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Lecture notes in computer science

Order-LWE and the Hardness of Ring-LWE with Entropic Secrets

Madalina Bolboceanu, Zvika Brakerski, Renen Perlman, Devika Sharma

Published Jan 1, 2019• 33 citations
Publisher
DOI
10.1007/978-3-030-34621-8_4

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(In)Security of Ring-LWE Under Partial Key Exposure

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Abstract We initiate the study of partial key exposure in Ring-LWE (RLWE)-based cryptosystems. Specifically, we (1) Introduce the search and decision Leaky R-LWE assumptions (Leaky R-SLWE, Leaky R-DLWE), to formalize the hardness of search/decision RLWE under leakage of some fraction of coordinates of the NTT transform of the RLWE secret. (2) Present and implement an efficient key exposure attack that, given certain 1/4-fraction of the coordinates of the NTT transform of the RLWE secret, along with samples from the RLWE distribution, recovers the full RLWE secret for standard parameter settings. (3) Present a search-to-decision reduction for Leaky R-LWE for certain types of key exposure. (4) Propose applications to the security analysis of RLWE-based cryptosystems under partial key exposure.

Journal of Mathematical Cryptology•Nov 17, 2020•4 citations
Abstract We initiate the study of partial key exposure in Ring-LWE (RLWE)-based cryptosystems. Specifically, we (1) Introduce the search and decision Leaky R-LWE assumptions (Leaky R-SLWE, Leaky R-DLWE), to formalize the hardness of search/decision RLWE under leakage of some fraction of coordinates of the NTT transform of the RLWE secret. (2) Present and implement an efficient key exposure attack that, given certain 1/4-fraction of the coordinates of the NTT transform of the RLWE secret, along with samples from the RLWE distribution, recovers the full RLWE secret for standard parameter settings. (3) Present a search-to-decision reduction for Leaky R-LWE for certain types of key exposure. (4) Propose applications to the security analysis of RLWE-based cryptosystems under partial key exposure.