{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T02:38:02Z","timestamp":1779935882733,"version":"3.53.1"},"publisher-location":"Cham","reference-count":41,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031587368","type":"print"},{"value":"9783031587375","type":"electronic"}],"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\/978-3-031-58737-5_10","type":"book-chapter","created":{"date-parts":[[2024,4,27]],"date-time":"2024-04-27T07:01:52Z","timestamp":1714201312000},"page":"255-285","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["New Limits of\u00a0Provable Security and\u00a0Applications to\u00a0ElGamal Encryption"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8698-4244","authenticated-orcid":false,"given":"Sven","family":"Sch\u00e4ge","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,28]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","unstructured":"Auerbach, B., Cash, D., Fersch, M., Kiltz, E.: Memory-tight reductions. In: Katz, J., Shacham, H. (eds.) CRYPTO\u00a02017, Part\u00a0I, LNCS, vol. 10401, pp. 101\u2013132. Springer, Heidelberg, August 2017. https:\/\/doi.org\/10.1007\/978-3-319-63688-7_4","DOI":"10.1007\/978-3-319-63688-7_4"},{"key":"10_CR2","doi-asserted-by":"publisher","unstructured":"Bader, C., Jager, T., Li, Y., Sch\u00e4ge, S.: On the impossibility of tight cryptographic reductions. In: Fischlin, M., Coron, J.S. (eds.) EUROCRYPT\u00a02016, Part\u00a0II. LNCS, vol.\u00a09666, pp. 273\u2013304. Springer, Heidelberg, May 2016.https:\/\/doi.org\/10.1007\/978-3-662-49896-5_10","DOI":"10.1007\/978-3-662-49896-5_10"},{"key":"10_CR3","doi-asserted-by":"publisher","unstructured":"Baecher, P., Brzuska, C., Fischlin, M.: Notions of black-box reductions, revisited. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT\u00a02013, Part\u00a0I. LNCS, vol.\u00a08269, pp. 296\u2013315. Springer, Heidelberg, December 2013. https:\/\/doi.org\/10.1007\/978-3-642-42033-7_16","DOI":"10.1007\/978-3-642-42033-7_16"},{"key":"10_CR4","doi-asserted-by":"publisher","unstructured":"Baldimtsi, F., Lysyanskaya, A.: On the security of one-witness blind signature schemes. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT\u00a02013, Part\u00a0II. LNCS, vol.\u00a08270, pp. 82\u201399. Springer, Heidelberg, December 2013. https:\/\/doi.org\/10.1007\/978-3-642-42045-0_5","DOI":"10.1007\/978-3-642-42045-0_5"},{"key":"10_CR5","doi-asserted-by":"publisher","unstructured":"Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO\u00a02001. LNCS, vol.\u00a02139, pp. 213\u2013229. Springer, Heidelberg, August 2001. https:\/\/doi.org\/10.1007\/3-540-44647-8_13","DOI":"10.1007\/3-540-44647-8_13"},{"key":"10_CR6","doi-asserted-by":"publisher","unstructured":"Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Nyberg, K. (ed.) EUROCRYPT\u201998. LNCS, vol.\u00a01403, pp. 59\u201371. Springer, Heidelberg, May\/June 1998. https:\/\/doi.org\/10.1007\/BFb0054117","DOI":"10.1007\/BFb0054117"},{"key":"10_CR7","doi-asserted-by":"publisher","unstructured":"Bresson, E., Monnerat, J., Vergnaud, D.: Separation results on the \u201cone-more\u201d computational problems. In: Malkin, T. (ed.) CT-RSA\u00a02008. LNCS, vol.