{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T19:06:42Z","timestamp":1783969602627,"version":"3.55.0"},"publisher-location":"Berlin, Heidelberg","reference-count":67,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642403484","type":"print"},{"value":"9783642403491","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-40349-1_15","type":"book-chapter","created":{"date-parts":[[2013,7,19]],"date-time":"2013-07-19T14:36:58Z","timestamp":1374244618000},"page":"250-272","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":76,"title":["McBits: Fast Constant-Time Code-Based Cryptography"],"prefix":"10.1007","author":[{"given":"Daniel J.","family":"Bernstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tung","family":"Chou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Schwabe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"15_CR1","unstructured":"AFIPS conference proceedings, volume 32: 1968 Spring Joint Computer Conference, Reston, Virginia. Thompson Book Company (1968)"},{"key":"15_CR2","doi-asserted-by":"crossref","unstructured":"Ajtai, M., Koml\u00f3s, J., Szemer\u00e9di, E.: An O(n log n) sorting network. In: STOC 1983 [38], pp. 1\u20139 (1983)","DOI":"10.1145\/800061.808726"},{"key":"15_CR3","unstructured":"Batcher, K.E.: Sorting networks and their applications. In: [1], pp. 307\u2013314 (1968)"},{"key":"15_CR4","unstructured":"Bene\u015d, V.E.: Mathematical theory of connecting networks and telephone traffic. Academic Press (1965)"},{"key":"15_CR5","unstructured":"Berlekamp, E.R.: Algebraic coding theory. McGraw-Hill (1968)"},{"issue":"111","key":"15_CR6","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1090\/S0025-5718-1970-0276200-X","volume":"24","author":"E. R. Berlekamp","year":"1970","unstructured":"Berlekamp, E.R.: Factoring polynomials over large finite fields. Mathematics of Computation 24, 713\u2013715 (1970)","journal-title":"Mathematics of Computation"},{"key":"15_CR7","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/11502760_3","volume-title":"Fast Software Encryption","author":"Daniel J. Bernstein","year":"2005","unstructured":"Bernstein, D.J.: The Poly1305-AES message-authentication code. In: FSE 2005 [34], pp. 32\u201349 (2005)"},{"key":"15_CR8","unstructured":"Bernstein, D.J.: qhasm software package (2007), http:\/\/cr.yp.to\/qhasm.html"},{"key":"15_CR9","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J.: The Salsa20 family of stream ciphers. In: [59], pp. 84\u201397 (2008)","DOI":"10.1007\/978-3-540-68351-3_8"},{"key":"15_CR10","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/978-3-642-03356-8_19","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"Daniel J. Bernstein","year":"2009","unstructured":"Bernstein, D.J.: Batch binary Edwards. In: Crypto 2009 [35], pp. 317\u2013336 (2009)"},{"key":"15_CR11","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1007\/978-3-642-25405-5_13","volume-title":"Post-Quantum Cryptography","author":"Daniel J. Bernstein","year":"2011","unstructured":"Bernstein, D.J.: Simplified high-speed high-distance list decoding for alternant codes. In: PQCrypto 2011 [67], pp. 200\u2013216 (2011)"},{"key":"15_CR12","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.): Post-quantum cryptography. Springer (2009)","DOI":"10.1007\/978-3-540-88702-7"},{"key":"15_CR13","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Duif, N., Lange, T., Schwabe, P., Yang, B.