{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T23:24:58Z","timestamp":1769556298489,"version":"3.49.0"},"publisher-location":"Singapore","reference-count":68,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819987238","type":"print"},{"value":"9789819987245","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023]]},"DOI":"10.1007\/978-981-99-8724-5_7","type":"book-chapter","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T08:02:20Z","timestamp":1702886540000},"page":"208-242","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Sigma Protocols from\u00a0Verifiable Secret Sharing and\u00a0Their Applications"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4772-6565","authenticated-orcid":false,"given":"Min","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2553-1281","authenticated-orcid":false,"given":"Yu","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5676-2353","authenticated-orcid":false,"given":"Chuanzhou","family":"Yao","sequence":"additional","affiliation":[]},{"given":"Zhichao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"7_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1007\/978-3-030-64840-4_25","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"M Abe","year":"2020","unstructured":"Abe, M., Ambrona, M., Bogdanov, A., Ohkubo, M., Rosen, A.: Non-interactive composition of sigma-protocols via share-then-hash. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 749\u2013773. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64840-4_25"},{"key":"7_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/978-3-030-90459-3_15","volume-title":"Theory of Cryptography","author":"M Abe","year":"2021","unstructured":"Abe, M., Ambrona, M., Bogdanov, A., Ohkubo, M., Rosen, A.: Acyclicity programming for sigma-protocols. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13042, pp. 435\u2013465. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90459-3_15"},{"key":"7_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1007\/978-3-030-97121-2_21","volume-title":"Public-Key Cryptography - PKC 2022","author":"DF Aranha","year":"2022","unstructured":"Aranha, D.F., Bennedsen, E.M., Campanelli, M., Ganesh, C., Orlandi, C., Takahashi, A.: ECLIPSE: enhanced compiling method for Pedersen-committed zkSNARK engines. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) PKC 2022. LNCS, vol. 13177, pp. 584\u2013614. Springer, Cham (2022)"},{"key":"7_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/978-3-030-84245-1_19","volume-title":"Advances in Cryptology \u2013 CRYPTO 2021","author":"T Attema","year":"2021","unstructured":"Attema, T., Cramer, R., Kohl, L.: A compressed $$\\Sigma $$-protocol theory for\u00a0lattices. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 549\u2013579. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-84245-1_19"},{"key":"7_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/978-3-319-96878-0_22","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"S Agrawal","year":"2018","unstructured":"Agrawal, S., Ganesh, C., Mohassel, P.: Non-interactive zero-knowledge proofs for composite statements. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 643\u2013673. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_22"},{"key":"7_CR6","doi-asserted-by":"crossref","unstructured":"Aranha, D.F., El Housni, Y., Guillevic, A.: A survey of elliptic curves for proof systems. IACR Cryptology ePrint Archive (2022)","DOI":"10.1007\/s10623-022-01135-y"},{"key":"7_CR7","unstructured":"Ames, S., Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Lightweight sublinear arguments without a trusted setup. In: ACM CCS, Ligero (2017)"},{"key":"7_CR8","doi-asserted-by":"crossref","unstructured":"B\u00fcnz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Short proofs for confidential transactions and more. In: IEEE S &P, Bulletproofs (2018)","DOI":"10.1109\/SP.2018.00020"},{"key":"7_CR9","unstructured":"Ben-Sasson, E., Bentov, I., Horesh, Y., Riabzev, M.: Scalable, transparent, and post-quantum secure computational integrity (2018). http:\/\/eprint.iacr.org\/2018\/046"},{"key":"7_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/978-3-662-49896-5_12","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"J Bootle","year":"2016","unstructured":"Bootle, J., Cerulli, A., Chaidos, P., Groth, J., Petit, C.: Efficient zero-knowledge arguments for arithmetic circuits in the discrete log setting. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 327\u2013357. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_12"},{"key":"7_CR11","doi-asserted-by":"crossref","unstructured":"Ben-Sasson, E., Chiesa, A., Garman, C., Green, M., Miers, I., Tromer, E., Virza, M.: Decentralized anonymous payments from bitcoin. In: IEEE S &P, Zerocash (2014)","DOI":"10.1109\/SP.2014.36"},{"key":"7_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/978-3-030-17653-2_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"E Ben-Sasson","year":"2019","unstructured":"Ben-Sasson, E., Chiesa, A., Riabzev, M., Spooner, N., Virza, M., Ward, N.P.: Aurora: transparent succinct arguments for R1CS. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 103\u2013128. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17653-2_4"},{"key":"7_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-3-662-53644-5_2","volume-title":"Theory of Cryptography","author":"E Ben-Sasson","year":"2016","unstructured":"Ben-Sasson, E., Chiesa, A., Spooner, N.: Interactive oracle proofs. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 31\u201360. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_2"},{"key":"7_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-3-030-45727-3_7","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"W Beullens","year":"2020","unstructured":"Beullens, W.: Sigma protocols for MQ, PKP and SIS, and fishy signature schemes. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12107, pp. 183\u2013211. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45727-3_7"},{"key":"7_CR15","doi-asserted-by":"crossref","unstructured":"Bhadauria R., Fang Z., Hazay C., Venkitasubramaniam M., Xie T., Zhang Y.: Ligero++: a new optimized sublinear IoP. In: ACM CCS (2020)","DOI":"10.1145\/3372297.3417893"},{"key":"7_CR16","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC (1988)","DOI":"10.1145\/62212.62213"},{"key":"7_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1007\/978-3-030-17253-4_10","volume-title":"Public-Key Cryptography \u2013 PKC 2019","author":"M Backes","year":"2019","unstructured":"Backes, M., Hanzlik, L., Herzberg, A., Kate, A., Pryvalov, I.: Efficient non-interactive zero-knowledge proofs in cross-domains without trusted setup. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11442, pp. 286\u2013313. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17253-4_10"},{"key":"7_CR18","doi-asserted-by":"crossref","unstructured":"Chaum, D., Cr\u00e9peau, C., Damg\u00e5rd, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC (1988)","DOI":"10.1007\/3-540-48184-2_43"},{"key":"7_CR19","doi-asserted-by":"crossref","unstructured":"Chase, M., et al.: Post-quantum zero-knowledge and signatures from symmetric-key primitives. In: ACM CCS (2017)","DOI":"10.1145\/3133956.3133997"},{"key":"7_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/3-540-48658-5_19","volume-title":"Advances in Cryptology \u2014 CRYPTO \u201994","author":"R Cramer","year":"1994","unstructured":"Cramer, R., Damg\u00e5rd, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174\u2013187. Springer, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48658-5_19"},{"key":"7_CR21","doi-asserted-by":"crossref","unstructured":"Cohen, J.D., Fischer, M.J.: A robust and verifiable cryptographically secure election scheme (extended abstract). In: FOCS (1985)","DOI":"10.1109\/SFCS.1985.2"},{"key":"7_CR22","doi-asserted-by":"crossref","unstructured":"Campanelli, M., Fiore, D., Querol, A.: Modular design and composition of succinct zero-knowledge proofs. In: ACM CCS, Legosnark (2019)","DOI":"10.1145\/3319535.3339820"},{"key":"7_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/978-3-662-53015-3_18","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"M Chase","year":"2016","unstructured":"Chase, M., Ganesh, C., Mohassel, P.: Efficient zero-knowledge proof of algebraic and non-algebraic statements with applications to privacy preserving credentials. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 499\u2013530. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53015-3_18"},{"key":"7_CR24","doi-asserted-by":"crossref","unstructured":"Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: FOCS (1985)","DOI":"10.1109\/SFCS.1985.64"},{"key":"7_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1007\/978-3-030-45721-1_26","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"A Chiesa","year":"2020","unstructured":"Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.: Marlin: preprocessing zkSNARKs with universal and updatable srs. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 738\u2013768. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_26"},{"key":"7_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/3-540-44987-6_7","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2001","author":"J Camenisch","year":"2001","unstructured":"Camenisch, J., Lysyanskaya, A.: An efficient system for non-transferable anonymous credentials with optional anonymity revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93\u2013118. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-44987-6_7"},{"key":"7_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1007\/978-3-030-45721-1_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"A Chiesa","year":"2020","unstructured":"Chiesa, A., Ojha, D., Spooner, N.: Fractal: post-quantum and transparent recursive proofs from holography. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 769\u2013793. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_27"},{"key":"7_CR28","unstructured":"Cramer, R.: Modular design of secure yet practical cryptographic protocols. Ph.D. thesis (1996)"},{"key":"7_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/978-3-030-88323-2_14","volume-title":"Information Security and Cryptology","author":"H Cui","year":"2021","unstructured":"Cui, H., Zhang, K.: A simple post-quantum non-interactive zero-knowledge proof from garbled circuits. In: Yu, Yu., Yung, M. (eds.) Inscrypt 2021. LNCS, vol. 13007, pp. 269\u2013280. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-88323-2_14"},{"key":"7_CR30","doi-asserted-by":"crossref","unstructured":"Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: FOCS (1987)","DOI":"10.1109\/SFCS.1987.4"},{"key":"7_CR31","doi-asserted-by":"crossref","unstructured":"Feige, U., Fiat, A., Shamir, A.: Zero knowledge proofs of identity. In: STOC (1987)","DOI":"10.1145\/28395.28419"},{"key":"7_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1007\/3-540-47721-7_12","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 86","author":"A Fiat","year":"1987","unstructured":"Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186\u2013194. Springer, Heidelberg (1987). https:\/\/doi.org\/10.1007\/3-540-47721-7_12"},{"key":"7_CR33","doi-asserted-by":"crossref","unstructured":"Franklin, M.K., Yung, M.: Communication complexity of secure computation (extended abstract). In: STOC (1992)","DOI":"10.1145\/129712.129780"},{"key":"7_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1007\/978-3-642-38348-9_37","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"R Gennaro","year":"2013","unstructured":"Gennaro, R., Gentry, C., Parno, B., Raykova, M.: Quadratic span programs and succinct NIZKs without PCPs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 626\u2013645. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_37"},{"key":"7_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/978-3-662-46803-6_9","volume-title":"Advances in Cryptology - EUROCRYPT 2015","author":"J Groth","year":"2015","unstructured":"Groth, J., Kohlweiss, M.: One-out-of-many proofs: or how to leak a secret and spend a coin. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 253\u2013280. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-46803-6_9"},{"key":"7_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/978-3-540-30539-2_20","volume-title":"Advances in Cryptology - ASIACRYPT 2004","author":"R Gennaro","year":"2004","unstructured":"Gennaro, R., Leigh, D., Sundaram, R., Yerazunis, W.: Batching Schnorr identification scheme with applications to privacy-preserving authorization and low-bandwidth communication devices. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 276\u2013292. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-30539-2_20"},{"key":"7_CR37","unstructured":"Giacomelli, I., Madsen, J., Orlandi, C.: Faster zero-knowledge for Boolean circuits. In: USENIX, Zkboo (2016)"},{"key":"7_CR38","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: STOC (1985)","DOI":"10.1145\/22145.22178"},{"key":"7_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/3-540-47721-7_11","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 86","author":"O Goldreich","year":"1987","unstructured":"Goldreich, O., Micali, S., Wigderson, A.: How to prove all NP statements in zero-knowledge and a methodology of cryptographic protocol design (extended abstract). In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 171\u2013185. Springer, Heidelberg (1987). https:\/\/doi.org\/10.1007\/3-540-47721-7_11"},{"key":"7_CR40","doi-asserted-by":"crossref","unstructured":"Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC (1987)","DOI":"10.1145\/28395.28420"},{"key":"7_CR41","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/0-387-34799-2_16","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 88","author":"LC Guillou","year":"1990","unstructured":"Guillou, L.C., Quisquater, J.-J.: A \u201cparadoxical\u2019\u2019 indentity-based signature scheme resulting from zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 216\u2013231. Springer, New York (1990). https:\/\/doi.org\/10.1007\/0-387-34799-2_16"},{"key":"7_CR42","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1007\/978-3-642-03356-8_12","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"J Groth","year":"2009","unstructured":"Groth, J.: Linear algebra with sub-linear zero-knowledge arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192\u2013208. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-03356-8_12"},{"key":"7_CR43","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/978-3-642-17373-8_19","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"J Groth","year":"2010","unstructured":"Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321\u2013340. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-17373-8_19"},{"key":"7_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/978-3-662-49896-5_11","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"J Groth","year":"2016","unstructured":"Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 305\u2013326. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_11"},{"key":"7_CR45","doi-asserted-by":"crossref","unstructured":"Hoffmann, M., Kloo\u00df, M., Rupp, A.: Efficient zero-knowledge arguments in the discrete log setting, revisited. In: ACM CCS (2019)","DOI":"10.1145\/3319535.3354251"},{"key":"7_CR46","doi-asserted-by":"crossref","unstructured":"Ishai, Y., Kushilevitz, E., Ostrovsky, R.: Efficient arguments without short PCPs. In: IEEE CCC (2007)","DOI":"10.1109\/CCC.2007.10"},{"key":"7_CR47","doi-asserted-by":"crossref","unstructured":"Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: STOC (2007)","DOI":"10.1145\/1250790.1250794"},{"key":"7_CR48","doi-asserted-by":"crossref","unstructured":"Jawurek, M., Kerschbaum, F., Orlandi, C.: Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently. In: ACM CCS (2013)","DOI":"10.1145\/2508859.2516662"},{"key":"7_CR49","doi-asserted-by":"crossref","unstructured":"Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: STOC (1992)","DOI":"10.1145\/129712.129782"},{"key":"7_CR50","doi-asserted-by":"crossref","unstructured":"Katz, J., Kolesnikov, V., Wang, X.: Improved non-interactive zero knowledge with applications to post-quantum signatures. In: ACM CCS (2018)","DOI":"10.1145\/3243734.3243805"},{"key":"7_CR51","unstructured":"Kalai, Y.T., Raz, R.: Interactive PCP. In: ICALP (2008)"},{"key":"7_CR52","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-030-90453-1_1","volume-title":"Theory of Cryptography","author":"J Lee","year":"2021","unstructured":"Lee, J.: Dory: efficient, transparent arguments for generalised inner products and polynomial commitments. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13043, pp. 1\u201334. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90453-1_1"},{"key":"7_CR53","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-642-28914-9_10","volume-title":"Theory of Cryptography","author":"H Lipmaa","year":"2012","unstructured":"Lipmaa, H.: Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169\u2013189. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28914-9_10"},{"key":"7_CR54","doi-asserted-by":"crossref","unstructured":"Maurer, U.: Zero-knowledge proofs of knowledge for group homomorphisms. Des. Codes Cryptogr. 77, 663\u2013676 (2015)","DOI":"10.1007\/s10623-015-0103-5"},{"key":"7_CR55","doi-asserted-by":"crossref","unstructured":"Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge snarks from linear-size universal and updatable structured reference strings. : ACM CCS (2019)","DOI":"10.1145\/3319535.3339817"},{"key":"7_CR56","unstructured":"Micali, S.: CS proofs (extended abstracts). In: FOCS (1994)"},{"key":"7_CR57","doi-asserted-by":"crossref","unstructured":"Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC (1990)","DOI":"10.1145\/100216.100273"},{"key":"7_CR58","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/3-540-48071-4_3","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 92","author":"T Okamoto","year":"1993","unstructured":"Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31\u201353. Springer, Heidelberg (1993). https:\/\/doi.org\/10.1007\/3-540-48071-4_3"},{"key":"7_CR59","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/3-540-46766-1_9","volume-title":"Advances in Cryptology \u2014 CRYPTO \u201991","author":"TP Pedersen","year":"1992","unstructured":"Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129\u2013140. Springer, Heidelberg (1992). https:\/\/doi.org\/10.1007\/3-540-46766-1_9"},{"key":"7_CR60","doi-asserted-by":"crossref","unstructured":"Pippenger, N.: On the evaluation of powers and monomials. SIAM J. Comput. (1980)","DOI":"10.1137\/0209022"},{"key":"7_CR61","doi-asserted-by":"crossref","unstructured":"Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: STOC (1989)","DOI":"10.1145\/73007.73014"},{"key":"7_CR62","doi-asserted-by":"crossref","unstructured":"Reingold, O., Rothblum, G.N., Rothblum, R.D.: Constant-round interactive proofs for delegating computation. In: STOC (2016)","DOI":"10.1145\/2897518.2897652"},{"key":"7_CR63","unstructured":"Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS (1999)"},{"key":"7_CR64","doi-asserted-by":"crossref","unstructured":"Schnorr, C.-P.: Efficient signature generation by smart cards. J. Cryptol. (1991)","DOI":"10.1007\/BF00196725"},{"key":"7_CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1007\/978-3-030-56877-1_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2020","author":"S Setty","year":"2020","unstructured":"Setty, S.: Spartan: efficient and general-purpose zkSNARKs without trusted setup. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12172, pp. 704\u2013737. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56877-1_25"},{"key":"7_CR66","doi-asserted-by":"crossref","unstructured":"Shamir, A.: How to share a secret. CACM (1979)","DOI":"10.1145\/359168.359176"},{"key":"7_CR67","doi-asserted-by":"crossref","unstructured":"Thaler, J.: Proofs, arguments, and zero-knowledge. Found. Trends\u00ae Privacy Secur. (2022)","DOI":"10.1561\/9781638281252"},{"key":"7_CR68","doi-asserted-by":"crossref","unstructured":"Zhang, J., Xie, T., Zhang, Y., Song, D.: Transparent polynomial delegation and its applications to zero knowledge proof. In: IEEE S &P (2020)","DOI":"10.1109\/SP40000.2020.00052"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2023"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-99-8724-5_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T01:02:21Z","timestamp":1766019741000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-99-8724-5_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9789819987238","9789819987245"],"references-count":68,"URL":"https:\/\/doi.org\/10.1007\/978-981-99-8724-5_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"19 December 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ASIACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on the Theory and Application of Cryptology and Information Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Guangzhou","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 December 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 December 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"asiacrypt2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2023\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"HotCRP","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"375","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"106","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"12","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}