---
_id: '14457'
abstract:
- lang: eng
  text: "Threshold secret sharing allows a dealer to split a secret s into n shares,
    such that any t shares allow for reconstructing s, but no t-1 shares reveal any
    information about s. Leakage-resilient secret sharing requires that the secret
    remains hidden, even when an adversary additionally obtains a limited amount of
    leakage from every share. Benhamouda et al. (CRYPTO’18) proved that Shamir’s secret
    sharing scheme is one bit leakage-resilient for reconstruction threshold t≥0.85n
    and conjectured that the same holds for t = c.n for any constant 0≤c≤1.  Nielsen
    and Simkin (EUROCRYPT’20) showed that this is the best one can hope for by proving
    that Shamir’s scheme is not secure against one-bit leakage when t0c.n/log(n).\r\nIn
    this work, we strengthen the lower bound of Nielsen and Simkin. We consider noisy
    leakage-resilience, where a random subset of leakages is replaced by uniformly
    random noise. We prove a lower bound for Shamir’s secret sharing, similar to that
    of Nielsen and Simkin, which holds even when a constant fraction of leakages is
    replaced by random noise. To this end, we first prove a lower bound on the share
    size of any noisy-leakage-resilient sharing scheme. We then use this lower bound
    to show that there exist universal constants c1, c2,  such that for sufficiently
    large n it holds that Shamir’s secret sharing scheme is not noisy-leakage-resilient
    for t≤c1.n/log(n), even when a c2 fraction of leakages are replaced by random
    noise.\r\n\r\n\r\n\r\n"
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Charlotte
  full_name: Hoffmann, Charlotte
  id: 0f78d746-dc7d-11ea-9b2f-83f92091afe7
  last_name: Hoffmann
  orcid: 0000-0003-2027-5549
- first_name: Mark
  full_name: Simkin, Mark
  last_name: Simkin
citation:
  ama: 'Hoffmann C, Simkin M. Stronger lower bounds for leakage-resilient secret sharing.
    In: <i>8th International Conference on Cryptology and Information Security in
    Latin America</i>. Vol 14168. Springer Nature; 2023:215-228. doi:<a href="https://doi.org/10.1007/978-3-031-44469-2_11">10.1007/978-3-031-44469-2_11</a>'
  apa: 'Hoffmann, C., &#38; Simkin, M. (2023). Stronger lower bounds for leakage-resilient
    secret sharing. In <i>8th International Conference on Cryptology and Information
    Security in Latin America</i> (Vol. 14168, pp. 215–228). Quito, Ecuador: Springer
    Nature. <a href="https://doi.org/10.1007/978-3-031-44469-2_11">https://doi.org/10.1007/978-3-031-44469-2_11</a>'
  chicago: Hoffmann, Charlotte, and Mark Simkin. “Stronger Lower Bounds for Leakage-Resilient
    Secret Sharing.” In <i>8th International Conference on Cryptology and Information
    Security in Latin America</i>, 14168:215–28. Springer Nature, 2023. <a href="https://doi.org/10.1007/978-3-031-44469-2_11">https://doi.org/10.1007/978-3-031-44469-2_11</a>.
  ieee: C. Hoffmann and M. Simkin, “Stronger lower bounds for leakage-resilient secret
    sharing,” in <i>8th International Conference on Cryptology and Information Security
    in Latin America</i>, Quito, Ecuador, 2023, vol. 14168, pp. 215–228.
  ista: 'Hoffmann C, Simkin M. 2023. Stronger lower bounds for leakage-resilient secret
    sharing. 8th International Conference on Cryptology and Information Security in
    Latin America. LATINCRYPT: Conference on Cryptology and Information Security in
    Latin America, LNCS, vol. 14168, 215–228.'
  mla: Hoffmann, Charlotte, and Mark Simkin. “Stronger Lower Bounds for Leakage-Resilient
    Secret Sharing.” <i>8th International Conference on Cryptology and Information
    Security in Latin America</i>, vol. 14168, Springer Nature, 2023, pp. 215–28,
    doi:<a href="https://doi.org/10.1007/978-3-031-44469-2_11">10.1007/978-3-031-44469-2_11</a>.
  short: C. Hoffmann, M. Simkin, in:, 8th International Conference on Cryptology and
    Information Security in Latin America, Springer Nature, 2023, pp. 215–228.
conference:
  end_date: 2023-10-06
  location: Quito, Ecuador
  name: 'LATINCRYPT: Conference on Cryptology and Information Security in Latin America'
  start_date: 2023-10-03
date_created: 2023-10-29T23:01:16Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2023-10-31T11:43:12Z
day: '01'
department:
- _id: KrPi
doi: 10.1007/978-3-031-44469-2_11
intvolume: '     14168'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://eprint.iacr.org/2023/1017
month: '10'
oa: 1
oa_version: Preprint
page: 215-228
publication: 8th International Conference on Cryptology and Information Security in
  Latin America
publication_identifier:
  eissn:
  - 1611-3349
  isbn:
  - '9783031444685'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stronger lower bounds for leakage-resilient secret sharing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14168
year: '2023'
...