-Y.: High-speed highsecurity signatures. In: CHES 2011 [57] (2011)","DOI":"10.1007\/978-3-642-23951-9_9"},{"key":"15_CR14","unstructured":"Bernstein, D.J., Lange, T. (eds.): eBACS: ECRYPT Benchmarking of Cryptographic Systems. accessed 10 June 2013 (2013), http:\/\/bench.cr.yp.to"},{"key":"15_CR15","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-3-540-88403-3_3","volume-title":"Post-Quantum Cryptography","author":"Daniel J. Bernstein","year":"2008","unstructured":"Bernstein, D.J., Lange, T., Peters, C.: Attacking and defending the McEliece cryptosystem. In: PQCrypto 2008 [23], pp. 31\u201346 (2008)"},{"key":"15_CR16","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/978-3-642-33027-8_19","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2012","author":"Daniel J. Bernstein","year":"2012","unstructured":"Bernstein, D.J., Schwabe, P.: NEON crypto. In: CHES 2012 [58], pp. 320\u2013339 (2012)"},{"key":"15_CR17","doi-asserted-by":"crossref","unstructured":"Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak and the SHA-3 standardization(2013), http:\/\/csrc.nist.gov\/groups\/ST\/hash\/sha-3\/documents\/Keccak-slides-at-NIST.pdf","DOI":"10.1007\/978-3-642-38348-9_19"},{"key":"15_CR18","doi-asserted-by":"crossref","unstructured":"Biryukov, A., Gong, G., Stinson, D.R. (eds.): Selected areas in cryptography\u20137th international workshop, SAC 2010, Waterloo, Ontario, Canada, August 12-13, 2010, revised selected papers. LNCS, vol. 6544. Springer (2011)","DOI":"10.1007\/978-3-642-19574-7"},{"key":"15_CR19","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/978-3-540-88403-3_4","volume-title":"Post-Quantum Cryptography","author":"Bhaskar Biswas","year":"2008","unstructured":"Biswas, B., Sendrier, N.: McEliece cryptosystem implementation: theory and practice. In: [23], pp. 47\u201362 (2008)"},{"issue":"1","key":"15_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02920362","volume":"6","author":"J. L. Bordewijk","year":"1957","unstructured":"Bordewijk, J.L.: Inter-reciprocity applied to electrical networks. Applied Scientific Research B: Electrophysics, Acoustics, Optics, Mathematical Methods 6, 1\u201374 (1956)","journal-title":"Applied Scientific Research"},{"issue":"3","key":"15_CR21","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/S0022-0000(74)80029-2","volume":"8","author":"A. Borodin","year":"1974","unstructured":"Borodin, A., Moenck, R.T.: Fast modular transforms. Journal of Computer and System Sciences 8, 366\u2013386 (1974); older version, not a subset, in [48]. ISSN 0022-0000","journal-title":"Journal of Computer and System Sciences"},{"key":"15_CR22","doi-asserted-by":"crossref","unstructured":"Boyd, C. (ed.): Advances in cryptology\u2013ASIACRYPT 2001, proceedings of the 7th international conference on the theory and application of cryptology and information security held on the Gold Coast, December 9-13, 2001. LNCS, vol. 2248. Springer (2001)","DOI":"10.1007\/3-540-45682-1"},{"key":"15_CR23","series-title":"Lecture Notes in Computer Science","volume-title":"Post-Quantum Cryptography","year":"2008","unstructured":"Buchmann, J., Ding, J. (eds.): Post-quantum cryptography, second international workshop, PQCrypto 2008, Cincinnati, OH, USA, October 17-19, 2008, proceedings. LNCS, vol. 5299. Springer (2008)"},{"issue":"2","key":"15_CR24","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0097-3165(89)90020-4","volume":"50","author":"David G Cantor","year":"1989","unstructured":"Cantor, D.G.: On arithmetical algorithms over finite fields. Journal of Combinatorial Theory, Series A 50, 285\u2013300 (1989)","journal-title":"Journal of Combinatorial Theory, Series A"},{"key":"15_CR25","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/3-540-45682-1_10","volume-title":"Advances in Cryptology \u2014 ASIACRYPT 2001","author":"Nicolas T. Courtois","year":"2001","unstructured":"Courtois, N., Finiasz, M., Sendrier, N.: How to achieve a McEliece-based digital signature scheme. In: Asiacrypt 2001 [22], pp. 157\u2013174 (2001)"},{"key":"15_CR26","unstructured":"De Feo, L., Schost, \u00c9.: transalpyne: a language for automatic