{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T16:07:07Z","timestamp":1750694827394,"version":"3.40.3"},"publisher-location":"Cham","reference-count":46,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031780226"},{"type":"electronic","value":"9783031780233"}],"license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-78023-3_19","type":"book-chapter","created":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T10:50:40Z","timestamp":1733136640000},"page":"581-613","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Secret-Sharing Schemes for\u00a0High Slices"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6572-4195","authenticated-orcid":false,"given":"Amos","family":"Beimel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7495-5980","authenticated-orcid":false,"given":"Oriol","family":"Farr\u00e0s","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7419-1454","authenticated-orcid":false,"given":"Or","family":"Lasri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7860-8151","authenticated-orcid":false,"given":"Oded","family":"Nir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"19_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/978-3-030-03807-6_12","volume-title":"Theory of Cryptography","author":"B Applebaum","year":"2018","unstructured":"Applebaum, B., Arkis, B.: On the power of amortization in secret sharing: d-Uniform Secret Sharing and CDS with Constant Information Rate. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 317\u2013344. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03807-6_12"},{"key":"19_CR2","doi-asserted-by":"crossref","unstructured":"Applebaum, B., Beimel, A., Farr\u00e0s, O., Nir, O., Peter, N.: Secret-sharing schemes for general and uniform access structures. In: EUROCRYPT 2019, vol. 11478. LNCS, pp. 441\u2013471 (2019)","DOI":"10.1007\/978-3-030-17659-4_15"},{"key":"19_CR3","doi-asserted-by":"crossref","unstructured":"Abram, D., Beimel, A., Ishai, Y., Kushilevitz, E., Narayanan, V.: Cryptography from planted graphs: Security with logarithmic-size messages. In: TCC 2023, vol. 14369. LNCS, pp. 286\u2013315 (2023)","DOI":"10.1007\/978-3-031-48615-9_11"},{"key":"19_CR4","first-page":"1553","volume":"2023","author":"B Applebaum","year":"2023","unstructured":"Applebaum, B., Beimel, A., Ishai, Y., Kushilevitz, E., Liu, T., Vaikuntanathan, V.: Succinct computational secret sharing. In: STOC 2023, 1553\u20131566 (2023)","journal-title":"Succinct computational secret sharing. In: STOC"},{"key":"19_CR5","unstructured":"Applebaum, B., Beimel, A., Nir, O., Peter, N., Pitassi, T.: Secret sharing, slice formulas, and monotone real circuits. In: ITCS 2022, vol. 215. LIPIcs, pp. 8:1\u20138:23 (2022)"},{"key":"19_CR6","doi-asserted-by":"crossref","unstructured":"Applebaum, B., Beimel, A., Nir, O., Peter, N.: Better secret sharing via robust conditional disclosure of secrets. In: STOC 2020, pp. 280\u2013293 (2020)","DOI":"10.1145\/3357713.3384293"},{"key":"19_CR7","doi-asserted-by":"crossref","unstructured":"Applebaum, B., Nir, O.: Upslices, downslices, and secret-sharing with complexity of 1.5$$ ^{\\text{n}}$$. In: CRYPTO 2021, vol. 12827. LNCS, pp. 627\u2013655 (2021)","DOI":"10.1007\/978-3-030-84252-9_21"},{"issue":"3","key":"19_CR8","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1109\/18.335890","volume":"40","author":"A Beimel","year":"1994","unstructured":"Beimel, A., Chor, B.: Universally ideal secret sharing schemes. IEEE Trans. Inf. Theory 40(3), 786\u2013794 (1994)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"19_CR9","doi-asserted-by":"crossref","unstructured":"Beimel, A.: Secret-sharing schemes: a survey. In: Coding and Cryptology \u2013 Third International Workshop, IWCC 2011, vol. 6639. LNCS, pp. 11\u201346 (2011)","DOI":"10.1007\/978-3-642-20901-7_2"},{"key":"19_CR10","unstructured":"Beimel, A.: Lower bounds for secret-sharing schemes for k-hypergraphs. In: ITC 2023, vol. 267. LIPIcs, pp. 16:1\u201316:13 (2023)"},{"key":"19_CR11","unstructured":"Berkowitz, S.: On some relationships between monotone and nonmonotone circuit complexity. Technical report, Department of Computer Science, University of Toronto (1982)"},{"key":"19_CR12","first-page":"664","volume":"2020","author":"A Beimel","year":"2020","unstructured":"Beimel, A., Farr\u00e0s, O.: The share size of secret-sharing schemes for almost all access structures and graphs. IACR Cryptol. ePrint Arch. 2020, 664 (2020)","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"19_CR13","doi-asserted-by":"crossref","unstructured":"Beimel, A., Farr\u00e0s, O.: The share size of secret-sharing schemes for almost all access structures and