{"scopus_import":"1","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-10-29T23:01:16Z","oa_version":"Preprint","oa":1,"alternative_title":["LNCS"],"status":"public","title":"Stronger lower bounds for leakage-resilient secret sharing","quality_controlled":"1","date_updated":"2023-10-31T11:43:12Z","month":"10","article_processing_charge":"No","day":"01","type":"conference","abstract":[{"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","lang":"eng"}],"main_file_link":[{"url":"https://eprint.iacr.org/2023/1017","open_access":"1"}],"department":[{"_id":"KrPi"}],"date_published":"2023-10-01T00:00:00Z","publication_status":"published","year":"2023","volume":14168,"intvolume":"     14168","publication_identifier":{"isbn":["9783031444685"],"eissn":["1611-3349"],"issn":["0302-9743"]},"author":[{"first_name":"Charlotte","last_name":"Hoffmann","id":"0f78d746-dc7d-11ea-9b2f-83f92091afe7","full_name":"Hoffmann, Charlotte","orcid":"0000-0003-2027-5549"},{"full_name":"Simkin, Mark","first_name":"Mark","last_name":"Simkin"}],"publication":"8th International Conference on Cryptology and Information Security in Latin America","page":"215-228","doi":"10.1007/978-3-031-44469-2_11","_id":"14457","language":[{"iso":"eng"}],"citation":{"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.","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.","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>.","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.","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>","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>"},"conference":{"location":"Quito, Ecuador","end_date":"2023-10-06","name":"LATINCRYPT: Conference on Cryptology and Information Security in Latin America","start_date":"2023-10-03"}}