transposition (2010), http:\/\/www.prism.uvsq.fr\/~dfl\/talks\/plmms-08-07-10.pdf"},{"key":"15_CR27","unstructured":"Engeler, E., Caviness, B.F., Lakshman, Y.N. (eds.): Proceedings of the 1996 international symposium on symbolic and algebraic computation, ISSAC \u201996, Zurich, Switzerland, July 24-26, 1996. Association for Computing Machinery (1996)"},{"key":"15_CR28","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-1-4684-2001-2_4","volume-title":"Complexity of Computer Computations","author":"Charles M. Fiduccia","year":"1972","unstructured":"Fiduccia, C.M.: On obtaining upper bounds on the complexity of matrix multiplication. In: [47], pp. 31\u201340 (1972)"},{"key":"15_CR29","unstructured":"Fiduccia, C.M.: On the algebraic complexity of matrix multiplication. Ph.D. thesis. Brown University (1973)"},{"key":"15_CR30","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/978-3-642-19574-7_11","volume-title":"Selected Areas in Cryptography","author":"Matthieu Finiasz","year":"2011","unstructured":"Finiasz, M.: Parallel-CFS\u2013strengthening the CFS McEliece-based signature scheme. In: SAC 2010 [18], pp. 159\u2013170 (2011)"},{"key":"15_CR31","doi-asserted-by":"crossref","unstructured":"Galbraith, S., Nandi, M. (eds.): Progress in cryptology\u2013Indocrypt 2012\u201313th international conference on cryptology in India, Kolkata, India, December 9-12, 2012, proceedings. LNCS, vol. 7668. Springer (2012)","DOI":"10.1007\/978-3-642-34931-7"},{"issue":"12","key":"15_CR32","doi-asserted-by":"publisher","first-page":"6265","DOI":"10.1109\/TIT.2010.2079016","volume":"56","author":"Shuhong Gao","year":"2010","unstructured":"Gao, S., Mateer, T.: Additive fast Fourier transforms over finite fields. IEEE Transactions on Information Theory 56, 6265\u20136272 (2010)","journal-title":"IEEE Transactions on Information Theory"},{"key":"15_CR33","doi-asserted-by":"crossref","unstructured":"von zur Gathen, J., Gerhard, J.: Arithmetic and factorization of polynomials over F2 (extended abstract). In: ISSAC \u201996 [27], pp. 1\u20139 (1996)","DOI":"10.1145\/236869.236882"},{"key":"15_CR34","doi-asserted-by":"crossref","unstructured":"Gilbert, H., Handschuh, H. (eds.): Fast software encryption: 12th international workshop, FSE 2005, Paris, France, February 21-23, 2005, revised selected papers. LNCS, vol. 3557. Springer (2005)","DOI":"10.1007\/b137506"},{"key":"15_CR35","doi-asserted-by":"crossref","unstructured":"Halevi, S. (ed.): Advances in cryptology\u2013CRYPTO 2009, 29th annual international cryptology conference, Santa Barbara, CA, USA, August 16-20, 2009, proceedings. LNCS, vol. 5677. Springer (2009)","DOI":"10.1007\/978-3-642-03356-8"},{"key":"15_CR36","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-642-11925-5_6","volume-title":"Topics in Cryptology - CT-RSA 2010","author":"Jens Hermans","year":"2010","unstructured":"Hermans, J., Vercauteren, F., Preneel, B.: Speed records for NTRU. In: CT-RSA 2010 [55], pp. 73\u201388 (2010)"},{"key":"15_CR37","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/978-3-642-33027-8_20","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2012","author":"Stefan Heyse","year":"2012","unstructured":"Heyse, S., G\u00fcneysu, T.: Towards one cycle per bit asymmetric encryption: codebased cryptography on reconfigurable hardware. In: CHES 2012 [58], pp. 340\u2013355 (2012)"},{"key":"15_CR38","unstructured":"Johnson, D.S., Fagin, R., Fredman, M.L., Harel, D., Karp, R.M., Lynch, N.A.,Papadimitriou, C.H., Rivest, R.L., Ruzzo, W.L., Seiferas, J.I. (eds.): Proceedings of the 15th annual ACM symposium on theory of computing, 25-27 April, 1983,Boston Massachusetts, USA. Association for Computing Machinery (1983)"},{"key":"15_CR39","unstructured":"Karp, R.M. (chairman): 13th annual symposium