TY - GEN
T1 - Constructing Leakage-Resilient Shamir’s Secret Sharing
T2 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024
AU - Maji, Hemanta K.
AU - Nguyen, Hai H.
AU - Paskin-Cherniavsky, Anat
AU - Ye, Xiuyu
N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - Probing physical bits in hardware has compromised cryptographic systems. This work investigates how to instantiate Shamir’s secret sharing so that the physical probes into its shares reveal statistically insignificant information about the secret. Over prime fields, Maji, Nguyen, Paskin-Cherniavsky, Suad, and Wang (EUROCRYPT 2021) proved that choosing random evaluation places achieves this objective with high probability. Our work extends their randomized construction to composite order fields – particularly for fields with characteristic 2. Next, this work presents an algorithm to classify evaluation places as secure or vulnerable against physical-bit probes for some specific cases. Our security analysis of the randomized construction is Fourier-analytic, and the classification techniques are combinatorial. Our analysis relies on (1) contemporary Bézout-theorem-type algebraic complexity results that bound the number of simultaneous zeroes of a system of polynomial equations over composite order fields and (2) characterization of the zeroes of an appropriate generalized Vandermonde determinant.
AB - Probing physical bits in hardware has compromised cryptographic systems. This work investigates how to instantiate Shamir’s secret sharing so that the physical probes into its shares reveal statistically insignificant information about the secret. Over prime fields, Maji, Nguyen, Paskin-Cherniavsky, Suad, and Wang (EUROCRYPT 2021) proved that choosing random evaluation places achieves this objective with high probability. Our work extends their randomized construction to composite order fields – particularly for fields with characteristic 2. Next, this work presents an algorithm to classify evaluation places as secure or vulnerable against physical-bit probes for some specific cases. Our security analysis of the randomized construction is Fourier-analytic, and the classification techniques are combinatorial. Our analysis relies on (1) contemporary Bézout-theorem-type algebraic complexity results that bound the number of simultaneous zeroes of a system of polynomial equations over composite order fields and (2) characterization of the zeroes of an appropriate generalized Vandermonde determinant.
UR - http://www.scopus.com/inward/record.url?scp=85192844534&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-031-58737-5_11
DO - https://doi.org/10.1007/978-3-031-58737-5_11
M3 - منشور من مؤتمر
SN - 9783031587368
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 286
EP - 315
BT - Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
A2 - Joye, Marc
A2 - Leander, Gregor
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 26 May 2024 through 30 May 2024
ER -