{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:17:51Z","timestamp":1775053071164,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540772712","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-77272-9_7","type":"book-chapter","created":{"date-parts":[[2007,12,6]],"date-time":"2007-12-06T11:56:55Z","timestamp":1196942215000},"page":"99-117","source":"Crossref","is-referenced-by-count":4,"title":["Non-linear Cryptanalysis Revisited: Heuristic Search for Approximations to S-Boxes"],"prefix":"10.1007","author":[{"given":"Juan M. E.","family":"Tapiador","sequence":"first","affiliation":[]},{"given":"John A.","family":"Clark","sequence":"additional","affiliation":[]},{"given":"Julio C.","family":"Hernandez-Castro","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"7_CR1","unstructured":"Aoki, K.: The Complete Distribution of Linear Probabilities of MARS\u2019 s-box. IACR Eprint Archive (2000), \n                      \n                        http:\/\/eprint.iacr.org\/2000\/033.pdf"},{"key":"7_CR2","series-title":"Lecture Notes in Computer Science","first-page":"36","volume-title":"AUSCRYPT 1990","author":"L. Brown","year":"1990","unstructured":"Brown, L., Kwan, M., Pieprzyk, J., Seberry, J.: Improving Resistance to Differential Cryptanalysis and the Redesign of LOKI. In: Seberry, J., Pieprzyk, J.P. (eds.) AUSCRYPT 1990. LNCS, vol.\u00a0453, pp. 36\u201350. Springer, Heidelberg (1990)"},{"key":"7_CR3","series-title":"Lecture Notes in Computer Science","first-page":"50","volume-title":"FSE 2000","author":"L. Burnett","year":"2001","unstructured":"Burnett, L., Carter, G., Dawson, E., Millan, W.: Efficient Methods for Generating MARS-like S-boxes. In: Schneier, B. (ed.) FSE 2000. LNCS, vol.\u00a01978, pp. 50\u201357. Springer, Heidelberg (2001)"},{"key":"7_CR4","unstructured":"Burwick, C., Coppersmith, D., D\u2019Avignon, E., Gennaro, R., Halevi, S., Jutla, C., Matyas Jr., S.M., O\u2019Connor, L., Peyravian, M., Safford, D., Zunic, N.: MARS \u2013 A Candidate Cipher for AES. In: Proc. 1st AES Conference, NIST (1998)"},{"key":"7_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1007\/3-540-39799-X_16","volume-title":"CRYPTO 1985","author":"D. Chaum","year":"1986","unstructured":"Chaum, D., Evertse, J.-H.: Cryptanalysis of DES with a Reduced Number of Rounds; Sequences of Linear Factors in Block Ciphers. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol.\u00a0218, pp. 192\u2013211. Springer, Heidelberg (1986)"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1007\/10718964_20","volume-title":"ACISP 2000","author":"J.A. Clark","year":"2000","unstructured":"Clark, J.A., Jacob, J.L.: Two Stage Optimisation in the Design of Boolean Functions. In: Clark, A., Boyd, C., Dawson, E.P. (eds.) ACISP 2000. LNCS, vol.\u00a01841, pp. 242\u2013254. Springer, Heidelberg (2000)"},{"key":"7_CR7","volume-title":"CEC 2003","author":"J.A. Clark","year":"2004","unstructured":"Clark, J.A., et al.: Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion. In: CEC 2003, IEEE Computer Society Press, Los Alamitos (2004)"},{"key":"7_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/3-540-39118-5_23","volume-title":"EUROCRYPT 1987","author":"J.-H. Evertse","year":"1988","unstructured":"Evertse, J.-H.: Linear Structures in Blockciphers. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol.\u00a0304, pp. 249\u2013266. Springer, Heidelberg (1988)"},{"issue":"5","key":"7_CR9","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1038\/scientificamerican0573-15","volume":"228","author":"H. Feistel","year":"1973","unstructured":"Feistel, H.: Cryptography and Computer Privacy. Scientific American\u00a0228(5), 15\u201323 (1973)","journal-title":"Scientific American"},{"key":"7_CR10","unstructured":"Fuller, J., Millan, W., Dawson, E.: Efficient Algorithms for Analysis of Cryptographic Boolean Functions. In: AWOCA 2002, Frasier Island, Australia (2002)"},{"key":"7_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/3-540-49264-X_3","volume-title":"EUROCRYPT 1995","author":"C. Harpes","year":"1995","unstructured":"Harpes, C., Kramer, G.G., Massey, J.L.: A Generalization of Linear Cryptanalysis and the Applicability of Matsui\u2019s Piling-Up Lemma. In: Guillou, L.C., Quisquater, J.J. (eds.) EUROCRYPT 1995. LNCS, vol.\u00a0921, pp. 24\u201338. Springer, Heidelberg (1995)"},{"key":"7_CR12","unstructured":"IBM MARS Team. Comments on MARS\u2019s Linear Analysis (2000), \n                      \n                        http:\/\/www.research.ibm.com\/security\/mars.html"},{"key":"7_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1007\/3-540-48658-5_4","volume-title":"CRYPTO 1994","author":"B.S. Kaliski","year":"1994","unstructured":"Kaliski, B.S., Robshaw, M.J.B.: Linear Cryptnalaysis using Multiple Approximations. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol.\u00a0839, pp. 26\u201339. Springer, Heidelberg (1994)"},{"issue":"4598","key":"7_CR14","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S. Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science\u00a0220(4598), 671\u2013680 (1983)","journal-title":"Science"},{"key":"7_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1007\/3-540-68339-9_20","volume-title":"EUROCRYPT 1996","author":"L.R. Knudsen","year":"1996","unstructured":"Knudsen, L.R., Robshaw, M.J.B.: Non-Linear Approximations in Linear Cryptanalysis. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol.\u00a01070, pp. 224\u2013236. Springer, Heidelberg (1996)"},{"key":"7_CR16","unstructured":"Knudsen, L.R., Raddum, H.: Linear Approximations to the MARS S-box. NESSIE Public Report NESSIE\/DOC\/UIB\/001A\/WP3 (2000)"},{"key":"7_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/3-540-48285-7_33","volume-title":"EUROCRYPT 1993","author":"M. Matsui","year":"1994","unstructured":"Matsui, M.: Linear Cryptanalysis Method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol.\u00a0765, pp. 386\u2013397. Springer, Heidelberg (1994)"},{"key":"7_CR18","series-title":"Lecture Notes in Computer Science","first-page":"1","volume-title":"CRYPTO 1994","author":"M. Matsui","year":"1994","unstructured":"Matsui, M.: The First Experimental Cryptanalysis of the Data Encryption Standard. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol.\u00a0839, pp. 1\u201311. Springer, Heidelberg (1994)"},{"key":"7_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/BFb0053451","volume-title":"EUROCRYPT 1994","author":"M. Matsui","year":"1995","unstructured":"Matsui, M.: On Correlation between the Order of S-boxes and the Strength of DES. In: EUROCRYPT 1994. LNCS, vol.\u00a0850, pp. 366\u2013375. Springer, Heidelberg (1995)"},{"key":"7_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BFb0028471","volume-title":"ICICS 1997","author":"W. Millan","year":"1997","unstructured":"Millan, W., Clark, A., Dawson, E.: Smart Hill-Climbing Finds Better Boolean Functions. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol.\u00a01334, pp. 149\u2013158. Springer, Heidelberg (1997)"},{"key":"7_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/BFb0054148","volume-title":"EUROCRYPT 1998","author":"W. Millan","year":"1998","unstructured":"Millan, W., Clark, A., Dawson, E.: Heuristic Design of Cryptographically Strong Balanced Boolean Functions. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 489\u2013499. Springer, Heidelberg (1998)"},{"key":"7_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BFb0053732","volume-title":"ACISP 1998","author":"W. Millan","year":"1998","unstructured":"Millan, W.: How to Improve the Non-Linearity of Bijective S-boxes. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol.\u00a01438, pp. 181\u2013192. Springer, Heidelberg (1998)"},{"key":"7_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/BFb0054148","volume-title":"EUROCRYPT 1998","author":"W. Millan","year":"1998","unstructured":"Millan, W., Burnett, L., Carter, G., Clark, A., Dawson, E.: Evolutionary Heuristics for Finding Cryptographically Strong S-boxes. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 489\u2013499. Springer, Heidelberg (1998)"},{"key":"7_CR24","volume-title":"CEC 2003","author":"W. Millan","year":"2003","unstructured":"Millan, W., et al.: Evolutionary Generation of Bent Functions for Cryptography. In: CEC 2003, IEEE Computer Society Press, Los Alamitos (2003)"},{"key":"7_CR25","unstructured":"Nakahara, J., Preneel, B., Vandewalle, J.: Experimental Non-Linear Cryptanalysis. COSIC Internal Report, 17 pages. Katholieke Universiteit Leuven (2003)"},{"key":"7_CR26","unstructured":"National Bureau of Standards (NBS). Data Encryption Standard. U.S. Department of Commerce, FIPS Publication 46 (January 1977)"},{"key":"7_CR27","unstructured":"National Institute of Standards and Technology (NIST). Data Encryption Standard. FIPS Publication 46-2. (December 30, 1993)"},{"key":"7_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/3-540-39568-7_29","volume-title":"CRYPTO 1984","author":"J.A. Reeds","year":"1985","unstructured":"Reeds, J.A., Manferdelli, J.L.: DES Has no Per Round Linear Factors. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol.\u00a0196, pp. 377\u2013389. Springer, Heidelberg (1985)"},{"key":"7_CR29","unstructured":"Robshaw, M., Yin, Y.L.: Potential Flaws in the Conjectured Resistance of MARS to Linear Cryptanalysis. In: Manuscript presented at the rump session in the 3rd AES Conference (2000)"},{"key":"7_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-3-540-25937-4_11","volume-title":"FSE 2004","author":"P. Stanica","year":"2004","unstructured":"Stanica, P., Maitra, S., Clark, J.A.: Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol.\u00a03017, pp. 161\u2013177. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Cryptography and Coding"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-77272-9_7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T11:06:58Z","timestamp":1619521618000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-77272-9_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540772712"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-77272-9_7","relation":{},"subject":[]}}