on switching and automata theory.IEEE Computer Society (1972)"},{"key":"15_CR40","doi-asserted-by":"crossref","unstructured":"Kim, K. (ed.): Public key cryptography: proceedings of the 4th internationalworkshop on practice and theory in public key cryptosystems (PKC 2001) held on Cheju Island, February 13-15, 2001. LNCS, vol. 1992. Springer (2001)","DOI":"10.1007\/3-540-44586-2"},{"key":"15_CR41","unstructured":"Knuth, D.E.: The art of computer programming, volume 2: seminumerical algorithms,3rd edn. Addison-Wesley (1997)"},{"key":"15_CR42","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-44586-2_2","volume-title":"Public Key Cryptography","author":"Kazukuni Kobara","year":"2001","unstructured":"Kobara, K., Imai, H.: Semantically secure McEliece public-key cryptosystems\u2013conversions for McEliece PKC. In: PKC 2001 [40], pp. 19\u201335 (2001)"},{"key":"15_CR43","doi-asserted-by":"crossref","unstructured":"Landais, G., Sendrier, N.: CFS software implementation (2012); see also newer version [44]","DOI":"10.1007\/978-3-642-34931-7_27"},{"key":"15_CR44","first-page":"474","volume-title":"Lecture Notes in Computer Science","author":"Gregory Landais","year":"2012","unstructured":"Landais, G., Sendrier, N.: Implementing CFS. In: Indocrypt 2012 [31], pp. 474\u2013488 (2012); see also older version [43]"},{"key":"15_CR45","unstructured":"Lupanov, O.B.: On rectifier and contact-rectifier circuits. Doklady Akademii Nauk SSSR 111, 1171\u20131174 (1956). ISSN 0002-3264"},{"key":"15_CR46","unstructured":"McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. JPLDSN Progress Report, pp. 114\u2013116 (1978)"},{"key":"15_CR47","doi-asserted-by":"crossref","unstructured":"Miller, R.E., Thatcher, J.W. (eds.): Complexity of computer computations.Plenum Press(1972)","DOI":"10.1007\/978-1-4684-2001-2"},{"key":"15_CR48","doi-asserted-by":"crossref","unstructured":"Moenck, R.T., Borodin, A.: Fast modular transforms via division. In: [39], pp.90\u201396 (1972); newer version, not a superset, in [21]","DOI":"10.1109\/SWAT.1972.5"},{"key":"15_CR49","unstructured":"Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problemsof Control and Information Theory 15, 159\u2013166 (1986)"},{"key":"15_CR50","unstructured":"Oliveira, T., L\u00f3pez, J., Aranha, D.F., Rodr\u00edguez-Henr\u00edquez, F.: Two is the fastest prime (2013), http:\/\/eprint.iacr.org\/2013\/131"},{"key":"15_CR51","doi-asserted-by":"crossref","unstructured":"Overbeck, R., Sendrier, N.: Code-based cryptography. In: [12], pp. 95\u2013145 (2009)","DOI":"10.1007\/978-3-540-88702-7_4"},{"issue":"2","key":"15_CR52","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1109\/TIT.1975.1055350","volume":"21","author":"N. Patterson","year":"1975","unstructured":"Patterson, N.J.: The algebraic decoding of Goppa codes. IEEE Transactions on Information Theory 21, 203\u2013207 (1975)","journal-title":"IEEE Transactions on Information Theory"},{"key":"15_CR53","unstructured":"Persichetti, E.: Improving the efficiency of code-based cryptography. Ph.D. thesis.University of Auckland (2012)"},{"key":"15_CR54","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/978-3-642-12929-2_7","volume-title":"Post-Quantum Cryptography","author":"Christiane Peters","year":"2010","unstructured":"Peters, C.: Information-set decoding for linear codes over Fq. In: PQCrypto 2010 [60], pp. 81\u201394 (2010)"},{"key":"15_CR55","doi-asserted-by":"crossref","unstructured":"Pieprzyk, J. (ed.): Topics in cryptology\u2013CT-RSA 2010, the cryptographers\u2019 track at the RSA Conference 2010, San Francisco, CA, USA, March 1-5, 2010, proceedings. LNCS, vol. 5985. Springer (2010)","DOI":"10.1007\/978-3-642-11925-5"},{"key":"15_CR56","doi-asserted-by":"crossref","unstructured":"Pieprzyk, J., Sadeghi, A.