\u00a04964, pp. 71\u201387. Springer, Heidelberg, April 2008. https:\/\/doi.org\/10.1007\/978-3-540-79263-5_5","DOI":"10.1007\/978-3-540-79263-5_5"},{"key":"10_CR8","unstructured":"Brown, D.R.L.: Irreducibility to the one-more evaluation problems: more may be less. Cryptology ePrint Archive, Report 2007\/435 (2007). http:\/\/eprint.iacr.org\/"},{"key":"10_CR9","doi-asserted-by":"publisher","unstructured":"Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge (extended abstract). In: 32nd ACM STOC, pp. 235\u2013244. ACM Press, May 2000. https:\/\/doi.org\/10.1145\/335305.335334","DOI":"10.1145\/335305.335334"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: 51st FOCS, pp. 541\u2013550. IEEE Computer Society Press, October 2010. https:\/\/doi.org\/10.1109\/FOCS.2010.86","DOI":"10.1109\/FOCS.2010.86"},{"key":"10_CR11","doi-asserted-by":"publisher","unstructured":"Chung, K., Lin, H., Mahmoody, M., Pass, R.: On the power of nonuniformity in proofs of security. In: Kleinberg, R.D. (ed.) ITCS \u201913, Berkeley, CA, USA, 9-12 January 2013, pp. 389\u2013400. ACM (2013). https:\/\/doi.org\/10.1145\/2422436.2422480","DOI":"10.1145\/2422436.2422480"},{"key":"10_CR12","doi-asserted-by":"publisher","unstructured":"Coron, J.S.: Optimal security proofs for PSS and other signature schemes. In: Knudsen, L.R. (ed.) EUROCRYPT\u00a02002, LNCS, vol.\u00a02332, pp. 272\u2013287. Springer, Heidelberg, Apr\/May 2002. https:\/\/doi.org\/10.1007\/3-540-46035-7_18","DOI":"10.1007\/3-540-46035-7_18"},{"key":"10_CR13","doi-asserted-by":"publisher","unstructured":"Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO\u201998, LNCS, vol.\u00a01462, pp. 13\u201325. Springer, Heidelberg, August 1998. https:\/\/doi.org\/10.1007\/BFb0055717","DOI":"10.1007\/BFb0055717"},{"key":"10_CR14","doi-asserted-by":"publisher","unstructured":"Damg\u00e5rd, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier\u2019s probabilistic public-key system. In: Kim, K. (ed.) PKC\u00a02001. LNCS, vol.\u00a01992, pp. 119\u2013136. Springer, Heidelberg, February 2001. https:\/\/doi.org\/10.1007\/3-540-44586-2_9","DOI":"10.1007\/3-540-44586-2_9"},{"key":"10_CR15","doi-asserted-by":"publisher","unstructured":"Deng, Y., Goyal, V., Sahai, A.: Resolving the simultaneous resettability conjecture and a new non-black-box simulation strategy. In: 50th FOCS, pp. 251\u2013260. IEEE Computer Society Press, October 2009. https:\/\/doi.org\/10.1109\/FOCS.2009.59","DOI":"10.1109\/FOCS.2009.59"},{"issue":"6","key":"10_CR16","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644\u2013654 (1976). https:\/\/doi.org\/10.1109\/TIT.1976.1055638","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"Dodis, Y., Oliveira, R., Pietrzak, K.: On the generic insecurity of the full domain hash. In: Shoup, V. (ed.) CRYPTO\u00a02005. LNCS, vol.\u00a03621, pp. 449\u2013466. Springer, Heidelberg, August 2005. https:\/\/doi.org\/10.1007\/11535218_27","DOI":"10.1007\/11535218_27"},{"key":"10_CR18","doi-asserted-by":"publisher","unstructured":"Dodis, Y., Reyzin, L.: On the power of claw-free permutations. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 02. LNCS, vol.\u00a02576, pp. 55\u201373. Springer, Heidelberg, September 2003. https:\/\/doi.org\/10.1007\/3-540-36413-7_5","DOI":"10.1007\/3-540-36413-7_5"},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO\u201984. LNCS, vol. 196, pp. 10\u201318. Springer, Heidelberg, August 1984","DOI":"10.1007\/3-540-39568-7_2"},{"key":"10_CR20","doi-asserted-by":"publisher","unstructured":"Fischlin, M., Fleischhacker, N.: Limitations of the meta-reduction technique: the case of Schnorr signatures. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT\u00a02013. LNCS, vol.\u00a07881, pp. 444\u2013460. Springer, Heidelberg, May 2013. https:\/\/doi.org\/10.1007\/978-3-642-38348-9_27","DOI":"10.1007\/978-3-642-38348-9_27"},{"key":"10_CR21","doi-asserted-by":"publisher","unstructured":"Fleischhacker, N., Jager, T., Schr\u00f6der, D.: On tight security proofs for Schnorr signatures. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT\u00a02014, Part\u00a0I. LNCS, vol.