{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T10:59:33Z","timestamp":1777546773692,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540716761","type":"print"},{"value":"9783540716778","type":"electronic"}],"license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-71677-8_16","type":"book-chapter","created":{"date-parts":[[2007,6,20]],"date-time":"2007-06-20T14:05:58Z","timestamp":1182348358000},"page":"233-248","source":"Crossref","is-referenced-by-count":28,"title":["High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems"],"prefix":"10.1007","author":[{"given":"Jintai","family":"Ding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuyun","family":"Nie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"16_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/3-540-36288-6_20","volume-title":"Public Key Cryptography - PKC 2003","author":"M.-L. Akkar","year":"2002","unstructured":"Akkar, M.-L., Courtois, N.T., Duteuil, R., Goubin, L.: A fast and secure implementation of Sflash. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol.\u00a02567, pp. 267\u2013278. Springer, Heidelberg (2002)"},{"key":"16_CR2","series-title":"Lecture Notes in Computer Science","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, Springer, Heidelberg (2004)"},{"key":"16_CR3","unstructured":"Bardet, M., Fauge, J-C., Salvy, B., Yang, B-Y.: Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems. In: MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry, Porto Conte, Alghero, Sardinia, Italy, May 27th - June 1st (2005)"},{"key":"16_CR4","series-title":"Lecture Notes in Computer Science","first-page":"266","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"T. Nicolas","year":"2001","unstructured":"Nicolas, T.: Courtois The security of hidden field equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 266\u2013281. Springer, Heidelberg (2001)"},{"key":"16_CR5","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":"16_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/3-540-36178-2_17","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"N. Courtois","year":"2002","unstructured":"Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol.\u00a02501, pp. 267\u2013287. Springer, Heidelberg (2002)"},{"key":"16_CR7","unstructured":"Chen, J., Moh, T.: On the Goubin-Courtois attack on TTM. Cryptology ePrint Archive, 72 (2001), http:\/\/eprint.iacr.org\/2001\/072"},{"issue":"6","key":"16_CR8","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory\u00a022(6), 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory"},{"key":"16_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/978-3-540-24632-9_22","volume-title":"Public Key Cryptography \u2013 PKC 2004","author":"J. Ding","year":"2004","unstructured":"Ding, J.: A new variant of the Matsumoto-Imai cryptosystem through perturbation. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol.\u00a02947, pp. 305\u2013318. Springer, Heidelberg (2004)"},{"key":"16_CR10","doi-asserted-by":"crossref","unstructured":"Ding, J., Gower, J.: Inoculating Multivariate Schemes Against Differential Attacks. Accepted for PKC-2006, IACR eprint 2005\/255 (2005)","DOI":"10.1007\/11745853_19"},{"key":"16_CR11","series-title":"Lecture Notes in Computer Science","first-page":"68","volume-title":"Applied Cryptography and Network Security","author":"J. Ding","year":"2003","unstructured":"Ding, J., Schmidt, D.S.: A common defect of the TTM cryptosystem. In: Zhou, J., Yung, M., Han, Y. (eds.) ACNS 2003. LNCS, vol.\u00a02846, pp. 68\u201378. Springer, Heidelberg (2003), http:\/\/eprint.iacr.org"},{"key":"16_CR12","unstructured":"Ding, J., Schmidt, D.S.: The new TTM implementation is not secure. In: Niederreiter, H., Feng, K.Q., Xing, C.P. (eds.) Proceedings of International Workshop on Coding, Cryptography and Combinatorics (CCC 2003), pp. 106\u2013121 (2003)"},{"key":"16_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/978-3-540-30580-4_20","volume-title":"Public Key Cryptography - PKC 2005","author":"J. Ding","year":"2005","unstructured":"Ding, J., Schmidt, D.S.: Cryptanalysis of HFEV and the internal perturbation of HFE. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 288\u2013301. Springer, Heidelberg (2005)"},{"key":"16_CR14","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.S.: Rainbow, a new multivariate public key signature scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol.\u00a03531, pp. 164\u2013175. Springer, Heidelberg (2005)"},{"issue":"1\u20133","key":"16_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). Journal of Pure and Applied Algebra\u00a0139(1\u20133), 61\u201388 (1999)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"16_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/11426639_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"P.-A. Fouque","year":"2005","unstructured":"Fouque, P.-A., Granboulan, L., Stern, J.: Differential Cryptanalysis for Multivariate Schemes. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 341\u2013353. Springer, Heidelberg (2005)"},{"key":"16_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/3-540-44448-3_4","volume-title":"Advances in Cryptology - ASIACRYPT 2000","author":"L. Goubin","year":"2000","unstructured":"Goubin, L., Courtois, N.: Cryptanalysis of the TTM cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol.\u00a01976, pp. 44\u201357. Springer, Heidelberg (2000)"},{"key":"16_CR18","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.J. (ed.) CRYPTO 1999. LNCS, vol.\u00a01666, pp. 19\u201330. Springer, Heidelberg (1999)"},{"key":"16_CR19","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":"16_CR20","doi-asserted-by":"crossref","unstructured":"Moh, T.T.: A fast public key system with signature and master key functions. In: Lecture Notes at EE department of Stanford University (May 1999), http:\/\/www.usdsi.com\/ttm.html","DOI":"10.1080\/00927879908826559"},{"key":"16_CR21","unstructured":"Moh, T., Chen, J.M., Yang, B.: Building Instances of TTM Immune to the Goubin-Courtois Attack and the Ding-Schmidt Attack. IACR eprint 2004\/168 (2004), http:\/\/eprint.iacr.org"},{"key":"16_CR22","unstructured":"NESSIE. European project IST-1999-12324 on New European Schemes for Signature, Integrity and Encryption. http:\/\/www.cryptonessie.org"},{"key":"16_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1007\/3-540-44750-4_20","volume-title":"Advances in Cryptology - CRYPTO \u201995","author":"J. Patarin","year":"1995","unstructured":"Patarin, J.: Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt\u201988. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol.\u00a0963, pp. 248\u2013261. Springer, Heidelberg (1995)"},{"key":"16_CR24","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 isomorphism 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":"16_CR25","unstructured":"Patarin, J.: The oil and vinegar signature scheme. In: Dagstuhl Workshop on Cryptography, September 1997 (1997)"},{"key":"16_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1007\/3-540-45353-9_22","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"J. Patarin","year":"2001","unstructured":"Patarin, J., Courtois, N., Goubin, L.: Flash, a fast multivariate signature algorithm. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 298\u2013307. Springer, Heidelberg (2001)"},{"key":"16_CR27","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.\u00a0Matsumoto and H.\u00a0Imai. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 35\u201350. Springer, Heidelberg (1998)"},{"key":"16_CR28","unstructured":"PQCrypto 2006: International Workshop on Post-Quantum Cryptography (2006), http:\/\/postquantum.cr.yp.to\/"},{"issue":"2","key":"16_CR29","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R. Rivest","year":"1978","unstructured":"Rivest, R., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public key cryptosystems. ACM\u00a021(2), 120\u2013126 (1978)","journal-title":"ACM"},{"issue":"2","key":"16_CR30","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"P. Shor","year":"1999","unstructured":"Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev.\u00a041(2), 303\u2013332 (1999)","journal-title":"SIAM Rev."},{"key":"16_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/978-3-540-30580-4_17","volume-title":"Public Key Cryptography - PKC 2005","author":"L.-C. Wang","year":"2005","unstructured":"Wang, L.-C., Hu, Y.-H., Lai, F., Chou, C.-Y., Yang, B.-Y.: Tractable Rational Map Signature. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 244\u2013257. Springer, Heidelberg (2005)"},{"key":"16_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/11605805_9","volume-title":"Topics in Cryptology \u2013 CT-RSA 2006","author":"L.-C. Wang","year":"2006","unstructured":"Wang, L.-C., Yang, B.-y., Hu, Y.-H., Lai, F.: A Medium-Field Multivariate Public key Encryption Scheme. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol.\u00a03860, pp. 132\u2013149. Springer, Heidelberg (2006)"},{"key":"16_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1007\/11506157_43","volume-title":"Information Security and Privacy","author":"B. Yang","year":"2005","unstructured":"Yang, B., Chen, J.: Building Secure Tame-like Multivariate Public key Cryptosystems\u2013The New TTS. In: Boyd, C., Gonz\u00e1lez Nieto, J.M. (eds.) ACISP 2005. LNCS, vol.\u00a03574, pp. 518\u2013531. Springer, Heidelberg (2005)"}],"container-title":["Lecture Notes in Computer Science","Public Key Cryptography \u2013 PKC 2007"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-71677-8_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T08:41:35Z","timestamp":1683880895000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-71677-8_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540716761","9783540716778"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-71677-8_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}