{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:20:50Z","timestamp":1764980450773,"version":"3.46.0"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In a recent paper the authors and their collaborators proposed a new hard problem, called the\n                    <jats:italic>finite field isomorphism problem<\/jats:italic>\n                    , and they used it to construct a fully homomorphic encryption scheme. In this paper, we investigate how one might build a digital signature scheme from this new problem. Intuitively, the hidden field isomorphism allows us to convert short vectors in the underlying lattice of one field into generic looking vectors in an isomorphic field.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2015-0050","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T13:48:20Z","timestamp":1592228900000},"page":"39-54","source":"Crossref","is-referenced-by-count":1,"title":["A signature scheme from the finite field isomorphism problem"],"prefix":"10.1515","volume":"14","author":[{"given":"Jeffrey","family":"Hoffstein","sequence":"first","affiliation":[{"name":"Brown University , Providence , United States of America"}]},{"given":"Joseph H.","family":"Silverman","sequence":"additional","affiliation":[{"name":"Brown University , Providence , United States of America"}]},{"given":"William","family":"Whyte","sequence":"additional","affiliation":[{"name":"OnBoard Security , Wilmington , United States of America"}]},{"given":"Zhenfei","family":"Zhang","sequence":"additional","affiliation":[{"name":"OnBoard Security , Wilmington , United States of America"}]}],"member":"374","published-online":{"date-parts":[[2020,6,14]]},"reference":[{"key":"2025120600161803810_j_jmc-2015-0050_ref_001_w2aab3b7e2595b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Wieb Bosma, John Cannon and Catherine Playoust, The Magma algebra system. I. The user language., J. Symbolic Comput. 24 (1997), 235\u2013265.","DOI":"10.1006\/jsco.1996.0125"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_002_w2aab3b7e2595b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Yuanmi Chen and Phong Q. Nguyen, BKZ 2.0: Better Lattice Security Estimates, in: ASIACRYPT, pp. 1\u201320, 2011.","DOI":"10.1007\/978-3-642-25385-0_1"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_003_w2aab3b7e2595b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Yarkin Dor\u00f6z, Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman, Berk Sunar, William Whyte and Zhenfei Zhang, Fully Homomorphic Encryption from the Finite Field Isomorphism Problem, PKC 2018 (2018).","DOI":"10.1007\/978-3-319-76578-5_5"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_004_w2aab3b7e2595b1b6b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"L\u00e9o Ducas, Alain Durmus, Tancr\u00e8de Lepoint and Vadim Lyubashevsky, Lattice Signatures and Bimodal Gaussians, CRYPTO 2013 (Ran Canetti and Juan A. Garay, eds.), LNCS 8042, Springer, 2013, pp. 40\u201356.","DOI":"10.1007\/978-3-642-40041-4_3"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_005_w2aab3b7e2595b1b6b1ab2b1b5Aa","doi-asserted-by":"crossref","unstructured":"L\u00e9o Ducas and Phong Q. Nguyen, Learning a Zonotope and More: Cryptanalysis of NTRUSign Countermeasures, in: Advances in Cryptology - ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, December 2-6, 2012. Proceedings, pp. 433\u2013450, 2012.","DOI":"10.1007\/978-3-642-34961-4_27"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_006_w2aab3b7e2595b1b6b1ab2b1b6Aa","doi-asserted-by":"crossref","unstructured":"Oded Goldreich, Shafi Goldwasser and Shai Halevi, Public-Key Cryptosystems from Lattice Reduction Problems, in: CRYPTO, pp. 112\u2013131, 1997.","DOI":"10.1007\/BFb0052231"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_007_w2aab3b7e2595b1b6b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"Jeffrey Hoffstein, Nick Howgrave-Graham, Jill Pipher, Joseph H. Silverman and William Whyte, NTRUSIGN: Digital Signatures Using the NTRU Lattice, in: Topics in Cryptology - CT-RSA 2003, The Cryptographers' Track at the RSA Conference 2003, San Francisco, CA, USA, April 13-17, 2003, Proceedings, pp. 122\u2013140, 2003.","DOI":"10.1007\/3-540-36563-X_9"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_008_w2aab3b7e2595b1b6b1ab2b1b8Aa","doi-asserted-by":"crossref","unstructured":"Jeffrey