{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:33:47Z","timestamp":1764239627900},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642129285"},{"type":"electronic","value":"9783642129292"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-12929-2_12","type":"book-chapter","created":{"date-parts":[[2010,5,31]],"date-time":"2010-05-31T05:17:53Z","timestamp":1275283073000},"page":"153-164","source":"Crossref","is-referenced-by-count":4,"title":["Secure Variants of the Square Encryption Scheme"],"prefix":"10.1007","author":[{"given":"Crystal Lee","family":"Clough","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jintai","family":"Ding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"12_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/978-3-540-88403-3_2","volume-title":"Post-Quantum Cryptography","author":"J. Baena","year":"2008","unstructured":"Baena, J., Clough, C., Ding, J.: Square-Vinegar Signature Scheme. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol.\u00a05299, pp. 17\u201330. Springer, Heidelberg (2008)"},{"key":"12_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/978-3-642-10366-7_27","volume-title":"ASIACRYPT 2009","author":"O. Billet","year":"2009","unstructured":"Billet, O., Gilles, M.-R.: Cryptanalysis of the Square Cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol.\u00a05912, pp. 451\u2013468. Springer, Heidelberg (2009)"},{"key":"12_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1007\/978-3-642-00862-7_17","volume-title":"CT-RSA 2009","author":"C. Clough","year":"2009","unstructured":"Clough, C., Baena, J., Ding, J., Yang, B.-Y., Chen, M.: Square, a new multivariate encryption scheme. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol.\u00a05473, pp. 252\u2013264. Springer, Heidelberg (2009)"},{"key":"12_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1007\/3-540-45353-9_20","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"N. Courtois","year":"2001","unstructured":"Courtois, N.: The security of hidden field equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 266\u2013281. Springer, Heidelberg (2001)"},{"key":"12_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1007\/978-3-540-70583-3_56","volume-title":"Automata, Languages and Programming","author":"J. Ding","year":"2008","unstructured":"Ding, J., Dubois, V., Yang, B.-Y., Owen Chen, C.-H., Cheng Could, C.-M.: Could SFLASH be Repaired? In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol.\u00a05126, pp. 691\u2013701. Springer, Heidelberg (2008)"},{"key":"12_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/11745853_19","volume-title":"Public Key Cryptography - PKC 2006","author":"J. Ding","year":"2006","unstructured":"Ding, J., Gower, J.E., et al.: Inoculating Multivariate Schemes against differential attacks. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol.\u00a03958, pp. 290\u2013301. Springer, Heidelberg (2006)"},{"key":"12_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/11496137_12","volume-title":"Applied Cryptography and Network Security","author":"J. Ding","year":"2005","unstructured":"Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol.\u00a03531, pp. 164\u2013175. Springer, Heidelberg (2005)"},{"key":"12_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/978-3-540-85886-7_15","volume-title":"Information Security","author":"J. Ding","year":"2008","unstructured":"Ding, J., Schmidt, D., Werner, F.: Algebraic attack on HFE revisited. In: Wu, T.-C., Lei, C.-L., Rijmen, V., Lee, D.-T. (eds.) ISC 2008. LNCS, vol.\u00a05222, pp. 215\u2013227. Springer, Heidelberg (2008)"},{"key":"12_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1007\/11787006_14","volume-title":"Automata, Languages and Programming","author":"V. Dubois","year":"2006","unstructured":"Dubois, V., Granboulan, L., Stern, J.: An efficient provable distinguisher for HFE. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol.\u00a04052, pp. 156\u2013167. Springer, Heidelberg (2006)"},{"issue":"1-3","key":"12_CR10","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"J.-C. Faug\u00e9re","year":"1999","unstructured":"Faug\u00e9re, J.-C.: A new efficient algorithm for computing Gr\u00f6bner bases \n                    \n                      \n                    \n                    $(F\\sb 4)$\n                  . J. Pure Appl. Algebra\u00a0139(1-3), 61\u201388 (1999); Effective methods in algebraic geometry (Saint-Malo, 1998)","journal-title":"J. Pure Appl. Algebra"},{"key":"12_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/978-3-540-45146-4_3","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"J.-C. Faug\u00e8re","year":"2003","unstructured":"Faug\u00e8re, J.-C., Joux, A.: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gr\u00f6bner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol.\u00a02729, pp. 44\u201360. Springer, Heidelberg (2003)"},{"key":"12_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/978-3-540-79499-8_31","volume-title":"Information Security and Cryptology","author":"X. Jiang","year":"2008","unstructured":"Jiang, X., Ding, J., Hu, L.: Public Key Analysis-Kipnis-Shamir Attack on HFE Revisited. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol.\u00a04990, pp. 399\u2013411. Springer, Heidelberg (2008)"},{"key":"12_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/3-540-48405-1_2","volume-title":"Advances in Cryptology - CRYPTO \u201999","author":"A. Kipnis","year":"1999","unstructured":"Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol.\u00a01666, pp. 19\u201330. Springer, Heidelberg (1999)"},{"key":"12_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/3-540-45961-8_39","volume-title":"Advances in Cryptology - EUROCRYPT \u201988","author":"T. Matsumoto","year":"1988","unstructured":"Matsumoto, T., Imai, H.: Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: G\u00fcnther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol.\u00a0330, pp. 419\u2013453. Springer, Heidelberg (1988)"},{"key":"12_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-540-88403-3_14","volume-title":"Post-Quantum Cryptography","author":"M.S.E. Mohamed","year":"2008","unstructured":"Mohamed, M.S.E., Mohamed, W., Ding, J., Buchmann, J.: MXL2: Solving Polynomial Equations over GF (2) Using an Improved Mutant Strategy. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol.\u00a05299, pp. 203\u2013215. Springer, Heidelberg (2008)"},{"key":"12_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/3-540-68339-9_4","volume-title":"Advances in Cryptology - EUROCRYPT \u201996","author":"J. Patarin","year":"1996","unstructured":"Patarin, J.: Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): Two new families of asymmetric algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol.\u00a01070, pp. 33\u201348. Springer, Heidelberg (1996)"},{"key":"12_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/3-540-49649-1_4","volume-title":"Advances in Cryptology - ASIACRYPT\u201998","author":"J. Patarin","year":"1998","unstructured":"Patarin, J., Goubin, L., Courtois, N.: C*-+ and HM: Variations around two schemes of T. Matsumoto and H. Imai. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 35\u201350. Springer, Heidelberg (1998)"}],"container-title":["Lecture Notes in Computer Science","Post-Quantum Cryptography"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-12929-2_12.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T11:48:58Z","timestamp":1619783338000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-12929-2_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642129285","9783642129292"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-12929-2_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}