{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:40:38Z","timestamp":1775839238192,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642150302","type":"print"},{"value":"9783642150319","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-15031-9_14","type":"book-chapter","created":{"date-parts":[[2010,8,7]],"date-time":"2010-08-07T15:34:35Z","timestamp":1281195275000},"page":"203-218","source":"Crossref","is-referenced-by-count":44,"title":["Fast Exhaustive Search for Polynomial Systems in ${\\mathbb{F}_2}$"],"prefix":"10.1007","author":[{"given":"Charles","family":"Bouillaguet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hsieh-Chung","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen-Mou","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tung","family":"Chou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruben","family":"Niederhagen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adi","family":"Shamir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo-Yin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"14_CR1","unstructured":"Bard, G.V., Courtois, N.T., Jefferson, C.: Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers, http:\/\/eprint.iacr.org\/2007\/024"},{"key":"14_CR2","unstructured":"Bardet, M., Faug\u00e8re, J.-C., Salvy, B.: On the complexity of Gr\u00f6bner basis computation of semi-regular overdetermined algebraic equations. In: Proc. Int\u2019l Conference on Polynomial System Solving, pp. 71\u201374 (2004) INRIA report RR-5049"},{"key":"14_CR3","unstructured":"Bardet, M., Faug\u00e8re, J.-C., Salvy, B., Yang, B.-Y.: Asymptotic expansion of the degree of regularity for semi-regular systems of equations. In: Proc. MEGA 2005 (2005)"},{"key":"14_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/11761679_8","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"C. Berbain","year":"2006","unstructured":"Berbain, C., Gilbert, H., Patarin, J.: QUAD: A practical stream cipher with provable security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 109\u2013128. Springer, Heidelberg (2006)"},{"key":"14_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-01001-9_28","volume-title":"Eurocrypt 2009","author":"D.J. Bernstein","year":"2010","unstructured":"Bernstein, D.J., Chen, T.-R., Cheng, C.-M., Lange, T., Yang, B.-Y.: ECM on graphics cards. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol.\u00a05479, pp. 483\u2013501. Springer, Heidelberg (2010)"},{"issue":"3","key":"14_CR6","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1515\/JMC.2009.009","volume":"3","author":"L. Bettale","year":"2009","unstructured":"Bettale, L., Faug\u00e9re, J.-C., Perret, L.: Hybrid approach for solving multivariate systems over finite fields. J. Math. Crypto.\u00a03(3), 177\u2013197 (2009)","journal-title":"J. Math. Crypto."},{"key":"14_CR7","unstructured":"Bouillaguet, C., Faug\u00e9re, J.-C., Fouque, P.-A., Perret, L.: Differential-algebraic algorithms for the isomorphism of polynomials problem, http:\/\/eprint.iacr.org\/2009\/583"},{"key":"14_CR8","unstructured":"Bouillaguet, C., Fouque, P.-A., Joux, A., Treger, J.: A family of weak keys in HFE (and the corresponding practical key-recovery), http:\/\/eprint.iacr.org\/2009\/619"},{"key":"14_CR9","unstructured":"Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Innsbruck (1965)"},{"key":"14_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-3-642-12678-9_5","volume-title":"Africacrypt 2010","author":"J. Buchmann","year":"2010","unstructured":"Buchmann, J., Cabarcas, D., Ding, J., Mohamed, M.S.E.: Flexible Partial Enlargement to Accelerate Gr\u00f6bner Basis Computation over $\\mathbb{F_2}$ . In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol.\u00a06055, pp. 69\u201381. Springer, Heidelberg (2010)"},{"key":"14_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/978-3-540-71039-4_6","volume-title":"Fast Software Encryption","author":"N. Courtois","year":"2008","unstructured":"Courtois, N., Bard, G.V., Wagner, D.: Algebraic and slide attacks on Keeloq. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol.\u00a05086, pp. 97\u2013115. Springer, Heidelberg (2008)"},{"key":"14_CR12","unstructured":"Courtois, N., Goubin, L., Patarin, J.: SFLASH: Primitive specification (second revised version) (2002), https:\/\/www.cosic.esat.kuleuven.be\/nessie"},{"key":"14_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1007\/3-540-45539-6_27","volume-title":"Advances in Cryptology - EUROCRYPT 2000","author":"N.T. Courtois","year":"2000","unstructured":"Courtois, N.T., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol.\u00a01807, pp. 392\u2013407. Springer, Heidelberg (2000), Extended ver., http:\/\/www.minrank.org\/xlfull.pdf"},{"key":"14_CR14","unstructured":"de Bruijn, N.: Asymptotic methods in analysis. 2nd edition. Bibliotheca Mathematica. Vol. 4., 200 p. P. Noordhoff Ltd. XII, Groningen (1961)"},{"key":"14_CR15","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"J.-C. Faug\u00e8re","year":"1999","unstructured":"Faug\u00e8re, J.-C.: A new efficient algorithm for computing Gr\u00f6bner bases (F 4). J. of Pure and Applied Algebra\u00a0139, 61\u201388 (1999)","journal-title":"J. of Pure and Applied Algebra"},{"key":"14_CR16","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.-C.: A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero (F 5). In: ACM ISSAC\u00a02002, pp. 75\u201383 (2002)","DOI":"10.1145\/780506.780516"},{"key":"14_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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 Equations (HFE) using Gr\u00f6bner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol.\u00a02729, pp. 44\u201360. Springer, Heidelberg (2003)"},{"key":"14_CR18","unstructured":"Fog, A.: Instruction Tables. Copenhagen University, College of Engineering, Lists of Instruction Latencies, Throughputs and micro-operation breakdowns for Intel, AMD, and VIA CPUs (February 2010), http:\/\/www.agner.org\/optimize\/instruction_tables.pdf"},{"key":"14_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/3-540-68697-5_4","volume-title":"Advances in Cryptology - CRYPTO \u201996","author":"J. Patarin","year":"1996","unstructured":"Patarin, J.: Asymmetric cryptography with a hidden monomial. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol.\u00a01109, pp. 45\u201360. Springer, Heidelberg (1996)"},{"key":"14_CR20","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), Extended ver.: http:\/\/www.minrank.org\/hfe.pdf"},{"key":"14_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/3-540-45353-9_21","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"J. Patarin","year":"2001","unstructured":"Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-bit long digital signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 282\u2013297. Springer, Heidelberg (2001), http:\/\/www.minrank.org\/quartz\/"},{"key":"14_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1007\/BFb0054126","volume-title":"Advances in Cryptology - EUROCRYPT \u201998","author":"J. Patarin","year":"1998","unstructured":"Patarin, J., Goubin, L., Courtois, N.: Improved algorithms for Isomorphisms of Polynomials. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 184\u2013200. Springer, Heidelberg (1998); Extended ver.: http:\/\/www.minrank.org\/ip6long.ps"},{"key":"14_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/978-3-540-77360-3_15","volume-title":"Selected Areas in Cryptography","author":"H. Raddum","year":"2007","unstructured":"Raddum, H.: MRHS equation systems. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol.\u00a04876, pp. 232\u2013245. Springer, Heidelberg (2007)"},{"key":"14_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/978-3-540-74619-5_22","volume-title":"Fast Software Encryption","author":"M. Sugita","year":"2007","unstructured":"Sugita, M., Kawazoe, M., Perret, L., Imai, H.: Algebraic cryptanalysis of 58-round SHA-1. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol.\u00a04593, pp. 349\u2013365. Springer, Heidelberg (2007)"},{"key":"14_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/978-3-540-27800-9_24","volume-title":"Information Security and Privacy","author":"B.-Y. Yang","year":"2004","unstructured":"Yang, B.-Y., Chen, J.-M.: Theoretical analysis of XL over small fields. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol.\u00a03108, pp. 277\u2013288. Springer, Heidelberg (2004)"},{"key":"14_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/978-3-540-30191-2_31","volume-title":"Information and Communications Security","author":"B.-Y. Yang","year":"2004","unstructured":"Yang, B.-Y., Chen, J.-M., Courtois, N.: On Asymptotic Security Estimates in XL and Gr\u00f6bner Bases-Related Algebraic Cryptanalysis. In: L\u00f3pez, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol.\u00a03269, pp. 401\u2013413. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems, CHES 2010"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-15031-9_14.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T03:00:43Z","timestamp":1606186843000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-15031-9_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642150302","9783642150319"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-15031-9_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010]]}}}