graphs. In: TCC 2020, vol. 12552. LNCS, pp. 499\u2013529 (2020)","DOI":"10.1007\/978-3-030-64381-2_18"},{"key":"19_CR14","unstructured":"Beimel, A., Farr\u00e0s, O., Lasri, O., Nir, O.: Secret-sharing schemes for high slices. Technical Report 2024\/602, IACR Cryptology ePrint Archive (2024)"},{"issue":"3","key":"19_CR15","first-page":"2083","volume":"68","author":"A Beimel","year":"2022","unstructured":"Beimel, A., Farr\u00e0s, O., Mintz, Y., Peter, N.: Linear secret-sharing schemes for forbidden graph access structures. IEEE-TIT 68(3), 2083\u20132100 (2022)","journal-title":"IEEE-TIT"},{"key":"19_CR16","doi-asserted-by":"crossref","unstructured":"Bogdanov, A., Guo, S., Komargodski, I.: Threshold secret sharing requires a linear size alphabet. In: TCC 2016, vol. 9986. LNCS, pp. 471\u2013484 (2016)","DOI":"10.1007\/978-3-662-53644-5_18"},{"key":"19_CR17","doi-asserted-by":"crossref","unstructured":"Beimel, A., Ishai, Y., Kumaresan, R., Kushilevitz, E.: On the cryptographic complexity of the worst functions. In: TCC 2014, vol. 8349. LNCS, pp. 317\u2013342 (2014)","DOI":"10.1007\/978-3-642-54242-8_14"},{"key":"19_CR18","doi-asserted-by":"crossref","unstructured":"Beimel, A., Kushilevitz, E., Nissim, P.: The complexity of multiparty PSM protocols and related models. In: EUROCRYPT 2018, vol. 10821. LNCS, pp. 287\u2013318 (2018)","DOI":"10.1007\/978-3-319-78375-8_10"},{"key":"19_CR19","doi-asserted-by":"crossref","unstructured":"Benaloh, J.C., Leichter, J.: Generalized secret sharing and monotone functions. In: CRYPTO \u201988, vol. 403. LNCS, pp. 27\u201335 (1988)","DOI":"10.1007\/0-387-34799-2_3"},{"key":"19_CR20","doi-asserted-by":"crossref","unstructured":"Blakley, G.R.: Safeguarding cryptographic keys. In: Proc. of the 1979 AFIPS National Computer Conference, vol.\u00a048. AFIPS Conference proceedings, pp. 313\u2013317 (1979)","DOI":"10.1109\/MARK.1979.8817296"},{"key":"19_CR21","unstructured":"Bogdanov, A.: Csirmaz\u2019s duality conjecture and threshold secret sharing. In: ITC, vol. 267. LIPIcs, pp. 3:1\u20133:6 (2023)"},{"key":"19_CR22","doi-asserted-by":"crossref","unstructured":"Beimel, A., Peter, N.: Optimal linear multiparty conditional disclosure of secrets protocols. In: ASIACRYPT 2018, vol. 11274. LNCS, pp. 332\u2013362 (2018)","DOI":"10.1007\/978-3-030-03332-3_13"},{"issue":"9","key":"19_CR23","doi-asserted-by":"publisher","first-page":"5600","DOI":"10.1109\/TIT.2013.2264504","volume":"59","author":"I Cascudo","year":"2013","unstructured":"Cascudo, I., Cramer, R., Xing, C.: Bounds on the threshold gap in secret sharing and its applications. IEEE Trans. Inf. Theory 59(9), 5600\u20135612 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"19_CR24","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/BF02620136","volume":"6","author":"B Chor","year":"1993","unstructured":"Chor, B., Kushilevitz, E.: Secret sharing over infinite domains. J. Cryptology 6(2), 87\u201396 (1993)","journal-title":"J. Cryptology"},{"issue":"4","key":"19_CR25","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s001459900029","volume":"10","author":"L Csirmaz","year":"1997","unstructured":"Csirmaz, L.: The size of a share must be large. J. Cryptology 10(4), 223\u2013231 (1997)","journal-title":"J. Cryptology"},{"issue":"1","key":"19_CR26","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1515\/jmc-2019-0045","volume":"15","author":"L Csirmaz","year":"2020","unstructured":"Csirmaz, L.: Secret sharing and duality. J. Math. Cryptol. 15(1), 157\u2013173 (2020)","journal-title":"J. Math. Cryptol."},{"issue":"1\u20133","key":"19_CR27","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0012-365X(96)00124-0","volume":"170","author":"P Erd\u00f6s","year":"1997","unstructured":"Erd\u00f6s, P., Pyber, L.: Covering a graph by complete bipartite graphs. Discret. Math. 170(1\u20133), 249\u2013251 (1997)","journal-title":"Discret. Math."},{"key":"19_CR28","unstructured":"Fehr, S.: Span programs over rings and how to share a secret from a module. Master\u2019s thesis, ETH Zurich (1998)"},{"key":"19_CR29","doi-asserted-by":"crossref","unstructured":"Farr\u00e0s, O., Hansen, T.B., Kaced, T., Padr\u00f3, C.: On the information ratio of non-perfect secret sharing schemes. Algorithmica 79(4), 987\u20131013 (2017)","DOI":"10.1007\/s00453-016-0217-9"},{"key":"19_CR30","unstructured":"G\u00e1l. A.: Combinatorial Methods in Boolean Function Complexity. Ph.D. thesis, U. of Chicago (1995)"},{"issue":"3","key":"19_CR31","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1006\/jcss.1999.1689","volume":"60","author":"Y Gertner","year":"2000","unstructured":"Gertner, Y., Ishai, Y., Kushilevitz, E., Malkin, T.: Protecting data privacy in private information retrieval schemes. J. Comput. Syst. Sci. 60(3), 592\u2013629 (2000)","journal-title":"J. Comput. Syst. Sci."