\u00a08873, pp. 512\u2013531. Springer, Heidelberg, December 2014. https:\/\/doi.org\/10.1007\/978-3-662-45611-8_27","DOI":"10.1007\/978-3-662-45611-8_27"},{"key":"10_CR22","doi-asserted-by":"publisher","unstructured":"Fuchsbauer, G., Kiltz, E., Loss, J.: The algebraic group model and its applications. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO\u00a02018, Part\u00a0II. LNCS, vol. 10992, pp. 33\u201362. Springer, Heidelberg, August 2018. https:\/\/doi.org\/10.1007\/978-3-319-96881-0_2","DOI":"10.1007\/978-3-319-96881-0_2"},{"key":"10_CR23","doi-asserted-by":"publisher","unstructured":"Garg, S., Bhaskar, R., Lokam, S.V.: Improved bounds on security reductions for discrete log based signatures. In: Wagner, D. (ed.) CRYPTO\u00a02008. LNCS, vol.\u00a05157, pp. 93\u2013107. Springer, Heidelberg, August 2008. https:\/\/doi.org\/10.1007\/978-3-540-85174-5_6","DOI":"10.1007\/978-3-540-85174-5_6"},{"key":"10_CR24","doi-asserted-by":"publisher","unstructured":"Hanaoka, G., Matsuda, T., Schuldt, J.C.N.: On the impossibility of constructing efficient key encapsulation and programmable hash functions in prime order groups. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO\u00a02012. LNCS, vol.\u00a07417, pp. 812\u2013831. Springer, Heidelberg, August 2012. https:\/\/doi.org\/10.1007\/978-3-642-32009-5_47","DOI":"10.1007\/978-3-642-32009-5_47"},{"key":"10_CR25","doi-asserted-by":"publisher","unstructured":"Hofheinz, D., Jager, T., Knapp, E.: Waters signatures with optimal security reduction. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC\u00a02012. LNCS, vol.\u00a07293, pp. 66\u201383. Springer, Heidelberg, May 2012. https:\/\/doi.org\/10.1007\/978-3-642-30057-8_5","DOI":"10.1007\/978-3-642-30057-8_5"},{"key":"10_CR26","doi-asserted-by":"publisher","unstructured":"Kakvi, S.A., Kiltz, E.: Optimal security proofs for full domain hash, revisited. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT\u00a02012. LNCS, vol.\u00a07237, pp. 537\u2013553. Springer, Heidelberg, April 2012. https:\/\/doi.org\/10.1007\/978-3-642-29011-4_32","DOI":"10.1007\/978-3-642-29011-4_32"},{"key":"10_CR27","unstructured":"Lindell, Y.: Is ElGamal IND-CCA1 Secure? \u2013 answer. https:\/\/crypto.stackexchange.com\/questions\/26867\/is-elgamal-ind-cca1 (2015). Accessed 03 April 2022"},{"key":"10_CR28","doi-asserted-by":"publisher","unstructured":"Lindell, Y.: Fast secure two-party ECDSA signing. In: Katz, J., Shacham, H. (eds.) CRYPTO\u00a02017, Part\u00a0II. LNCS, vol. 10402, pp. 613\u2013644. Springer, Heidelberg, August 2017. https:\/\/doi.org\/10.1007\/978-3-319-63715-0_21","DOI":"10.1007\/978-3-319-63715-0_21"},{"key":"10_CR29","unstructured":"Lipmaa, H.: On the CCA1-security of Elgamal and Damg\u00e5rd\u2019s Elgamal. Cryptology ePrint Archive, Report 2008\/234 (2008). https:\/\/ia.cr\/2008\/234"},{"key":"10_CR30","doi-asserted-by":"publisher","unstructured":"Morgan, A., Pass, R.: On the security loss of unique signatures. In: Beimel, A., Dziembowski, S. (eds.) TCC\u00a02018, Part\u00a0I. LNCS, vol. 11239, pp. 507\u2013536. Springer, Heidelberg, November 2018. https:\/\/doi.org\/10.1007\/978-3-030-03807-6_19","DOI":"10.1007\/978-3-030-03807-6_19"},{"key":"10_CR31","doi-asserted-by":"publisher","unstructured":"Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT\u201999. LNCS, vol.\u00a01592, pp. 223\u2013238. Springer, Heidelberg, May 1999. https:\/\/doi.org\/10.1007\/3-540-48910-X_16","DOI":"10.1007\/3-540-48910-X_16"},{"key":"10_CR32","doi-asserted-by":"publisher","unstructured":"Paillier, P., Vergnaud, D.: Discrete-log-based signatures may not be equivalent to discrete log. In: Roy, B.K. (ed.) ASIACRYPT\u00a02005. LNCS, vol.