TY - GEN
T1 - Lossiness and entropic hardness for ring-LWE
AU - Brakerski, Zvika
AU - Döttling, Nico
N1 - Z. Brakerski—Supported by the Binational Science Foundation (Grant No. 2016726), and by the European Union Horizon 2020 Research and Innovation Program via ERC Project REACT (Grant 756482) and via Project PROMETHEUS (Grant 780701). N. Döttling—This work is partially funded by the Helmholtz Association within the project “Trustworthy Federated Data Analytics” (TFDA) (funding number ZT-I-OO1 4). Publisher Copyright: © International Association for Cryptologic Research 2020.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - The hardness of the Ring Learning with Errors problem (RLWE) is a central building block for efficiency-oriented lattice-based cryptography. Many applications use an “entropic” variant of the problem where the so-called “secret” is not distributed uniformly as prescribed but instead comes from some distribution with sufficient min-entropy. However, the hardness of the entropic variant has not been substantiated thus far. For standard LWE (not over rings) entropic results are known, using a “lossiness approach” but it was not known how to adapt this approach to the ring setting. In this work we present the first such results, where entropic security is established either under RLWE or under the Decisional Small Polynomial Ratio (DSPR) assumption which is a mild variant of the NTRU assumption. In the context of general entropic distributions, our results in the ring setting essentially match the known lower bounds (Bolboceanu et al., Asiacrypt 2019; Brakerski and Döttling, Eurocrypt 2020).
AB - The hardness of the Ring Learning with Errors problem (RLWE) is a central building block for efficiency-oriented lattice-based cryptography. Many applications use an “entropic” variant of the problem where the so-called “secret” is not distributed uniformly as prescribed but instead comes from some distribution with sufficient min-entropy. However, the hardness of the entropic variant has not been substantiated thus far. For standard LWE (not over rings) entropic results are known, using a “lossiness approach” but it was not known how to adapt this approach to the ring setting. In this work we present the first such results, where entropic security is established either under RLWE or under the Decisional Small Polynomial Ratio (DSPR) assumption which is a mild variant of the NTRU assumption. In the context of general entropic distributions, our results in the ring setting essentially match the known lower bounds (Bolboceanu et al., Asiacrypt 2019; Brakerski and Döttling, Eurocrypt 2020).
UR - https://www.scopus.com/pages/publications/85098244288
U2 - 10.1007/978-3-030-64375-1_1
DO - 10.1007/978-3-030-64375-1_1
M3 - Conference contribution
SN - 9783030643744
T3 - Lecture Notes in Computer Science
SP - 1
EP - 27
BT - Theory of Cryptography - 18th International Conference, TCC 2020, Proceedings
A2 - Pass, Rafael
A2 - Pietrzak, Krzysztof
PB - Springer Science and Business Media B.V.
T2 - 18th International Conference on Theory of Cryptography, TCCC 2020
Y2 - 16 November 2020 through 19 November 2020
ER -