Hoffstein, Jill Pipher, John M. Schanck, Joseph H. Silverman and William Whyte, Transcript Secure Signatures Based on Modular Lattices, in: Post-Quantum Cryptography - 6th International Workshop, PQCrypto 2014, Waterloo, ON, Canada, October 1-3, 2014. Proceedings, pp. 142\u2013159, 2014.","DOI":"10.1007\/978-3-319-11659-4_9"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_009_w2aab3b7e2595b1b6b1ab2b1b9Aa","doi-asserted-by":"crossref","unstructured":"Jeffrey Hoffstein, Jill Pipher and Joseph H. Silverman, NTRU: A Ring-Based Public Key Cryptosystem, in: ANTS, pp. 267\u2013288, 1998.","DOI":"10.1007\/BFb0054868"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_010_w2aab3b7e2595b1b6b1ab2b1c10Aa","unstructured":"Jeffrey Hoffstein, Jill Pipher, William Whyte and Zhenfei Zhang, A signature scheme from Learning with Truncation, Cryptology ePrint Archive, Report 2017\/995, 2017, http:\/\/eprint.iacr.org\/2017\/995."},{"key":"2025120600161803810_j_jmc-2015-0050_ref_011_w2aab3b7e2595b1b6b1ab2b1c11Aa","doi-asserted-by":"crossref","unstructured":"Nick Howgrave-Graham, A Hybrid Lattice-Reduction and Meet-in-the-Middle Attack Against NTRU, in: CRYPTO, pp. 150\u2013169, 2007.","DOI":"10.1007\/978-3-540-74143-5_9"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_012_w2aab3b7e2595b1b6b1ab2b1c12Aa","doi-asserted-by":"crossref","unstructured":"K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1990.","DOI":"10.1007\/978-1-4757-2103-4"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_013_w2aab3b7e2595b1b6b1ab2b1c13Aa","doi-asserted-by":"crossref","unstructured":"Vadim Lyubashevsky, Fiat-shamir with aborts: Applications to lattice and factoring-based signatures, ASIACRYPT 2009, Springer, 2009, pp. 598\u2013616.","DOI":"10.1007\/978-3-642-10366-7_35"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_014_w2aab3b7e2595b1b6b1ab2b1c14Aa","doi-asserted-by":"crossref","unstructured":"Vadim Lyubashevsky, Lattice Signatures without Trapdoors, EUROCRYPT2012 (David Pointcheval and Thomas Johansson, eds.), LNCS 7237, Springer, 2012, pp. 738\u2013755.","DOI":"10.1007\/978-3-642-29011-4_43"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_015_w2aab3b7e2595b1b6b1ab2b1c15Aa","doi-asserted-by":"crossref","unstructured":"Gary L. Miller, Riemann's hypothesis and tests for primality, Journal of Computer and System Sciences13 (1976), 300 \u2013 317.","DOI":"10.1016\/S0022-0000(76)80043-8"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_016_w2aab3b7e2595b1b6b1ab2b1c16Aa","doi-asserted-by":"crossref","unstructured":"Phong Q. Nguyen and Oded Regev, Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures, J. Cryptology22 (2009), 139\u2013160.","DOI":"10.1007\/s00145-008-9031-0"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_017_w2aab3b7e2595b1b6b1ab2b1c17Aa","unstructured":"NIST, Post-Quantum Cryptography - Round 1 Submissions, https:\/\/csrc.nist.gov\/Projects\/Post-Quantum-Cryptography\/Round-1-Submissions."},{"key":"2025120600161803810_j_jmc-2015-0050_ref_018_w2aab3b7e2595b1b6b1ab2b1c18Aa","doi-asserted-by":"crossref","unstructured":"Michael O Rabin, Probabilistic algorithm for testing primality, Journal of Number Theory12 (1980), 128 \u2013 138.","DOI":"10.1016\/0022-314X(80)90084-0"},{"key":"2025120600161803810_j_jmc-2015-0050_ref_019_w2aab3b7e2595b1b6b1ab2b1c19Aa","doi-asserted-by":"crossref","unstructured":"Damien Stehl\u00e9 and Ron Steinfeld, Making NTRU as Secure as Worst-Case Problems over Ideal Lattices, in: Advances in Cryptology - EUROCRYPT2011 - 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tallinn, Estonia, May 15-19, 2011. Proceedings, pp. 27\u201347, 2011.","DOI":"10.1007\/978-3-642-20465-4_4"}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/jmc\/14\/1\/article-p39.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2015-0050\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2015-0050\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:16:34Z","timestamp":1764980194000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2015-0050\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,6,14]]},"published-print":{"date-parts":[[2020,6,14]]}},"alternative-id":["10.1515\/jmc-2015-0050"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2015-0050","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2020,1,1]]}}}