{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T19:21:18Z","timestamp":1792869678552,"version":"4.5.0"},"publisher-location":"Berlin, Heidelberg","reference-count":34,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642383472","type":"print"},{"value":"9783642383489","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38348-9_21","type":"book-chapter","created":{"date-parts":[[2013,5,9]],"date-time":"2013-05-09T00:46:38Z","timestamp":1368060398000},"page":"336-352","source":"Crossref","is-referenced-by-count":88,"title":["Practical Homomorphic MACs for Arithmetic Circuits"],"prefix":"10.1007","author":[{"given":"Dario","family":"Catalano","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dario","family":"Fiore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"21_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1007\/978-3-642-01957-9_18","volume-title":"Applied Cryptography and Network Security","author":"S. Agrawal","year":"2009","unstructured":"Agrawal, S., Boneh, D.: MACs: MAC-based integrity for network coding. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol.\u00a05536, pp. 292\u2013305. Springer, Heidelberg (2009)"},{"key":"21_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-28914-9_1","volume-title":"Theory of Cryptography","author":"J.H. Ahn","year":"2012","unstructured":"Ahn, J.H., Boneh, D., Camenisch, J., Hohenberger, S., Shelat, A., Waters, B.: Computing on authenticated data. In: Cramer, R. (ed.) TCC 2012. LNCS, vol.\u00a07194, pp. 1\u201320. Springer, Heidelberg (2012)"},{"key":"21_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-642-14165-2_14","volume-title":"Automata, Languages and Programming","author":"B. Applebaum","year":"2010","unstructured":"Applebaum, B., Ishai, Y., Kushilevitz, E.: From secrecy to soundness: Efficient verification via secure computation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010, Part I. LNCS, vol.\u00a06198, pp. 152\u2013163. Springer, Heidelberg (2010)"},{"key":"21_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/978-3-642-19379-8_2","volume-title":"Public Key Cryptography \u2013 PKC 2011","author":"N. Attrapadung","year":"2011","unstructured":"Attrapadung, N., Libert, B.: Homomorphic network coding signatures in the standard model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol.\u00a06571, pp. 17\u201334. Springer, Heidelberg (2011)"},{"key":"21_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/978-3-642-34961-4_23","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"N. Attrapadung","year":"2012","unstructured":"Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: New privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol.\u00a07658, pp. 367\u2013385. Springer, Heidelberg (2012)"},{"key":"21_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/978-3-642-36362-7_24","volume-title":"Public-Key Cryptography \u2013 PKC 2013","author":"N. Attrapadung","year":"2013","unstructured":"Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol.\u00a07778, pp. 386\u2013404. Springer, Heidelberg (2013)"},{"key":"21_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-642-22792-9_7","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"S. Benabbas","year":"2011","unstructured":"Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable delegation of computation over large datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol.\u00a06841, pp. 111\u2013131. Springer, Heidelberg (2011)"},{"key":"21_CR8","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again. In: ITCS 2012: Proceedings of the 3rd Symposium on Innovations in Theoretical Computer Science (2012)","DOI":"10.1145\/2090236.2090263"},{"key":"21_CR9","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: Recursive composition and bootstrapping for snarks and proof-carrying data. Cryptology ePrint Archive, Report 2012\/095 (2012), http:\/\/eprint.iacr.org","DOI":"10.1145\/2488608.2488623"},{"key":"21_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/978-3-642-00468-1_5","volume-title":"Public Key Cryptography \u2013 PKC 2009","author":"D. Boneh","year":"2009","unstructured":"Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: Signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol.\u00a05443, pp. 68\u201387. Springer, Heidelberg (2009)"},{"key":"21_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/978-3-642-20465-4_10","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"D. Boneh","year":"2011","unstructured":"Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol.\u00a06632, pp. 149\u2013168. Springer, Heidelberg (2011)"},{"key":"21_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-19379-8_1","volume-title":"Public Key Cryptography \u2013 PKC 2011","author":"D. Boneh","year":"2011","unstructured":"Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol.\u00a06571, pp. 1\u201316. Springer, Heidelberg (2011)"},{"key":"21_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-3-540-85538-5_3","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2008","author":"X. Boyen","year":"2008","unstructured":"Boyen, X.: The uber-assumption family: A unified complexity framework for bilinear groups. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol.\u00a05209, pp. 39\u201356. Springer, Heidelberg (2008)"},{"key":"21_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1007\/978-3-642-36594-2_38","volume-title":"Theory of Cryptography","author":"D. Catalano","year":"2013","unstructured":"Catalano, D., Fiore, D., Gennaro, R., Vamvourellis, K.: Algebraic (trapdoor) one way functions and their applications. In: Sahai, A. (ed.) TCC 2013. LNCS, vol.\u00a07785, pp. 680\u2013699. Springer, Heidelberg (2013)"},{"key":"21_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/978-3-642-20465-4_13","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"D. Catalano","year":"2011","unstructured":"Catalano, D., Fiore, D., Warinschi, B.: Adaptive pseudo-free groups and applications. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol.\u00a06632, pp. 207\u2013223. Springer, Heidelberg (2011)"},{"key":"21_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1007\/978-3-642-30057-8_40","volume-title":"Public Key Cryptography \u2013 PKC 2012","author":"D. Catalano","year":"2012","unstructured":"Catalano, D., Fiore, D., Warinschi, B.: Efficient network coding signatures in the standard model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol.\u00a07293, pp. 680\u2013696. Springer, Heidelberg (2012)"},{"key":"21_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-14623-7_26","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"K.-M. Chung","year":"2010","unstructured":"Chung, K.-M., Kalai, Y., Vadhan, S.: Improved delegation of computation using fully homomorphic encryption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol.\u00a06223, pp. 483\u2013501. Springer, Heidelberg (2010)"},{"key":"21_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/978-3-642-22792-9_9","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"K.-M. Chung","year":"2011","unstructured":"Chung, K.-M., Kalai, Y.T., Liu, F.-H., Raz, R.: Memory delegation. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol.\u00a06841, pp. 151\u2013168. Springer, Heidelberg (2011)"},{"key":"21_CR19","doi-asserted-by":"crossref","unstructured":"Fiore, D., Gennaro, R.: Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: 2012 ACM Conference on Computer and Communication Security. ACM Press (October 2012) Full version avaiable at, http:\/\/eprint.iacr.org\/2012\/281","DOI":"10.1145\/2382196.2382250"},{"key":"21_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1007\/978-3-642-30057-8_41","volume-title":"Public Key Cryptography \u2013 PKC 2012","author":"D.M. Freeman","year":"2012","unstructured":"Freeman, D.M.: Improved security for linearly homomorphic signatures: A generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol.\u00a07293, pp. 697\u2013714. Springer, Heidelberg (2012)"},{"key":"21_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/978-3-642-14623-7_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"R. Gennaro","year":"2010","unstructured":"Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: Outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol.\u00a06223, pp. 465\u2013482. Springer, Heidelberg (2010)"},{"key":"21_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1007\/978-3-642-13013-7_9","volume-title":"Public Key Cryptography \u2013 PKC 2010","author":"R. Gennaro","year":"2010","unstructured":"Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure network coding over the integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol.\u00a06056, pp. 142\u2013160. Springer, Heidelberg (2010)"},{"key":"21_CR23","doi-asserted-by":"crossref","unstructured":"Gennaro, R., Wichs, D.: Fully homomorphic message authenticators. Cryptology ePrint Archive, Report 2012\/290 (2012), http:\/\/eprint.iacr.org","DOI":"10.1007\/978-3-642-42045-0_16"},{"key":"21_CR24","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, Bethesda, Maryland, USA, May 31-June2, pp. 169\u2013178. ACM Press (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"21_CR25","doi-asserted-by":"crossref","unstructured":"Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, San Jose, California, USA, June\u00a06-8, pp. 99\u2013108. ACM Press (2011)","DOI":"10.1145\/1993636.1993651"},{"key":"21_CR26","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, Victoria, British Columbia, Canada, May\u00a017-20, pp. 113\u2013122. ACM Press (2008)","DOI":"10.1145\/1374376.1374396"},{"key":"21_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1007\/3-540-45760-7_17","volume-title":"Topics in Cryptology - CT-RSA 2002","author":"R. Johnson","year":"2002","unstructured":"Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol.\u00a02271, pp. 244\u2013262. Springer, Heidelberg (2002)"},{"key":"21_CR28","doi-asserted-by":"crossref","unstructured":"Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: 24th ACM STOC, Victoria, British Columbia, Canada, May\u00a04-6, pp. 723\u2013732. ACM Press (1992)","DOI":"10.1145\/129712.129782"},{"key":"21_CR29","unstructured":"Micali, S.: Cs proofs. In: 35th FOCS, Santa Fe, New Mexico, November\u00a020-22 (1994)"},{"issue":"2","key":"21_CR30","first-page":"481","volume":"E85-A","author":"S. Mitsunari","year":"2002","unstructured":"Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Transactions on Fundamentals\u00a0E85-A(2), 481\u2013484 (2002)","journal-title":"IEICE Transactions on Fundamentals"},{"key":"21_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1007\/978-3-642-28914-9_24","volume-title":"Theory of Cryptography","author":"B. Parno","year":"2012","unstructured":"Parno, B., Raykova, M., Vaikuntanathan, V.: How to delegate and verify in public: Verifiable computation from attribute-based encryption. In: Cramer, R. (ed.) TCC 2012. LNCS, vol.\u00a07194, pp. 422\u2013439. Springer, Heidelberg (2012)"},{"key":"21_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/978-3-540-89255-7_7","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"H. Shacham","year":"2008","unstructured":"Shacham, H., Waters, B.: Compact proofs of retrievability. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol.\u00a05350, pp. 90\u2013107. Springer, Heidelberg (2008)"},{"issue":"3-4","key":"21_CR33","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1561\/0400000039","volume":"5","author":"A. Shpilka","year":"2010","unstructured":"Shpilka, A., Yehudayoff, A.: Arithmetic circuits: A survey of recent results and open questions. Foundations and Trends in Theoretical Computer Science\u00a05(3-4), 207\u2013388 (2010)","journal-title":"Foundations and Trends in Theoretical Computer Science"},{"key":"21_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-540-78524-8_1","volume-title":"Theory of Cryptography","author":"P. Valiant","year":"2008","unstructured":"Valiant, P.: Incrementally verifiable computation or proofs of knowledge imply time\/Space efficiency. In: Canetti, R. (ed.) TCC 2008. LNCS, vol.\u00a04948, pp. 1\u201318. Springer, Heidelberg (2008)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2013"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38348-9_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T09:17:43Z","timestamp":1746004663000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-38348-9_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642383472","9783642383489"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38348-9_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}