-R., Manulis, M. (eds.): Cryptology and network security\u201311th international conference, CANS 2012, Darmstadt, Germany, December12-14, 2012, proceedings. LNCS, vol. 7712. Springer (2012)","DOI":"10.1007\/978-3-642-35404-5"},{"key":"15_CR57","doi-asserted-by":"crossref","unstructured":"Preneel, B., Takagi, T. (eds.): Cryptographic hardware and embedded systems\u2013CHES 2011, 13th international workshop, Nara, Japan, September 28-October1, 2011, proceedings. LNCS. Springer (2011)","DOI":"10.1007\/978-3-642-23951-9"},{"key":"15_CR58","doi-asserted-by":"crossref","unstructured":"[58] Prouff, E., Schaumont, P. (eds.): Cryptographic hardware and embeddedsystems\u2013CHES 2012\u201314th international workshop, Leuven, Belgium, September9-12, 2012, proceedings. LNCS, vol. 7428. Springer (2012)","DOI":"10.1007\/978-3-642-33027-8"},{"key":"15_CR59","doi-asserted-by":"crossref","unstructured":"Robshaw, M., Billet, O. (eds.): New stream cipher designs. LNCS, vol. 4986.Springer (2008)","DOI":"10.1007\/978-3-540-68351-3"},{"key":"15_CR60","doi-asserted-by":"crossref","unstructured":"Sendrier, N. (ed.): Post-quantum cryptography, third international workshop,PQCrypto, Darmstadt, Germany, May 25-28, 2010. LNCS, vol. 6061. Springer(2010)","DOI":"10.1007\/978-3-642-12929-2"},{"issue":"7","key":"15_CR61","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1145\/368370.368387","volume":"2","author":"D. L. Shell","year":"1959","unstructured":"Shell, D.L.: A high-speed sorting procedure. Communications of the ACM 2, 30\u201332 (1959)","journal-title":"Communications of the ACM"},{"key":"15_CR62","unstructured":"Shoup, V.: A proposal for an ISO standard for public key encryption (version 2.1)(2001), http:\/\/www.shoup.net\/papers"},{"key":"15_CR63","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-3-642-12929-2_8","volume-title":"Post-Quantum Cryptography","author":"Falko Strenzke","year":"2010","unstructured":"Strenzke, F.: A timing attack against the secret permutation in the McEliece PKC. In: PQCrypto 2010 [60], pp. 95\u2013107 (2010)"},{"key":"15_CR64","unstructured":"Strenzke, F.: Timing attacks against the syndrome inversion in code-based cryptosystems (2011), http:\/\/eprint.iacr.org\/2011\/683.pdf"},{"key":"15_CR65","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/978-3-642-35404-5_18","volume-title":"Cryptology and Network Security","author":"Falko Strenzke","year":"2012","unstructured":"Strenzke, F.: Fast and secure root finding for code-based cryptosystems. In: CANS 2012 [56], pp. 232\u2013246 (2012)"},{"issue":"3","key":"15_CR66","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1109\/49.1926","volume":"6","author":"Y. Wang","year":"1988","unstructured":"Wang, Y., Zhu, X.: A fast algorithm for Fourier transform over finite fields andits VLSI implementation. IEEE Journal on Selected Areas in Communications 6, 572\u2013577 (1988)","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"15_CR67","doi-asserted-by":"crossref","unstructured":"Yang, B.-Y. (ed.): Post-quantum cryptography, fourth international workshop,PQCrypto, Taipei, Taiwan, November 29-December 02, 2011. LNCS, vol. 7071.Springer (2011)","DOI":"10.1007\/978-3-642-25405-5"}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems - CHES 2013"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-40349-1_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T20:13:23Z","timestamp":1646165603000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-40349-1_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642403484","9783642403491"],"references-count":67,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40349-1_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]},"assertion":[{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}