{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:43:31Z","timestamp":1767339811926,"version":"build-2065373602"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031643804"},{"type":"electronic","value":"9783031643811"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"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":[[2024]]},"DOI":"10.1007\/978-3-031-64381-1_4","type":"book-chapter","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T23:01:56Z","timestamp":1719961316000},"page":"69-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["CDLS: Proving Knowledge of\u00a0Committed Discrete Logarithms with\u00a0Soundness"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3333-7764","authenticated-orcid":false,"given":"Sofia","family":"Celi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4632-9488","authenticated-orcid":false,"given":"Shai","family":"Levin","sequence":"additional","affiliation":[]},{"given":"Joe","family":"Rowell","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"4_CR1","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, Part III. LNCS, vol. 10993, pp. 643\u2013673. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_22"},{"key":"4_CR2","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-031-22318-1_5","volume-title":"TCC 2022, Part I","author":"T Attema","year":"2022","unstructured":"Attema, T., Fehr, S., Kloo\u00df, M.: Fiat-Shamir transformation of multi-round interactive proofs. In: Kiltz, E., Vaikuntanathan, V. (eds.) TCC 2022, Part I. LNCS, vol. 13747, pp. 113\u2013142. Springer, Heidelberg (2022). https:\/\/doi.org\/10.1007\/978-3-031-22318-1_5"},{"key":"4_CR3","doi-asserted-by":"publisher","unstructured":"Babai, L.: Trading group theory for randomness. In: Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, STOC 1985, pp. 421\u2013429. Association for Computing Machinery, New York (1985). https:\/\/doi.org\/10.1145\/22145.22192","DOI":"10.1145\/22145.22192"},{"key":"4_CR4","doi-asserted-by":"publisher","unstructured":"Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 103\u2013112. Association for Computing Machinery, New York (1988). https:\/\/doi.org\/10.1145\/62212.62222","DOI":"10.1145\/62212.62222"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1007\/3-540-45539-6_31","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2000","author":"F Boudot","year":"2000","unstructured":"Boudot, F.: Efficient proofs that a committed number lies in an interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431\u2013444. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/3-540-45539-6_31"},{"key":"4_CR6","unstructured":"Broker, R.: Constructing elliptic curves of prescribed order. Ph.D. thesis (2006)"},{"key":"4_CR7","doi-asserted-by":"publisher","unstructured":"B\u00fcnz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy, pp. 315\u2013334. IEEE Computer Society Press (2018). https:\/\/doi.org\/10.1109\/SP.2018.00020","DOI":"10.1109\/SP.2018.00020"},{"key":"4_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/978-3-540-89255-7_15","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"J Camenisch","year":"2008","unstructured":"Camenisch, J., Chaabouni, R., Shelat, A.: Efficient protocols for set membership and range proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234\u2013252. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-89255-7_15"},{"key":"4_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/3-540-48910-X_8","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201999","author":"J Camenisch","year":"1999","unstructured":"Camenisch, J., Michels, M.: Proving in zero-knowledge that a number is the product of two safe primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 107\u2013122. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48910-X_8"},{"key":"4_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1007\/BFb0052252","volume-title":"Advances in Cryptology \u2014 CRYPTO \u201997","author":"J Camenisch","year":"1997","unstructured":"Camenisch, J., Stadler, M.: Efficient group signature schemes for large groups. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410\u2013424. Springer, Heidelberg (1997). https:\/\/doi.org\/10.1007\/BFb0052252"},{"key":"4_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/3-540-48071-4_7","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 92","author":"D Chaum","year":"1993","unstructured":"Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89\u2013105. Springer, Heidelberg (1993). https:\/\/doi.org\/10.1007\/3-540-48071-4_7"},{"key":"4_CR12","unstructured":"Cramer, R.: Modular design of secure yet practical cryptographic protocols. Ph.D. thesis (1997)"},{"key":"4_CR13","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":"4_CR14","unstructured":"Damg\u00e5rd, I.: On sigma-protocols (2010). https:\/\/www.cs.au.dk\/~ivan\/Sigma.pdf. https:\/\/www.cs.au.dk\/~ivan\/Sigma.pdf"},{"key":"4_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/978-3-030-99277-4_4","volume-title":"Selected Areas in Cryptography","author":"A Faz-Hern\u00e1ndez","year":"2022","unstructured":"Faz-Hern\u00e1ndez, A., Ladd, W., Maram, D.: ZKAttest: ring and\u00a0group signatures for\u00a0existing ECDSA keys. In: AlTawy, R., H\u00fclsing, A. (eds.) SAC 2021. LNCS, vol. 13203, pp. 68\u201383. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99277-4_4"},{"issue":"2","key":"4_CR16","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF02351717","volume":"1","author":"U Feige","year":"1988","unstructured":"Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identity. J. Cryptol. 1(2), 77\u201394 (1988). https:\/\/doi.org\/10.1007\/BF02351717","journal-title":"J. Cryptol."},{"key":"4_CR17","doi-asserted-by":"publisher","unstructured":"Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: 22nd ACM STOC, pp. 416\u2013426. ACM Press (1990). https:\/\/doi.org\/10.1145\/100216.100272","DOI":"10.1145\/100216.100272"},{"key":"4_CR18","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":"4_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/BFb0052225","volume-title":"Advances in Cryptology \u2014 CRYPTO \u201997","author":"E Fujisaki","year":"1997","unstructured":"Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16\u201330. Springer, Heidelberg (1997). https:\/\/doi.org\/10.1007\/BFb0052225"},{"key":"4_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1007\/BFb0032038","volume-title":"Automata, Languages and Programming","author":"O Goldreich","year":"1990","unstructured":"Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 268\u2013282. Springer, Heidelberg (1990). https:\/\/doi.org\/10.1007\/BFb0032038"},{"key":"4_CR21","series-title":"Information Security and Cryptography","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-642-14303-8_6","volume-title":"Efficient Secure Two-Party Protocols","author":"C Hazay","year":"2010","unstructured":"Hazay, C., Lindell, Y.: Sigma protocols and efficient zero-knowledge$$^{1}$$. In: Hazay, C., Lindell, Y. (eds.) Efficient Secure Two-Party Protocols. ISC, pp. 147\u2013175. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14303-8_6"},{"key":"4_CR22","unstructured":"Krenn, S., Orr\u00f9, M.: Proposal: $$\\sigma $$-protocols (2021). https:\/\/docs.zkproof.org\/pages\/standards\/accepted-workshop4\/proposal-sigma.pdf"},{"key":"4_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/978-3-540-47942-0_9","volume-title":"Information and Communication Security","author":"KQ Nguyen","year":"1999","unstructured":"Nguyen, K.Q., Bao, F., Mu, Y., Varadharajan, V.: Zero-knowledge proofs of possession of digital signatures and its applications. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 103\u2013118. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/978-3-540-47942-0_9"},{"key":"4_CR24","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"},{"issue":"3","key":"4_CR25","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF00196725","volume":"4","author":"CP Schnorr","year":"1991","unstructured":"Schnorr, C.P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161\u2013174 (1991). https:\/\/doi.org\/10.1007\/BF00196725","journal-title":"J. Cryptol."},{"key":"4_CR26","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-0-387-09494-6_3","volume-title":"The Arithmetic of Elliptic Curves","author":"JH Silverman","year":"2009","unstructured":"Silverman, J.H.: The geometry of elliptic curves. In: Silverman, J.H. (ed.) The Arithmetic of Elliptic Curves. GTM, vol. 106, pp. 41\u2013114. Springer, New York (2009). https:\/\/doi.org\/10.1007\/978-0-387-09494-6_3"},{"key":"4_CR27","doi-asserted-by":"publisher","unstructured":"Wahby, R.S., Tzialla, I., Shelat, A., Thaler, J., Walfish, M.: Doubly-efficient zkSNARKs without trusted setup. In: 2018 IEEE Symposium on Security and Privacy, pp. 926\u2013943. IEEE Computer Society Press (2018). https:\/\/doi.org\/10.1109\/SP.2018.00060","DOI":"10.1109\/SP.2018.00060"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology - AFRICACRYPT 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-64381-1_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T23:02:27Z","timestamp":1719961347000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-64381-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031643804","9783031643811"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-64381-1_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"3 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"AFRICACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptology in Africa","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Douala","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cameroon","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"africacrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}