{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T11:26:18Z","timestamp":1765106778768,"version":"3.46.0"},"publisher-location":"Singapore","reference-count":35,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819550951","type":"print"},{"value":"9789819550968","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"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":[[2026]]},"DOI":"10.1007\/978-981-95-5096-8_16","type":"book-chapter","created":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T11:24:29Z","timestamp":1765106669000},"page":"511-543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constraint-Friendly Map-to-Elliptic-Curve-Group Relations and\u00a0Their Applications"],"prefix":"10.1007","author":[{"given":"Jens","family":"Groth","sequence":"first","affiliation":[]},{"given":"Harjasleen","family":"Malvai","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Miller","sequence":"additional","affiliation":[]},{"given":"Yi-Nuo","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,8]]},"reference":[{"key":"16_CR1","unstructured":"Abdalla, M., et al.: Nexus zkvm 3.0 specification. Technical report, Nexus, March 2025. Revised March 11, 2025"},{"key":"16_CR2","doi-asserted-by":"crossref","unstructured":"Albrecht, M., Grassi, L., Rechberger, C., Roy, A., Tiessen, T.: Mimc: efficient encryption and cryptographic hashing with minimal multiplicative complexity. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 191\u2013219. Springer (2016)","DOI":"10.1007\/978-3-662-53887-6_7"},{"key":"16_CR3","doi-asserted-by":"crossref","unstructured":"Arun, A., Setty, S., Thaler, J.: Jolt: snarks for virtual machines via lookups. In: Advances in Cryptology - EUROCRYPT 2024: 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques. Zurich, Switzerland, May 26\u201330, 2024, Proceedings, Part VI, pp. 3\u201333. Springer, Heidelberg (2024)","DOI":"10.1007\/978-3-031-58751-1_1"},{"key":"16_CR4","doi-asserted-by":"publisher","unstructured":"Brier, E., Coron, J.-S., Icart, T., Madore, D., Randriam, H., Tibouchi, M.: Efficient indifferentiable hashing into ordinary elliptic curves. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 237\u2013254. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14623-7_13","DOI":"10.1007\/978-3-642-14623-7_13"},{"key":"16_CR5","doi-asserted-by":"crossref","unstructured":"Blum, M., Evans, W., Gemmell, P., Kannan, S., Naor, M.: Checking the correctness of memories. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, SFCS \u201991, pp. 90\u201399. IEEE Computer Society, USA (1991)","DOI":"10.1109\/SFCS.1991.185352"},{"key":"16_CR6","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Hamburg, M., Krasnova, A., Lange, T.: Elligator: elliptic-curve points indistinguishable from uniform random strings. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, pp. 967\u2013980 (2013)","DOI":"10.1145\/2508859.2516734"},{"issue":"4","key":"16_CR7","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00145-004-0314-9","volume":"17","author":"D Boneh","year":"2004","unstructured":"Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. J. Cryptol. 17(4), 297\u2013319 (2004)","journal-title":"J. Cryptol."},{"key":"16_CR8","doi-asserted-by":"publisher","unstructured":"Bellare, M., Micciancio, D.: A new paradigm for collision-free hashing: incrementality at reduced cost. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 163\u2013192. Springer, Heidelberg (1997).https:\/\/doi.org\/10.1007\/3-540-69053-0_13","DOI":"10.1007\/3-540-69053-0_13"},{"key":"16_CR9","unstructured":"Brown, D.R.L.: The encrypted elliptic curve hash. IACR Cryptol. ePrint Arch., p. 12 (2008)"},{"key":"16_CR10","doi-asserted-by":"publisher","unstructured":"Clarke, D., Devadas, S., van Dijk, M., Gassend, B., Suh, G.E.: Incremental multiset hash functions and their application to memory integrity checking. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 188\u2013207. Springer, Heidelberg (2003).https:\/\/doi.org\/10.1007\/978-3-540-40061-5_12","DOI":"10.1007\/978-3-540-40061-5_12"},{"key":"16_CR11","doi-asserted-by":"crossref","unstructured":"Chavez-Saab, J., Rodr\u00edguez-Henr\u00edquez, F., Tibouchi, M.: Swiftec: Shallue-van de woestijne indifferentiable function to elliptic curves: Faster indifferentiable hashing to elliptic curves. In: Advances in Cryptology - ASIACRYPT 2022: 28th International Conference on the Theory and Application of Cryptology and Information Security. Taipei, Taiwan, December 5\u20139, 2022, Proceedings, Part I, pp. 63\u201392. Springer, Heidelberg (2022)","DOI":"10.1007\/978-3-031-22963-3_3"},{"issue":"281","key":"16_CR12","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1090\/S0025-5718-2012-02606-8","volume":"82","author":"RR Farashahi","year":"2013","unstructured":"Farashahi, R.R., Fouque, P.-A., Shparlinski, I.E., Tibouchi, M., Voloch, J.F.: Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Math. Comput. 82(281), 491\u2013512 (2013)","journal-title":"Math. Comput."},{"key":"16_CR13","doi-asserted-by":"crossref","unstructured":"Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R.S., Wood, C.A.: Rfc 9380: Hashing to elliptic curves (2023)","DOI":"10.17487\/RFC9380"},{"key":"16_CR14","doi-asserted-by":"publisher","unstructured":"Fouque, P.-A., Joux, A., Tibouchi, M.: Injective encodings to elliptic curves. In: Boyd, C., Simpson, L. (eds.) ACISP 2013. LNCS, vol. 7959, pp. 203\u2013218. Springer, Heidelberg (2013).https:\/\/doi.org\/10.1007\/978-3-642-39059-3_14","DOI":"10.1007\/978-3-642-39059-3_14"},{"issue":"4","key":"16_CR15","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1515\/JMC.2009.022","volume":"3","author":"RR Farashahi","year":"2009","unstructured":"Farashahi, R.R., Shparlinski, I.E., Voloch, J.F.: On hashing into elliptic curves. J. Math. Cryptol. 3(4), 353\u2013360 (2009)","journal-title":"J. Math. Cryptol."},{"key":"16_CR16","doi-asserted-by":"publisher","unstructured":"Fouque, P.-A., Tibouchi, M.: Deterministic encoding and hashing to odd hyperelliptic curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 265\u2013277. Springer, Heidelberg (2010).https:\/\/doi.org\/10.1007\/978-3-642-17455-1_17","DOI":"10.1007\/978-3-642-17455-1_17"},{"key":"16_CR17","unstructured":"Grassi, L., Khovratovich, D., Rechberger, C., Roy, A., Schofnegger, M.: Poseidon: a new hash function for $$\\{$$Zero-Knowledge$$\\}$$ proof systems. In: 30th USENIX Security Symposium (USENIX Security 21), pp. 519\u2013535 (2021)"},{"key":"16_CR18","doi-asserted-by":"crossref","unstructured":"Groth, J., Shoup, V.: On the security of ecdsa with additive key derivation and presignatures. In: Advances in Cryptology - EUROCRYPT 2022: Annual International Conference on the Theory and Applications of Cryptographic Techniques. Trondheim, Norway, May 30 - June 3, 2022, Proceedings, Part I, pp. 365\u2013396. Springer, Heidelberg (2022)","DOI":"10.1007\/978-3-031-06944-4_13"},{"key":"16_CR19","unstructured":"Hyper Oracle Team. zkpos with halo2-pairing for verifying aggregate bls signatures, January 2023https:\/\/ethresear.ch\/t\/zkpos-with-halo2-pairing-for-verifying-aggregate-bls-signatures\/14671. Accessed 15 May 2025"},{"key":"16_CR20","doi-asserted-by":"publisher","unstructured":"Icart, T.: How to hash into elliptic curves. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 303\u2013316. Springer, Heidelberg (2009).https:\/\/doi.org\/10.1007\/978-3-642-03356-8_18","DOI":"10.1007\/978-3-642-03356-8_18"},{"key":"16_CR21","doi-asserted-by":"crossref","unstructured":"Jager, T., Rupp, A.: The semi-generic group model and applications to pairing-based cryptography. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 539\u2013556. Springer (2010)","DOI":"10.1007\/978-3-642-17373-8_31"},{"key":"16_CR22","unstructured":"Koshelev, D.: Hashing to elliptic curves over highly $$2$$-adic fields $$\\mathbb{F} _{q}$$ with $$o(\\log (q))$$ operations in $$\\mathbb{F} _{q}$$. Cryptology ePrint Archive, Paper 2023\/121 (2023)"},{"key":"16_CR23","doi-asserted-by":"crossref","unstructured":"Koshelev, D.: Hashing to elliptic curves through cipolla\u2013lehmer\u2013m\u00fcller\u2019s square root algorithm. J. Cryptol. 