{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:57:33Z","timestamp":1772283453407,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":38,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540681595","type":"print"},{"value":"9783540681649","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-68164-9_10","type":"book-chapter","created":{"date-parts":[[2008,5,30]],"date-time":"2008-05-30T10:48:34Z","timestamp":1212144514000},"page":"143-155","source":"Crossref","is-referenced-by-count":5,"title":["Cryptanalysis of the TRMS Signature Scheme of PKC\u201905"],"prefix":"10.1007","author":[{"given":"Luk","family":"Bettale","sequence":"first","affiliation":[]},{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"additional","affiliation":[]},{"given":"Ludovic","family":"Perret","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Adams, W.W., Loustaunau, P.: An Introduction to Gr\u00f6bner Bases. Graduate Studies in Mathematics, vol.\u00a03, AMS (1994)","DOI":"10.1090\/gsm\/003"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1007\/978-3-540-30539-2_24","volume-title":"Advances in Cryptology - ASIACRYPT 2004","author":"G. Ars","year":"2004","unstructured":"Ars, G., Faug\u00e8re, J.-C., Imai, H., Kawazoe, M., Sugita, M.: Comparison Between XL and Gr\u00f6bner Basis Algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol.\u00a03329, pp. 338\u2013353. Springer, Heidelberg (2004)"},{"key":"10_CR3","unstructured":"Bardet, M.: Etude des syst\u00e8mes alg\u00e9briques surd\u00e9termin\u00e9s. Applications aux codes correcteurs et \u00e0 la cryptographie. Th\u00e8se de doctorat, Universit\u00e9 de Paris VI (2004)"},{"key":"10_CR4","unstructured":"Bardet, M., Faug\u00e8re, J.-C., Salvy, B.: On the complexity of Grbner basis computation of semi-regular overdetermined algebraic equations. In: Proc. International Conference on Polynomial System Solving (ICPSS), pp. 71\u201375 (2004), http:\/\/www-calfor.lip6.fr\/ICPSS\/papers\/43BF\/43BF.htm"},{"key":"10_CR5","unstructured":"Bardet, M., Faug\u00e8re, J.-C., Salvy, B., Yang, B.-Y.: Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems. In: Proc. of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry (2005)"},{"key":"10_CR6","volume-title":"Computer Algebra Symbolic and Algebraic Computation","author":"B. Buchberger","year":"1982","unstructured":"Buchberger, B., Collins, G.-E., Loos, R.: Computer Algebra Symbolic and Algebraic Computation, 2nd edn. Springer, Heidelberg (1982)","edition":"2"},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"Buchberger, B.: Gr\u00f6bner Bases\u00a0: an Algorithmic Method in Polynomial Ideal Theory. In: Recent trends in multidimensional systems theory, Reider ed. Bose (1985)","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"10_CR8","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":"10_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/11599593","volume-title":"Public Key Cryptography - PKC 2005","author":"C.-Y. Chou","year":"2005","unstructured":"Chou, C.-Y., Hu, Y.-H., Lai, F.-P., Wang, L.-C., Yang, B.-Y.: Tractable Rational Map Signature. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 244\u2013257. Springer, Heidelberg (2005)"},{"key":"10_CR10","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. Courtois","year":"2000","unstructured":"Courtois, N., 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)"},{"key":"10_CR11","unstructured":"Courtois, N., Goubin, L., Patarin, J.: SFLASH, a Fast Symmetric Signature Scheme for low-cost Smartcards \u2013 Primitive Specification and Supporting documentation, http:\/\/www.minrank.org\/sflash-b-v2.pdf"},{"key":"10_CR12","series-title":"Undergraduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2181-2","volume-title":"Ideals, Varieties, and algorithms: an Introduction to Computational Algebraic Geometry and Commutative algebra","author":"D.A. Cox","year":"1992","unstructured":"Cox, D.A., Little, J.B., O\u2019Shea, D.: Ideals, Varieties, and algorithms: an Introduction to Computational Algebraic Geometry and Commutative algebra. Undergraduate Texts in Mathematics. Springer, New York (1992)"},{"key":"10_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72540-4_15","volume-title":"Advances in Cryptology - EUROCRYPT 2007","author":"V. Dubois","year":"2007","unstructured":"Dubois, V., Fouque, P.-A., Stern, J.: Cryptanalysis of SFLASH with Slightly Modified Parameters. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol.\u00a04515, Springer, Heidelberg (2007)"},{"key":"10_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74143-5_1","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"V. Dubois","year":"2007","unstructured":"Dubois, V., Fouque, P.-A., Shamir, A., Stern, J.: Practical Cryptanalysis of SFLASH. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, Springer, Heidelberg (2007)"},{"key":"10_CR15","series-title":"Lecture Notes in Computer Science","first-page":"340","volume-title":"Advances in Cryptology","author":"W. Diffie","year":"1986","unstructured":"Diffie, W., Fell, H.J.: Analysis of a Public Key Approach Based on Polynomial Substitution. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol.\u00a0218, pp. 340\u2013349. Springer, Heidelberg (1986)"},{"key":"10_CR16","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"IT\u201322","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New Directions in Cryptography. IEEE Transactions on Information Theory\u00a0IT 22, 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"10_CR17","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1006\/jsco.1993.1051","volume":"16","author":"J.C. Faug\u00e8re","year":"1993","unstructured":"Faug\u00e8re, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient Computation of Zero-Dimensional Gr\u00f6bner Bases by Change of Ordering. Journal of Symbolic Computation\u00a016(4), 329\u2013344 (1993)","journal-title":"Journal of Symbolic Computation"},{"key":"10_CR18","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 Basis: F4. Journal of Pure and Applied Algebra\u00a0139, 61\u201368 (1999)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"10_CR19","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1145\/780506.780516","volume-title":"Proceedings of ISSAC","author":"J.-C. Faug\u00e8re","year":"2002","unstructured":"Faug\u00e8re, J.-C.: A New Efficient Algorithm for Computing Gr\u00f6bner Basis without Reduction to Zero: F5. In: Proceedings of ISSAC, pp. 75\u201383. ACM Press, New York (2002)"},{"key":"10_CR20","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":"10_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1007\/11761679_3","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"J.-C. Faug\u00e8re","year":"2006","unstructured":"Faug\u00e8re, J.-C., Perret, L.: Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 30\u201347. Springer, Heidelberg (2006)"},{"key":"10_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/11818175_21","volume-title":"Advances in Cryptology - CRYPTO 2006","author":"J.-C. Faug\u00e8re","year":"2006","unstructured":"Faug\u00e8re, J.-C., Perret, L.: Cryptanalysis of 2R\u2212 schemes. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol.\u00a04117, pp. 357\u2013372. Springer, Heidelberg (2006)"},{"key":"10_CR23","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1090\/conm\/168\/01688","volume":"168","author":"M.R. Fellows","year":"1994","unstructured":"Fellows, M.R., Koblitz, N.: Combinatorial cryptosystems galore! Contemporary Math.\u00a0168, 51\u201361 (1994)","journal-title":"Contemporary Math."},{"key":"10_CR24","volume-title":"Computers and Intractability. A Guide to the Theory of NP-Completeness","author":"M.R. Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.B.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)"},{"key":"10_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/978-3-540-30580-4_18","volume-title":"Public Key Cryptography - PKC 2005","author":"A. Joux","year":"2005","unstructured":"Joux, A., Kunz-Jacques, S., Muller, F., Ricordel, P.-M.: Cryptanalysis of the Tractable Rational Map Cryptosystem. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 258\u2013274. Springer, Heidelberg (2005)"},{"key":"10_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1007\/3-540-48910-X_15","volume-title":"Advances in Cryptology - EUROCRYPT \u201999","author":"A. Kipnis","year":"1999","unstructured":"Kipnis, A., Patarin, J., Goubin, L.: Unbalanced Oil and Vinegar Signature Schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol.\u00a01592, pp. 206\u2013222. Springer, Heidelberg (1999)"},{"key":"10_CR27","volume-title":"Algorithms and Computation in Mathematics","author":"N. Koblitz","year":"1998","unstructured":"Koblitz, N.: Algebraic Aspects of Cryptography. In: Algorithms and Computation in Mathematics, vol.\u00a03, Springer, Heidelberg (1998)"},{"key":"10_CR28","unstructured":"Levy\u2013dit\u2013Vehel, F., Mora, T., Perret, L., Traverso, C.: A Survey of Polly Cracker Systems (to appear)"},{"key":"10_CR29","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":"10_CR30","doi-asserted-by":"crossref","DOI":"10.3792\/chmm\/1263317740","volume-title":"The Algebraic Theory of Modular Systems","author":"F.S. Macaulay","year":"1916","unstructured":"Macaulay, F.S.: The Algebraic Theory of Modular Systems. Cambrige University Press, Cambrige (1916)"},{"key":"10_CR31","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 Fields 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":"10_CR32","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)"},{"issue":"2","key":"10_CR33","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R. Rivest","year":"1978","unstructured":"Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM\u00a021(2), 120\u2013126 (1978)","journal-title":"Communications of the ACM"},{"key":"10_CR34","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"P.W. Shor","year":"1997","unstructured":"Shor, P.W.: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. Computing\u00a026, 1484\u20131509 (1997)","journal-title":"SIAM J. Computing"},{"key":"10_CR35","unstructured":"Szanto, A.: Multivariate subresultants using jouanolous resultant matrices. Journal of Pure and Applied Algebra (to appear)"},{"key":"10_CR36","unstructured":"Wang, L., Chang, F.: Tractable Rational Map Cryptosystem.Cryptology ePrint archive, Report 2004\/046, http:\/\/eprint.iacr.org"},{"key":"10_CR37","unstructured":"Wolf, C.: Multivariate Quadratic Polynomials in Public Key Cryptography. Ph.D. thesis, Katholieke Universiteit Leuven, B. Preneel (supervisor), 156+xxiv pages (November 2005)"},{"key":"10_CR38","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.T.: 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","Progress in Cryptology \u2013 AFRICACRYPT 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-68164-9_10.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,11]],"date-time":"2021-09-11T11:36:10Z","timestamp":1631360170000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-68164-9_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540681595","9783540681649"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-68164-9_10","relation":{},"subject":[]}}