\u00a03788, pp. 1\u201320. Springer, Heidelberg, December 2005. https:\/\/doi.org\/10.1007\/11593447_1","DOI":"10.1007\/11593447_1"},{"key":"10_CR33","doi-asserted-by":"publisher","unstructured":"Paillier, P., Villar, J.L.: Trading one-wayness against chosen-ciphertext security in factoring-based encryption. In: Lai, X., Chen, K. (eds.) ASIACRYPT\u00a02006. LNCS, vol.\u00a04284, pp. 252\u2013266. Springer, Heidelberg, December 2006. https:\/\/doi.org\/10.1007\/11935230_17","DOI":"10.1007\/11935230_17"},{"key":"10_CR34","doi-asserted-by":"publisher","unstructured":"Pass, R.: Limits of provable security from standard assumptions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC. pp. 109\u2013118. ACM Press, June 2011. https:\/\/doi.org\/10.1145\/1993636.1993652","DOI":"10.1145\/1993636.1993652"},{"key":"10_CR35","doi-asserted-by":"publisher","unstructured":"Pass, R., Venkitasubramaniam, M.: On constant-round concurrent zero-knowledge. In: Canetti, R. (ed.) TCC\u00a02008. LNCS, vol.\u00a04948, pp. 553\u2013570. Springer, Heidelberg, March 2008. https:\/\/doi.org\/10.1007\/978-3-540-78524-8_30","DOI":"10.1007\/978-3-540-78524-8_30"},{"key":"10_CR36","doi-asserted-by":"publisher","unstructured":"Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT\u201996. LNCS, vol.\u00a01070, pp. 387\u2013398. Springer, Heidelberg, May 1996. https:\/\/doi.org\/10.1007\/3-540-68339-9_33","DOI":"10.1007\/3-540-68339-9_33"},{"key":"10_CR37","doi-asserted-by":"publisher","unstructured":"Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC\u00a02004. LNCS, vol.\u00a02951, pp. 1\u201320. Springer, Heidelberg, February 2004. https:\/\/doi.org\/10.1007\/978-3-540-24638-1_1","DOI":"10.1007\/978-3-540-24638-1_1"},{"key":"10_CR38","doi-asserted-by":"publisher","unstructured":"Richardson, R., Kilian, J.: On the concurrent composition of zero-knowledge proofs. In: Stern, J. (ed.) EUROCRYPT\u201999. LNCS, vol.\u00a01592, pp. 415\u2013431. Springer, Heidelberg, May 1999. https:\/\/doi.org\/10.1007\/3-540-48910-X_29","DOI":"10.1007\/3-540-48910-X_29"},{"key":"10_CR39","doi-asserted-by":"publisher","unstructured":"Seurin, Y.: On the exact security of Schnorr-type signatures in the random oracle model. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT\u00a02012. LNCS, vol.\u00a07237, pp. 554\u2013571. Springer, Heidelberg, April 2012. https:\/\/doi.org\/10.1007\/978-3-642-29011-4_33","DOI":"10.1007\/978-3-642-29011-4_33"},{"key":"10_CR40","unstructured":"Wu, J., Stinson, D.R.: On the security of the ElGamal encryption scheme and Damg\u00e5rd\u2019s variant. IACR Cryptol. ePrint Arch. p.\u00a0200 (2008). http:\/\/eprint.iacr.org\/2008\/200"},{"key":"10_CR41","doi-asserted-by":"publisher","unstructured":"Zhang, J., Zhang, Z., Chen, Y., Guo, Y., Zhang, Z.: Black-box separations for one-more (static) CDH and its generalization. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT\u00a02014, Part\u00a0II. LNCS, vol.\u00a08874, pp. 366\u2013385. Springer, Heidelberg, December 2014. https:\/\/doi.org\/10.1007\/978-3-662-45608-8_20","DOI":"10.1007\/978-3-662-45608-8_20"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-58737-5_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T00:03:28Z","timestamp":1777248208000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-58737-5_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031587368","9783031587375"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-58737-5_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"28 April 2024","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":"Zurich","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Switzerland","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":"26 May 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 May 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"43","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}