{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:02:11Z","timestamp":1786978931434,"version":"build-2736575974"},"publisher-location":"Cham","reference-count":61,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032253231","type":"print"},{"value":"9783032253248","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-25324-8_10","type":"book-chapter","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:44:25Z","timestamp":1778021065000},"page":"276-306","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Zebra: Arithmetic Garbled RAM for\u00a0Large Words from\u00a0DCR"],"prefix":"10.1007","author":[{"given":"Tianyao","family":"Gu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashrujit","family":"Ghoshal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elaine","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,6]]},"reference":[{"key":"10_CR1","unstructured":"Meta\u2019s oram implementation. https:\/\/github.com\/facebook\/oram"},{"key":"10_CR2","unstructured":"Private communication with worldcoin"},{"key":"10_CR3","unstructured":"Signal\u2019s oblivious ram implementation. https:\/\/github.com\/signalapp\/ContactDiscoveryService-Icelake"},{"key":"10_CR4","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/978-3-031-15985-5_15","volume-title":"Advances in Cryptology - CRYPTO 2022","author":"D Abram","year":"2022","unstructured":"Abram, D., Damg\u00e5rd, I., Orlandi, C., Scholl, P.: An algebraic framework for silent preprocessing with trustless setup and active security. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology - CRYPTO 2022, pp. 421\u2013452. Springer Nature Switzerland, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-15985-5_15"},{"key":"10_CR5","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-662-53644-5_1","volume-title":"Theory of Cryptography","author":"P Ananth","year":"2016","unstructured":"Ananth, P., Chen, Y.C., Chung, K.M., Lin, H., Lin, W.K.: Delegating ram computations with adaptive soundness and privacy. In: Hirt, M., Smith, A. (eds.) Theory of Cryptography, pp. 3\u201330. Springer, Berlin Heidelberg, Berlin, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_1"},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/978-3-030-03810-6_17","volume-title":"Theory of Cryptography","author":"P Ananth","year":"2018","unstructured":"Ananth, P., Lombardi, A.: Succinct garbling schemes from functional encryption through a local simulation paradigm. In: Beimel, A., Dziembowski, S. (eds.) Theory of Cryptography, pp. 455\u2013472. Springer International Publishing, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03810-6_17"},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-031-30617-4_1","volume-title":"Advances in Cryptology - EUROCRYPT 2023","author":"M Ball","year":"2023","unstructured":"Ball, M., Li, H., Lin, H., Liu, T.: New ways to garble arithmetic circuits. In: Hazay, C., Stam, M. (eds.) Advances in Cryptology - EUROCRYPT 2023, pp. 3\u201334. Springer Nature Switzerland, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30617-4_1"},{"key":"10_CR8","doi-asserted-by":"publisher","unstructured":"Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 503\u2013513. STOC 1990, Association for Computing Machinery, New York, NY, USA (1990). https:\/\/doi.org\/10.1145\/100216.100287","DOI":"10.1145\/100216.100287"},{"key":"10_CR9","doi-asserted-by":"crossref","unstructured":"Behera, A.R., Meyer, P., Orlandi, C., Roy, L., Scholl, P.: Privately constrained PRFs from DCR: Puncturing and bounded waring rank. Cryptology ePrint Archive, Paper 2025\/230 (2025). https:\/\/eprint.iacr.org\/2025\/230","DOI":"10.1007\/978-3-032-12287-2_11"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Bellare, M., Hoang, T., Keelveedhi, S., Rogaway, P.: Efficient garbling from a fixed-key blockcipher, pp. 478\u2013492 (2013). https:\/\/doi.org\/10.1109\/SP.2013.39","DOI":"10.1109\/SP.2013.39"},{"key":"10_CR11","doi-asserted-by":"publisher","unstructured":"Bitansky, N., Garg, S., Lin, H., Pass, R., Telang, S.: Succinct randomized encodings and their applications. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 439\u2013448. STOC 2015, Association for Computing Machinery, New York, NY, USA (2015). https:\/\/doi.org\/10.1145\/2746539.2746574","DOI":"10.1145\/2746539.2746574"},{"key":"10_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/978-3-662-53018-4_19","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"E Boyle","year":"2016","unstructured":"Boyle, E., Gilboa, N., Ishai, Y.: Breaking the circuit size barrier for secure computation under DDH. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 509\u2013539. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53018-4_19"},{"key":"10_CR13","doi-asserted-by":"publisher","unstructured":"Boyle, E., Naor, M.: Is there an oblivious ram lower bound? In: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, pp. 357\u2013368. ITCS 2016, Association for Computing Machinery, New York, NY, USA (2016). https:\/\/doi.org\/10.1145\/2840728.2840761","DOI":"10.1145\/2840728.2840761"},{"key":"10_CR14","unstructured":"Buterin, V.: A maximally simple l1 privacy roadmap. https:\/\/ethereum-magicians.org\/t\/a-maximally-simple-l1-privacy-roadmap\/23459"},{"key":"10_CR15","doi-asserted-by":"publisher","unstructured":"Canetti, R., Chen, Y., Holmgren, J., Raykova, M.: Adaptive succinct garbled ram or: how to delegate your database. In: Proceedings, Part II, of the 14th International Conference on Theory of Cryptography - Volume 9986, pp. 61\u201390. Springer-Verlag, Berlin, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_3","DOI":"10.1007\/978-3-662-53644-5_3"},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Canetti, R., Holmgren, J.: Fully succinct garbled ram. In: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, pp. 169\u2013178. ITCS 2016, Association for Computing Machinery, New York, NY, USA (2016). https:\/\/doi.org\/10.1145\/2840728.2840765","DOI":"10.1145\/2840728.2840765"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"Canetti, R., Holmgren, J., Jain, A., Vaikuntanathan, V.: Succinct garbling and indistinguishability obfuscation for ram programs. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 429\u2013437. STOC 2015, Association for Computing Machinery, New York, NY, USA (2015). https:\/\/doi.org\/10.1145\/2746539.2746621","DOI":"10.1145\/2746539.2746621"},{"key":"10_CR18","doi-asserted-by":"publisher","unstructured":"Chen, L., Moody, D., Regenscheid, A., Robinson, A., Randall, K.: Recommendations for discrete logarithm-based cryptography: elliptic curve domain parameters. Tech. Rep. NIST Special Publication (SP) 800-186, National Institute of Standards and Technology, Gaithersburg, MD (2023). https:\/\/doi.org\/10.6028\/NIST.SP.800-186","DOI":"10.6028\/NIST.SP.800-186"},{"key":"10_CR19","doi-asserted-by":"publisher","unstructured":"Chen, Y.C., Chow, S.S., Chung, K.M., Lai, R.W., Lin, W.K., Zhou, H.S.: Cryptography for parallel ram from indistinguishability obfuscation. In: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, Pp. 179\u2013190. ITCS 2016, Association for Computing Machinery, New York, NY, USA (2016). https:\/\/doi.org\/10.1145\/2840728.2840769","DOI":"10.1145\/2840728.2840769"},{"key":"10_CR20","doi-asserted-by":"crossref","unstructured":"Corrigan-Gibbs, H., Kogan, D.: Private information retrieval with sublinear online time. In: EUROCRYPT (2020)","DOI":"10.1007\/978-3-030-45721-1_3"},{"key":"10_CR21","doi-asserted-by":"publisher","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 40\u201349 (2013). https:\/\/doi.org\/10.1109\/FOCS.2013.13","DOI":"10.1109\/FOCS.2013.13"},{"key":"10_CR22","doi-asserted-by":"publisher","unstructured":"Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled ram. In: Proceedings of the 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 210\u2013229. FOCS 2015, IEEE Computer Society, USA (2015). https:\/\/doi.org\/10.1109\/FOCS.2015.22","DOI":"10.1109\/FOCS.2015.22"},{"key":"10_CR23","doi-asserted-by":"publisher","unstructured":"Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled ram from one-way functions. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, Pp. 449\u2013458. STOC 2015, Association for Computing Machinery, New York, NY, USA (2015). https:\/\/doi.org\/10.1145\/2746539.2746593","DOI":"10.1145\/2746539.2746593"},{"key":"10_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/978-3-642-55220-5_23","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"C Gentry","year":"2014","unstructured":"Gentry, C., Halevi, S., Lu, S., Ostrovsky, R., Raykova, M., Wichs, D.: Garbled RAM revisited. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 405\u2013422. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-55220-5_23"},{"issue":"3","key":"10_CR25","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1145\/233551.233553","volume":"43","author":"O Goldreich","year":"1996","unstructured":"Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. J. ACM 43(3), 431\u2013473 (1996). https:\/\/doi.org\/10.1145\/233551.233553","journal-title":"J. ACM"},{"key":"10_CR26","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-032-01913-4_8","volume-title":"Advances in Cryptology - CRYPTO 2025","author":"T Gu","year":"2025","unstructured":"Gu, T., Tinoco, A., Rajan, S.H.G., Shi, E.: Picogram: practical garbled ram from decisional Diffie-Hellman. In: Tauman Kalai, Y., Kamara, S.F. (eds.) Advances in Cryptology - CRYPTO 2025, pp. 247\u2013281. Springer Nature Switzerland, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-01913-4_8"},{"key":"10_CR27","doi-asserted-by":"publisher","unstructured":"Heath, D.: Efficient arithmetic in garbled circuits. In: Advances in Cryptology - EUROCRYPT 2024: 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zurich, Switzerland, May 26-30, 2024, Proceedings, Part V, pp. 3\u201331. Springer-Verlag, Berlin, Heidelberg (2024). https:\/\/doi.org\/10.1007\/978-3-031-58740-5_1","DOI":"10.1007\/978-3-031-58740-5_1"},{"key":"10_CR28","doi-asserted-by":"publisher","unstructured":"Heath, D., Kolesnikov, V., Ostrovsky, R.: Epigram: practical garbled ram. In: Advances in Cryptology - EUROCRYPT 2022: 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Trondheim, Norway, May 30 - June 3, 2022, Proceedings, Part I, pp. 3\u201333. Springer-Verlag, Berlin, Heidelberg (2022). https:\/\/doi.org\/10.1007\/978-3-031-06944-4_1","DOI":"10.1007\/978-3-031-06944-4_1"},{"key":"10_CR29","doi-asserted-by":"publisher","unstructured":"Heath, D., Kolesnikov, V., Ostrovsky, R.: Tri-state circuits: a circuit model that captures ram. In: Advances in Cryptology - CRYPTO 2023: 43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, August 20-24, 2023, Proceedings, Part IV, pp. 128\u2013160. Springer-Verlag, Berlin, Heidelberg (2023). https:\/\/doi.org\/10.1007\/978-3-031-38551-3_5","DOI":"10.1007\/978-3-031-38551-3_5"},{"key":"10_CR30","doi-asserted-by":"publisher","unstructured":"Hoover, A., Patel, S., Persiano, G., Yeo, K.: Plinko: single-server PIR with efficient updates via invertible PRFS. In: Advances in Cryptology - EUROCRYPT 2025 - 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4-8, 2025, Proceedings, Part VI. LNCS, vol. 15606, pp. 3\u201333. Springer (2025). https:\/\/doi.org\/10.1007\/978-3-031-91095-1_1","DOI":"10.1007\/978-3-031-91095-1_1"},{"key":"10_CR31","unstructured":"Intel: Intel paillier cryptosystem library (pailliercryptolib). https:\/\/github.com\/intel\/pailliercryptolib (2022). version 1.1.4, released December 22, 2022; archived by owner June 30, 2025"},{"key":"10_CR32","unstructured":"Ishai, Y., Li, H., Lin, H.: Succinct homomorphic MACs from groups and applications. Cryptology ePrint Archive, Paper 2024\/2073 (2024). https:\/\/eprint.iacr.org\/2024\/2073"},{"key":"10_CR33","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1007\/978-3-032-01884-7_13","volume-title":"Advances in Cryptology - CRYPTO 2025","author":"Y Ishai","year":"2025","unstructured":"Ishai, Y., Li, H., Lin, H.: A unified framework for succinct garbling from homomorphic secret sharing. In: Tauman Kalai, Y., Kamara, S.F. (eds.) Advances in Cryptology - CRYPTO 2025, pp. 390\u2013425. Springer Nature Switzerland, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-01884-7_13"},{"key":"10_CR34","doi-asserted-by":"crossref","unstructured":"Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions (2020)","DOI":"10.1145\/3406325.3451093"},{"key":"10_CR35","unstructured":"Jentzsch, S., Jentzsch, C.: EIP-1186: RPC-method to get merkle proofs \u2014 eth_getproof (2018). https:\/\/eips.ethereum.org\/EIPS\/eip-1186"},{"key":"10_CR36","unstructured":"Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: International Colloquium on Automata, Languages and Programming (2008). https:\/\/api.semanticscholar.org\/CorpusID:7746167"},{"key":"10_CR37","doi-asserted-by":"publisher","unstructured":"Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 419\u2013428. STOC 2015, Association for Computing Machinery, New York, NY, USA (2015). https:\/\/doi.org\/10.1145\/2746539.2746614","DOI":"10.1145\/2746539.2746614"},{"key":"10_CR38","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/978-3-319-96881-0_18","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"KG Larsen","year":"2018","unstructured":"Larsen, K.G., Nielsen, J.B.: Yes, there is an oblivious RAM lower bound! In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 523\u2013542. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_18"},{"key":"10_CR39","doi-asserted-by":"crossref","unstructured":"Lazzaretti, A., Papamanthou, C.: Treepir: sublinear-time and polylog-bandwidth private information retrieval from DDH. In: CRYPTO (2023)","DOI":"10.1007\/978-3-031-38545-2_10"},{"key":"10_CR40","doi-asserted-by":"publisher","unstructured":"Li, H., Liu, T.: How to garble mixed circuits that combine Boolean and arithmetic computations. In: Advances in Cryptology \u2013 EUROCRYPT 2024: 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zurich, Switzerland, May 26\u201330, 2024, Proceedings, Part VI, pp. 331\u2013360. Springer-Verlag, Berlin, Heidelberg (2024). https:\/\/doi.org\/10.1007\/978-3-031-58751-1_12","DOI":"10.1007\/978-3-031-58751-1_12"},{"key":"10_CR41","unstructured":"Lin, H., Pass, R.: Succinct garbling schemes and applications. IACR Cryptol. ePrint Arch. 2014, 766 (2014). https:\/\/api.semanticscholar.org\/CorpusID:18349655"},{"key":"10_CR42","doi-asserted-by":"publisher","unstructured":"Liu, H., Wang, X., Yang, K., Yu, Y.: BITGC: garbled circuits with 1 bit per gate. In: Advances in Cryptology \u2013 EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4\u20138, 2025, Proceedings, Part VII, pp. 437\u2013466. Springer-Verlag, Berlin, Heidelberg (2025). https:\/\/doi.org\/10.1007\/978-3-031-91098-2_16","DOI":"10.1007\/978-3-031-91098-2_16"},{"key":"10_CR43","doi-asserted-by":"publisher","unstructured":"Lu, S., Ostrovsky, R.: How to garble ram programs. In: Advances in Cryptology - EUROCRYPT 2013. LNCS, vol.\u00a07881, pp. 719\u2013734. Springer (2013). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_42","DOI":"10.1007\/978-3-642-38348-9_42"},{"key":"10_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1007\/978-3-319-63715-0_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"S Lu","year":"2017","unstructured":"Lu, S., Ostrovsky, R.: Black-box parallel garbled RAM. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 66\u201392. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63715-0_3"},{"key":"10_CR45","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/978-3-031-78023-3_3","volume-title":"Theory of Cryptography","author":"P Meyer","year":"2025","unstructured":"Meyer, P., Orlandi, C., Roy, L., Scholl, P.: Rate-1 arithmetic garbling from homomorphic secret sharing. In: Boyle, E., Mahmoody, M. (eds.) Theory of Cryptography, pp. 71\u201397. Springer Nature Switzerland, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-031-78023-3_3"},{"key":"10_CR46","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1007\/978-3-032-01884-7_14","volume-title":"Advances in Cryptology - CRYPTO 2025","author":"P Meyer","year":"2025","unstructured":"Meyer, P., Orlandi, C., Roy, L., Scholl, P.: Silent circuit relinearisation: sublinear-size (Boolean and arithmetic) garbled circuits from DCR. In: Tauman Kalai, Y., Kamara, S.F. (eds.) Advances in Cryptology - CRYPTO 2025, pp. 426\u2013458. Springer Nature Switzerland, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-01884-7_14"},{"key":"10_CR47","doi-asserted-by":"publisher","unstructured":"Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proceedings of the 1st ACM Conference on Electronic Commerce, pp. 129\u2013139. EC 1999, Association for Computing Machinery, New York, NY, USA (1999). https:\/\/doi.org\/10.1145\/336992.337028","DOI":"10.1145\/336992.337028"},{"key":"10_CR48","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1007\/978-3-030-77870-5_24","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"C Orlandi","year":"2021","unstructured":"Orlandi, C., Scholl, P., Yakoubov, S.: The rise of paillier: homomorphic secret sharing and public-key silent OT. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 678\u2013708. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77870-5_24"},{"key":"10_CR49","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/3-540-48910-x_16","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 1999","author":"P Paillier","year":"1999","unstructured":"Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) Advances in Cryptology \u2013 EUROCRYPT 1999, pp. 223\u2013238. Springer, Berlin Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48910-x_16"},{"key":"10_CR50","doi-asserted-by":"publisher","unstructured":"Park, A., Lin, W.K., Shi, E.: Nanogram: garbled ram with O(LOGN) overhead. In: Advances in Cryptology - EUROCRYPT 2023: 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Lyon, France, April 23-27, 2023, Proceedings, Part I, pp. 456\u2013486. Springer-Verlag, Berlin, Heidelberg (2023). https:\/\/doi.org\/10.1007\/978-3-031-30545-0_16","DOI":"10.1007\/978-3-031-30545-0_16"},{"key":"10_CR51","doi-asserted-by":"crossref","unstructured":"Ren, L., Mughees, M.H., Sun, I.: Simple and practical amortized sublinear private information retrieval using dummy subsets. In: Proceedings of the 2024 on ACM SIGSAC Conference on Computer and Communications Security, pp. 1420\u20131433. CCS 2024, Association for Computing Machinery, New York, NY, USA (2024)","DOI":"10.1145\/3658644.3690266"},{"key":"10_CR52","doi-asserted-by":"publisher","unstructured":"Rosulek, M., Roy, L.: Three halves make a whole? Beating the half-gates lower bound for garbled circuits. In: Advances in Cryptology \u2013 CRYPTO 2021: 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16\u201320, 2021, Proceedings, Part I, pp. 94\u2013124. Springer-Verlag, Berlin, Heidelberg (2021). https:\/\/doi.org\/10.1007\/978-3-030-84242-0_5","DOI":"10.1007\/978-3-030-84242-0_5"},{"key":"10_CR53","doi-asserted-by":"publisher","unstructured":"Roy, L., Singh, J.: Large message homomorphic secret sharing from DCR and applications. In: Advances in Cryptology \u2013 CRYPTO 2021: 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16\u201320, 2021, Proceedings, Part III, pp. 687\u2013717. Springer-Verlag, Berlin, Heidelberg (2021). https:\/\/doi.org\/10.1007\/978-3-030-84252-9_23","DOI":"10.1007\/978-3-030-84252-9_23"},{"key":"10_CR54","doi-asserted-by":"crossref","unstructured":"Shanks, D.: Class number, a theory of factorization and genera. In: Proceedings of the Symposium Pure Mathematics, vol.\u00a020, pp. 415\u2013440. American Mathematical Society, Providence, R.I. (1971)","DOI":"10.1090\/pspum\/020\/0316385"},{"key":"10_CR55","doi-asserted-by":"publisher","unstructured":"Stefanov, E., et al.: Path Oram: an extremely simple oblivious ram protocol. J. ACM 65(4) (2018). https:\/\/doi.org\/10.1145\/3177872","DOI":"10.1145\/3177872"},{"key":"10_CR56","unstructured":"team, T.F.: FLINT: Fast Library for Number Theory (2025), version 3.3.1. https:\/\/flintlib.org"},{"key":"10_CR57","doi-asserted-by":"publisher","unstructured":"Wang, X., Chan, H., Shi, E.: Circuit Oram: on tightness of the goldreich-ostrovsky lower bound. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 850\u2013861. CCS 2015, Association for Computing Machinery, New York, NY, USA (2015). https:\/\/doi.org\/10.1145\/2810103.2813634","DOI":"10.1145\/2810103.2813634"},{"key":"10_CR58","doi-asserted-by":"publisher","unstructured":"Yang, Y., Peceny, S., Heath, D., Kolesnikov, V.: Towards generic MPC compilers via variable instruction set architectures (visas). In: Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications Security, pp. 2516\u20132530. CCS 2023, Association for Computing Machinery, New York, NY, USA (2023). https:\/\/doi.org\/10.1145\/3576915.3616664","DOI":"10.1145\/3576915.3616664"},{"key":"10_CR59","doi-asserted-by":"publisher","unstructured":"Yao, A.C.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (SFCS 1986), pp. 162\u2013167 (1986). https:\/\/doi.org\/10.1109\/SFCS.1986.25","DOI":"10.1109\/SFCS.1986.25"},{"key":"10_CR60","doi-asserted-by":"publisher","unstructured":"Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole - reducing data transfer in garbled circuits using half gates. In: Oswald, E., Fischlin, M. (eds.) Advances in Cryptology - EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30, 2015, Proceedings, Part II. LNCS, vol.\u00a09057, pp. 220\u2013250. Springer (2015). https:\/\/doi.org\/10.1007\/978-3-662-46803-6_8","DOI":"10.1007\/978-3-662-46803-6_8"},{"key":"10_CR61","doi-asserted-by":"crossref","unstructured":"Zhou, M., Park, A., Shi, E., Zheng, W.: Piano: extremely simple, single-server pir with sublinear server computation. In: IEEE S& P (2024)","DOI":"10.1109\/SP54263.2024.00055"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2026"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-25324-8_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:44:31Z","timestamp":1778021071000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-25324-8_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032253231","9783032253248"],"references-count":61,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-25324-8_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"6 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rome","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":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 May 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 May 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"45","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}