{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:48:27Z","timestamp":1787705307832,"version":"build-2784847793"},"publisher-location":"Berlin, Heidelberg","reference-count":37,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662456071","type":"print"},{"value":"9783662456088","type":"electronic"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-45611-8_29","type":"book-chapter","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T10:34:07Z","timestamp":1415961247000},"page":"551-572","source":"Crossref","is-referenced-by-count":79,"title":["Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures"],"prefix":"10.1007","author":[{"given":"Fabrice","family":"Benhamouda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Camenisch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephan","family":"Krenn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vadim","family":"Lyubashevsky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory","family":"Neven","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"29_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-29011-4_29","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"G. Asharov","year":"2012","unstructured":"Asharov, G., Jain, A., L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol.\u00a07237, pp. 483\u2013501. Springer, Heidelberg (2012)"},{"key":"29_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1007\/BFb0054156","volume-title":"Advances in Cryptology - EUROCRYPT \u201998","author":"N. Asokan","year":"1998","unstructured":"Asokan, N., Shoup, V., Waidner, M.: Optimistic fair exchange of digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 591\u2013606. Springer, Heidelberg (1998)"},{"key":"29_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/3-540-44598-6_16","volume-title":"Advances in Cryptology - CRYPTO 2000","author":"G. Ateniese","year":"2000","unstructured":"Ateniese, G., Camenisch, J., Joye, M., Tsudik, G.: A practical and provably secure coalition-resistant group signature scheme. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol.\u00a01880, pp. 255\u2013270. Springer, Heidelberg (2000)"},{"key":"29_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1007\/3-540-48071-4_28","volume-title":"Advances in Cryptology - CRYPTO \u201992","author":"M. Bellare","year":"1993","unstructured":"Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol.\u00a0740, pp. 390\u2013420. Springer, Heidelberg (1993)"},{"key":"29_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1007\/3-540-39200-9_38","volume-title":"Advances in Cryptology \u2013 EUROCRPYT 2003","author":"M. Bellare","year":"2003","unstructured":"Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: Formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol.\u00a02656, pp. 614\u2013629. Springer, Heidelberg (2003)"},{"key":"29_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1007\/978-3-540-24676-3_4","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 56\u201373. Springer, Heidelberg (2004)"},{"issue":"2","key":"29_CR7","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s00145-007-9005-7","volume":"21","author":"D. Boneh","year":"2008","unstructured":"Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. Journal of Cryptology\u00a021(2), 149\u2013177 (2008)","journal-title":"Journal of Cryptology"},{"key":"29_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-540-28628-8_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 41\u201355. Springer, Heidelberg (2004)"},{"key":"29_CR9","doi-asserted-by":"crossref","unstructured":"Camenisch, J., Dubovitskaya, M., Neven, G.: Oblivious transfer with access control. In: ACM Conference on Computer and Communications Security, pp. 131\u2013140 (2009)","DOI":"10.1145\/1653662.1653679"},{"key":"29_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/978-3-642-32928-9_4","volume-title":"Security and Cryptography for Networks","author":"J. Camenisch","year":"2012","unstructured":"Camenisch, J., Neven, G., R\u00fcckert, M.: Fully anonymous attribute tokens from lattices. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol.\u00a07485, pp. 57\u201375. Springer, Heidelberg (2012)"},{"key":"29_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/11818175_5","volume-title":"Advances in Cryptology - CRYPTO 2006","author":"M. Chase","year":"2006","unstructured":"Chase, M., Lysyanskaya, A.: On signatures of knowledge. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol.\u00a04117, pp. 78\u201396. Springer, Heidelberg (2006)"},{"key":"29_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/3-540-46416-6_22","volume-title":"Advances in Cryptology - EUROCRYPT \u201991","author":"D. Chaum","year":"1991","unstructured":"Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol.\u00a0547, pp. 257\u2013265. Springer, Heidelberg (1991)"},{"key":"29_CR13","unstructured":"Cramer, R.: Modular Design of Secure yet Practical Cryptographic Protocols. Ph.D. thesis, CWI and University of Amsterdam (1997)"},{"key":"29_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1007\/3-540-45539-6_30","volume-title":"Advances in Cryptology - EUROCRYPT 2000","author":"I.B. Damg\u00e5rd","year":"2000","unstructured":"Damg\u00e5rd, I.B.: Efficient concurrent zero-knowledge in the auxiliary string model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol.\u00a01807, pp. 418\u2013430. Springer, Heidelberg (2000)"},{"key":"29_CR15","unstructured":"Damg\u00e5rd, I.: On \u03a3-Protocols. Lecture on Cryptologic Protocol Theory; Faculty of Science, University of Aarhus (2010)"},{"key":"29_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/3-540-36178-2_8","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"I.B. Damg\u00e5rd","year":"2002","unstructured":"Damg\u00e5rd, I.B., Fujisaki, E.: A statistically-hiding integer commitment scheme based on groups with hidden order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol.\u00a02501, pp. 125\u2013142. Springer, Heidelberg (2002)"},{"key":"29_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/3-540-44750-4_26","volume-title":"Advances in Cryptology - CRYPTO \u201995","author":"I.B. Damg\u00e5rd","year":"1995","unstructured":"Damg\u00e5rd, I.B., Goldreich, O., Okamoto, T., Wigderson, A.: Honest verifier vs dishonest verifier in public coin zero-knowledge proofs. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol.\u00a0963, pp. 325\u2013338. Springer, Heidelberg (1995)"},{"key":"29_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/978-3-642-32009-5_38","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"I. Damg\u00e5rd","year":"2012","unstructured":"Damg\u00e5rd, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol.\u00a07417, pp. 643\u2013662. Springer, Heidelberg (2012)"},{"key":"29_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/BFb0052225","volume-title":"Advances in Cryptology - CRYPTO \u201997","author":"E. Fujisaki","year":"1997","unstructured":"Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol.\u00a01294, pp. 16\u201330. Springer, Heidelberg (1997)"},{"key":"29_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-38348-9_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"S. Garg","year":"2013","unstructured":"Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol.\u00a07881, pp. 1\u201317. Springer, Heidelberg (2013)"},{"key":"29_CR21","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169\u2013178 (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"29_CR22","doi-asserted-by":"crossref","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197\u2013206 (2008)","DOI":"10.1145\/1374376.1374407"},{"key":"29_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/978-3-642-17373-8_23","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"S.D. Gordon","year":"2010","unstructured":"Gordon, S.D., Katz, J., Vaikuntanathan, V.: A group signature scheme from lattice assumptions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol.\u00a06477, pp. 395\u2013412. Springer, Heidelberg (2010)"},{"key":"29_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BFb0054868","volume-title":"Algorithmic Number Theory","author":"J. Hoffstein","year":"1998","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol.\u00a01423, pp. 267\u2013288. Springer, Heidelberg (1998)"},{"key":"29_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-642-42045-0_3","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"F. Laguillaumie","year":"2013","unstructured":"Laguillaumie, F., Langlois, A., Libert, B., Stehl\u00e9, D.: Lattice-based group signatures with logarithmic signature size. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol.\u00a08270, pp. 41\u201361. Springer, Heidelberg (2013)"},{"key":"29_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/978-3-642-36362-7_8","volume-title":"Public-Key Cryptography \u2013 PKC 2013","author":"S. Ling","year":"2013","unstructured":"Ling, S., Nguyen, K., Stehl\u00e9, D., Wang, H.: Improved zero-knowledge proofs of knowledge for the ISIS problem, and applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol.\u00a07778, pp. 107\u2013124. Springer, Heidelberg (2013)"},{"key":"29_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/978-3-540-78440-1_10","volume-title":"Public Key Cryptography \u2013 PKC 2008","author":"V. Lyubashevsky","year":"2008","unstructured":"Lyubashevsky, V.: Lattice-based identification schemes secure under active attacks. In: Cramer, R. (ed.) PKC 2008. LNCS, vol.\u00a04939, pp. 162\u2013179. Springer, Heidelberg (2008)"},{"key":"29_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1007\/978-3-642-10366-7_35","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2009","author":"V. Lyubashevsky","year":"2009","unstructured":"Lyubashevsky, V.: Fiat-shamir with aborts: Applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol.\u00a05912, pp. 598\u2013616. Springer, Heidelberg (2009)"},{"key":"29_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1007\/978-3-642-29011-4_43","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"V. Lyubashevsky","year":"2012","unstructured":"Lyubashevsky, V.: Lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol.\u00a07237, pp. 738\u2013755. Springer, Heidelberg (2012)"},{"key":"29_CR30","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. J. ACM\u00a060(6), 43 (2013), Preliminary version appeared in Gilbert, H. (ed.): EUROCRYPT 2010. LNCS, vol.\u00a06110, pp. 1\u201323. Springer, Heidelberg (2010)"},{"key":"29_CR31","doi-asserted-by":"crossref","unstructured":"Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: 22nd ACM STOC. pp. 427\u2013437. ACM Press (May 1990)","DOI":"10.1145\/100216.100273"},{"key":"29_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/3-540-46766-1_9","volume-title":"Advances in Cryptology - CRYPTO \u201991","author":"T.P. Pedersen","year":"1992","unstructured":"Pedersen, T.P.: Non-interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol.\u00a0576, pp. 129\u2013140. Springer, Heidelberg (1992)"},{"key":"29_CR33","doi-asserted-by":"crossref","unstructured":"Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: 40th FOCS, pp. 543\u2013553. IEEE Computer Society Press (October 1999)","DOI":"10.1109\/SFFCS.1999.814628"},{"key":"29_CR34","unstructured":"Santis, A.D., Persiano, G.: Zero-knowledge proofs of knowledge without interaction (extended abstract). In: 33rd FOCS, pp. 427\u2013436. IEEE Computer Society Press (October)"},{"key":"29_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/978-3-642-20465-4_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"D. Stehl\u00e9","year":"2011","unstructured":"Stehl\u00e9, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol.\u00a06632, pp. 27\u201347. Springer, Heidelberg (2011)"},{"key":"29_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/978-3-642-10366-7_36","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2009","author":"D. Stehl\u00e9","year":"2009","unstructured":"Stehl\u00e9, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol.\u00a05912, pp. 617\u2013635. Springer, Heidelberg (2009)"},{"key":"29_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/3-540-48329-2_2","volume-title":"Advances in Cryptology - CRYPTO \u201993","author":"J. Stern","year":"1994","unstructured":"Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol.\u00a0773, pp. 13\u201321. Springer, Heidelberg (1994)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2014"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-45611-8_29","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T17:53:33Z","timestamp":1747158813000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-45611-8_29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662456071","9783662456088"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-45611-8_29","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}