{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T21:51:40Z","timestamp":1774907500688,"version":"3.50.1"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319598789","type":"print"},{"value":"9783319598796","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-59879-6_17","type":"book-chapter","created":{"date-parts":[[2017,6,3]],"date-time":"2017-06-03T16:28:34Z","timestamp":1496507314000},"page":"289-308","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Key Recovery Attack for ZHFE"],"prefix":"10.1007","author":[{"given":"Daniel","family":"Cabarcas","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Smith-Tone","sequence":"additional","affiliation":[]},{"given":"Javier A.","family":"Verbel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,6,4]]},"reference":[{"key":"17_CR1","doi-asserted-by":"crossref","unstructured":"Baena, J.B., Cabarcas, D., Escudero, D.E., Porras-Barrera, J., Verbel, J.A.: Efficient ZHFE key generation. In: Takagi [27], pp. 213\u2013232. http:\/\/dx.doi.org\/10.1007\/978-3-319-29360-8_14","DOI":"10.1007\/978-3-319-29360-8_14"},{"issue":"1","key":"17_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10623-012-9617-2","volume":"69","author":"L Bettale","year":"2013","unstructured":"Bettale, L., Faug\u00e8re, J.C., Perret, L.: Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Des. Codes Crypt. 69(1), 1\u201352 (2013)","journal-title":"Des. Codes Crypt."},{"issue":"3\u20134","key":"17_CR3","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I. The user language. J. Symbolic Comput. 24(3\u20134), 235\u2013265 (1997). http:\/\/dx.doi.org\/10.1006\/jsco.1996.0125, computational algebra and number theory (London, 1993)","journal-title":"J. Symbolic Comput."},{"key":"17_CR4","doi-asserted-by":"crossref","unstructured":"Cartor, R., Gipson, R., Smith-Tone, D., Vates, J.: On the differential security of the HFEV- signature primitive. In: Takagi [27], pp. 162\u2013181. http:\/\/dx.doi.org\/10.1007\/978-3-319-29360-8_11","DOI":"10.1007\/978-3-319-29360-8_11"},{"key":"17_CR5","unstructured":"Chen, M.S., Yang, B.Y., Smith-Tone, D.: PFLASH - secure asymmetric signatures on smart cards. In: Lightweight Cryptography Workshop 2015 (2015). http:\/\/csrc.nist.gov\/groups\/ST\/lwc-workshop.2015\/papers\/session3-smith-tone-paper.pdf"},{"key":"17_CR6","doi-asserted-by":"crossref","unstructured":"Daniels, T., Smith-Tone, D.: Differential properties of the HFE cryptosystem. In: Mosca [20] , pp. 59\u201375. http:\/\/dx.doi.org\/10.1007\/978-3-319-11659-4_4","DOI":"10.1007\/978-3-319-11659-4_4"},{"key":"17_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1007\/978-3-642-22792-9_41","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"J Ding","year":"2011","unstructured":"Ding, J., Hodges, T.J.: Inverting HFE systems is quasi-polynomial for all fields. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 724\u2013742. Springer, Heidelberg (2011). http:\/\/dx.doi.org\/10.1007\/978-3-642-22792-9_41"},{"key":"17_CR8","doi-asserted-by":"crossref","unstructured":"Ding, J., Petzoldt, A., Wang, L.: The cubic simple matrix encryption scheme. In: Mosca [20], pp. 76\u201387. http:\/\/dx.doi.org\/10.1007\/978-3-319-11659-4_5","DOI":"10.1007\/978-3-319-11659-4_5"},{"key":"17_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164\u2013175. Springer, Heidelberg (2005). http:\/\/dx.doi.org\/10.1007\/11496137_12"},{"key":"17_CR10","doi-asserted-by":"crossref","unstructured":"Ding, J., Yang, B.Y.: Degree of regularity for HFEV and HFEV. In: Gaborit [15], pp. 52\u201366. http:\/\/dx.doi.org\/10.1007\/978-3-642-38616-9","DOI":"10.1007\/978-3-642-38616-9_4"},{"key":"17_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/978-3-642-17373-8_32","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"V Dubois","year":"2010","unstructured":"Dubois, V., Gama, N.: The degree of regularity of HFE systems. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 557\u2013576. Springer, Heidelberg (2010). http:\/\/dx.doi.org\/10.1007\/978-3-642-17373-8_32"},{"issue":"4","key":"17_CR12","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1016\/j.jsc.2010.10.014","volume":"46","author":"JC Faug\u00e8re","year":"2011","unstructured":"Faug\u00e8re, J.C., Din, M.S.E., Spaenlehauer, P.J.: Gr\u00f6bner bases of bihomogeneous ideals generated by polynomials of bidegree: algorithms and complexity. J. Symbolic Comput. 46(4), 406\u2013437 (2011)","journal-title":"J. Symbolic Comput."},{"key":"17_CR13","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.C., El Din, M.S., Spaenlehauer, P.J.: Computing loci of rank defects of linear matrices using gr\u00f6bner bases and applications to cryptology. In: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010, pp. 257\u2013264. ACM, New York (2010)","DOI":"10.1145\/1837934.1837984"},{"key":"17_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/978-3-662-46447-2_7","volume-title":"Public-Key Cryptography \u2013 PKC 2015","author":"J-C Faug\u00e8re","year":"2015","unstructured":"Faug\u00e8re, J.-C., Gligoroski, D., Perret, L., Samardjiska, S., Thomae, E.: A polynomial-time key-recovery attack on MQQ cryptosystems. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 150\u2013174. Springer, Heidelberg (2015). http:\/\/dx.doi.org\/10.1007\/978-3-662-46447-2_7"},{"key":"17_CR15","series-title":"Lecture Notes in Computer Science","volume-title":"Post-Quantum Cryptography","year":"2013","unstructured":"Gaborit, P. (ed.): PQCrypto 2013. LNCS, vol. 7932. Springer, Heidelberg (2013). http:\/\/dx.doi.org\/10.1007\/978-3-642-38616-9"},{"key":"17_CR16","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 \u2014 EUROCRYPT 99","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. 