},{"key":"19_CR32","doi-asserted-by":"crossref","unstructured":"Gay, R., Kerenidis, I., Wee, H.: Communication complexity of conditional disclosure of secrets and attribute-based encryption. In: CRYPTO 2015, vol. 9216. LNCS, pp. 485\u2013502 (2015)","DOI":"10.1007\/978-3-662-48000-7_24"},{"issue":"4","key":"19_CR33","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1137\/S0097539793244708","volume":"28","author":"J H\u00e5stad","year":"1999","unstructured":"H\u00e5stad, J., Impagliazzo, R., Levin, L.A., Luby, M.: Construction of a pseudo-random generator from any one-way function. SIAM J. Comput. 28(4), 1364\u20131396 (1999)","journal-title":"SIAM J. Comput."},{"key":"19_CR34","first-page":"99","volume":"87","author":"M Ito","year":"1987","unstructured":"Ito, M., Saito, A., Nishizeki, T.: Secret sharing schemes realizing general access structure. In Globecom 87, 99\u2013102 (1987)","journal-title":"In Globecom"},{"issue":"1","key":"19_CR35","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1109\/TIT.1983.1056621","volume":"29","author":"ED Karnin","year":"1983","unstructured":"Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theory 29(1), 35\u201341 (1983)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"19_CR36","unstructured":"Kilian, J., Nisan, N.: Unpublished result (1990)"},{"issue":"2","key":"19_CR37","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1007\/s00145-015-9226-0","volume":"30","author":"I Komargodski","year":"2017","unstructured":"Komargodski, I., Naor, M., Yogev, E.: Secret-sharing for NP. J. Cryptol. 30(2), 444\u2013469 (2017)","journal-title":"J. Cryptol."},{"key":"19_CR38","doi-asserted-by":"crossref","unstructured":"Krawczyk, H.: Secret sharing made short. In: CRYPTO \u201993, vol. 773. LNCS, pp. 136\u2013146 (1994)","DOI":"10.1007\/3-540-48329-2_12"},{"key":"19_CR39","doi-asserted-by":"crossref","unstructured":"Karchmer, M., Wigderson, A.: On span programs. In: 8th Structure in Complexity Theory, pp. 102\u2013111 (1993)","DOI":"10.1109\/SCT.1993.336536"},{"key":"19_CR40","doi-asserted-by":"crossref","unstructured":"Larsen, K.G., Simkin, M.: Secret sharing lower bound: either reconstruction is hard or shares are long. In: SCN 2020, vol. 12238. LNCS, 566\u2013578 (2020)","DOI":"10.1007\/978-3-030-57990-6_28"},{"key":"19_CR41","doi-asserted-by":"crossref","unstructured":"Liu, T., Vaikuntanathan, V.: Breaking the circuit-size barrier in secret sharing. In: 50th STOC, pp. 699\u2013708 (2018)","DOI":"10.1145\/3188745.3188936"},{"key":"19_CR42","doi-asserted-by":"crossref","unstructured":"Liu, T., Vaikuntanathan, V., Wee, H.: Towards breaking the exponential barrier for general secret sharing. In: EUROCRYPT 2018, vol. 10820. LNCS, pp. 567\u2013596 (2018)","DOI":"10.1007\/978-3-319-78381-9_21"},{"key":"19_CR43","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1145\/359168.359176","volume":"22","author":"A Shamir","year":"1979","unstructured":"Shamir, A.: How to share a secret. Commun. ACM 22, 612\u2013613 (1979)","journal-title":"Commun. ACM"},{"key":"19_CR44","unstructured":"Sun, H.-M., Shieh, S.-P.: Secret sharing in graph-based prohibited structures. In: INFOCOM \u201997, pp. 718\u2013724 (1997)"},{"key":"19_CR45","doi-asserted-by":"crossref","unstructured":"Vinod, V., Narayanan, A., Srinathan, K., Pandu Rangan, C., Kim, K.: On the power of computational secret sharing. In: Indocrypt 2003, vol. 2904. LNCS, pp. 162\u2013176 (2003)","DOI":"10.1007\/978-3-540-24582-7_12"},{"key":"19_CR46","unstructured":"Yao, A.C.: Unpublished manuscript. Presented at Oberwolfach and DIMACS Workshops (1989)"}],"container-title":["Lecture Notes in Computer Science","Theory of Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-78023-3_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T11:05:41Z","timestamp":1733137541000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-78023-3_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"ISBN":["9783031780226","9783031780233"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-78023-3_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024,12,3]]},"assertion":[{"value":"3 December 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TCC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Theory of Cryptography Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Milan","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tcc2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/tcc.iacr.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}