-22829-2_7" target="_blank" >http://dx.doi.org/10.1007/978-3-031-22829-2_7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-22829-2_7" target="_blank" >10.1007/978-3-031-22829-2_7</a>
Alternative languages
Result language
angličtina
Original language name
Protecting the Most Significant Bits in Scalar Multiplication Algorithms
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/VJ02010010" target="_blank" >VJ02010010: Tools for AI-enhanced Security Verification of Cryptographic Devices</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
12th International Conference on Security, Privacy, and Applied Cryptography Engineering, SPACE 2022
ISBN
9783031228285
ISSN
0302-9743
e-ISSN
—
Number of pages
20
Pages from-to
118-137
Publisher name
Springer
Place of publication
Jaipur
Event location
Jaipur
Event date
Jan 1, 2022
Type of event by nationality
CST - Celostátní akce
UT code for WoS article
000927578200007