1592, pp. 206\u2013222. Springer, Heidelberg (1999). http:\/\/dx.doi.org\/10.1007\/3-540-48910-X_15"},{"key":"17_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-48405-1_2","volume-title":"Advances in Cryptology \u2014 CRYPTO 99","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. 1666, pp. 19\u201330. Springer, Heidelberg (1999). doi:10.1007\/3-540-48405-1_2"},{"key":"17_CR18","doi-asserted-by":"crossref","unstructured":"Moody, D., Perlner, R.A., Smith-Tone, D.: An asymptotically optimal structural attack on the ABC multivariate encryption scheme. In: Mosca [20], pp. 180\u2013196. http:\/\/dx.doi.org\/10.1007\/978-3-319-11659-4_11","DOI":"10.1007\/978-3-319-11659-4_11"},{"key":"17_CR19","series-title":"Lecture Notes in Computer Science","first-page":"289","volume-title":"Post-Quantum Cryptography \u2013 PQCrypto 2017","author":"D Moody","year":"2017","unstructured":"Moody, D., Perlner, R.A., Smith-Tone, D.: Key recovery attack on the cubic ABC simple matrix multivariate encryption scheme. In: Lange, T., Takagi, T. (eds.) PQCrypto 2017. LNCS, vol. 10346, pp. 289\u2013308. Springer, Cham (2017)"},{"key":"17_CR20","series-title":"Lecture Notes in Computer Science","volume-title":"Post-Quantum Cryptography","year":"2014","unstructured":"Mosca, M. (ed.): PQCrypto 2014. LNCS, vol. 8772. Springer, Cham (2014). http:\/\/dx.doi.org\/10.1007\/978-3-319-11659-4"},{"key":"17_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 \u2014 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. 2020, pp. 282\u2013297. Springer, Heidelberg (2001). http:\/\/dx.doi.org\/10.1007\/3-540-45353-9_21"},{"key":"17_CR22","doi-asserted-by":"crossref","unstructured":"Perlner, R.A., Smith-Tone, D.: A classification of differential invariants for multivariate post-quantum cryptosystems. In: Gaborit [15], pp. 165\u2013173. http:\/\/dx.doi.org\/10.1007\/978-3-642-38616-9","DOI":"10.1007\/978-3-642-38616-9_11"},{"key":"17_CR23","doi-asserted-by":"crossref","unstructured":"Perlner, R.A., Smith-Tone, D.: Security analysis and key modification for ZHFE. In: Takagi[27], pp. 197\u2013212. http:\/\/dx.doi.org\/10.1007\/978-3-319-29360-8_13","DOI":"10.1007\/978-3-319-29360-8_13"},{"key":"17_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/978-3-319-11659-4_14","volume-title":"Post-Quantum Cryptography","author":"J Porras","year":"2014","unstructured":"Porras, J., Baena, J., Ding, J.: ZHFE, a new multivariate public key encryption scheme. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 229\u2013245. Springer, Cham (2014). doi:10.1007\/978-3-319-11659-4_14"},{"issue":"2","key":"17_CR25","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999). (electronic)","journal-title":"SIAM Rev."},{"key":"17_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1007\/978-3-642-25405-5_9","volume-title":"Post-Quantum Cryptography","author":"D Smith-Tone","year":"2011","unstructured":"Smith-Tone, D.: On the differential security of multivariate public key cryptosystems. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 130\u2013142. Springer, Heidelberg (2011). doi:10.1007\/978-3-642-25405-5_9"},{"key":"17_CR27","series-title":"Lecture Notes in Computer Science","volume-title":"Post-Quantum Cryptography","year":"2016","unstructured":"Takagi, T. (ed.): PQCrypto 2016. LNCS, vol. 9606. Springer, Cham (2016). http:\/\/dx.doi.org\/10.1007\/978-3-319-29360-8"},{"key":"17_CR28","doi-asserted-by":"crossref","unstructured":"Tao, C., Diene, A., Tang, S., Ding, J.: Simple matrix scheme for encryption. In: Gaborit [15], pp. 231\u2013242. http:\/\/dx.doi.org\/10.1007\/978-3-642-38616-9","DOI":"10.1007\/978-3-642-38616-9_16"},{"key":"17_CR29","unstructured":"Verbel, J.A.: Efficiency and security of ZHFE. Master\u2019s thesis, Universidad Nacional de Colombia, Sede Medell\u00edn (2016)"},{"key":"17_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/978-3-319-44524-3_17","volume-title":"Advances in Information and Computer Security","author":"W Zhang","year":"2016","unstructured":"Zhang, W., Tan, C.H.: On the security and key generation of the ZHFE encryption scheme. In: Ogawa, K., Yoshioka, K. (eds.) IWSEC 2016. LNCS, vol. 9836, pp. 289\u2013304. Springer, Cham (2016). doi:10.1007\/978-3-319-44524-3_17"}],"container-title":["Lecture Notes in Computer Science","Post-Quantum Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-59879-6_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T15:29:29Z","timestamp":1710343769000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-59879-6_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319598789","9783319598796"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-59879-6_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"4 June 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PQCrypto","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Post-Quantum Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Utrecht","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 June 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 June 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pqcrypto2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/2017.pqcrypto.org\/conference\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}