37(2), February 2024","DOI":"10.1007\/s00145-024-09490-w"},{"key":"16_CR24","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/978-3-031-97260-7_18","volume-title":"Progress in Cryptology - AFRICACRYPT 2025","author":"D Koshelev","year":"2026","unstructured":"Koshelev, D.: Simultaneously simple universal and indifferentiable hashing to elliptic curves. In: Nitaj, A., Petkova-Nikova, S., Rijmen, V. (eds.) Progress in Cryptology - AFRICACRYPT 2025, pp. 395\u2013413. Springer, Cham (2026)"},{"key":"16_CR25","unstructured":"Succinct Labs. Sp1 introduction (2025). https:\/\/docs.succinct.xyz\/docs\/sp1\/introduction. Accessed 09 Sept 2025"},{"issue":"4","key":"16_CR26","first-page":"476","volume":"60","author":"J Maitin-Shepard","year":"2017","unstructured":"Maitin-Shepard, J., Tibouchi, M., Aranha, D.F.: Elliptic curve multiset hash. Comput. J. 60(4), 476\u2013490 (2017)","journal-title":"Comput. J."},{"key":"16_CR27","unstructured":"RISC Zero. Risc zero zkvm api documentation (2025). https:\/\/dev.risczero.com\/api\/zkvm"},{"key":"16_CR28","unstructured":"Roy, U.: Sp1 turbo: the world\u2019s fastest zkvm just got faster (2025). https:\/\/blog.succinct.xyz\/sp1-turbo\/. Accessed 09 Sept 2025"},{"key":"16_CR29","unstructured":"Setty, S.T.V., Angel, S., Gupta, T., Lee, J.: Proving the correct execution of concurrent services in zero-knowledge. In: Arpaci-Dusseau, A.C., Voelker, G., (eds.) 13th USENIX Symposium on Operating Systems Design and Implementation, OSDI 2018, Carlsbad, CA, USA, October 8-10, 2018, pp. 339\u2013356. USENIX Association (2018)"},{"key":"16_CR30","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-69053-0_18","volume-title":"Advances in Cryptology \u2013 EUROCRYPT \u201997","author":"V Shoup","year":"1997","unstructured":"Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) Advances in Cryptology \u2013 EUROCRYPT \u201997, pp. 256\u2013266. Springer, Heidelberg (1997)"},{"issue":"3","key":"16_CR31","doi-asserted-by":"publisher","first-page":"293","DOI":"10.4064\/aa117-3-7","volume":"117","author":"M Ska\u0142ba","year":"2005","unstructured":"Ska\u0142ba, M.: Points on elliptic curves over finite fields. Acta Arith 117(3), 293\u2013301 (2005)","journal-title":"Acta Arith"},{"key":"16_CR32","doi-asserted-by":"crossref","unstructured":"Shallue, A., van\u00a0de Woestijne, C.: Construction of rational points on elliptic curves over finite fields. In: International Algorithmic Number Theory Symposium, pp. 510\u2013524 (2006)","DOI":"10.1007\/11792086_36"},{"issue":"1\u20132","key":"16_CR33","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10623-016-0288-2","volume":"82","author":"M Tibouchi","year":"2017","unstructured":"Tibouchi, M., Kim, T.: Improved elliptic curve hashing and point representation. Des. Codes Crypt. 82(1\u20132), 161\u2013177 (2017)","journal-title":"Des. Codes Crypt."},{"issue":"2","key":"16_CR34","doi-asserted-by":"publisher","first-page":"97","DOI":"10.4064\/ba55-2-1","volume":"55","author":"M Ulas","year":"2007","unstructured":"Ulas, M.: Rational points on certain hyperelliptic curves over finite fields. Bull. Polish Acad. Sci. Math. 55(2), 97\u2013104 (2007)","journal-title":"Bull. Polish Acad. Sci. Math."},{"key":"16_CR35","doi-asserted-by":"crossref","unstructured":"Wahby, R.S., Boneh, D.: Fast and simple constant-time hashing to the bls12-381 elliptic curve. Cryptology ePrint Archive (2019)","DOI":"10.46586\/tches.v2019.i4.154-179"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-5096-8_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T11:24:32Z","timestamp":1765106672000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-5096-8_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,8]]},"ISBN":["9789819550951","9789819550968"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-5096-8_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,8]]},"assertion":[{"value":"8 December 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"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":"Melbourne, VIC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 December 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 December 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"asiacrypt2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}